A Study of Role Expectations and Role Performance of High School Teachers in Relation to Region, Management and Gender

Teaching has been one of the oldest and most respected professions in the world. When a systematically organized human society came into existence, the need to mould its children on proper lines arose requiring persons who could perform this role that is teachers. The main objective of the present study is to study the influence of region, gender and management on the role expectation and role performance of high school teachers. Role expectation and role performance of high school teachers’ questionnaire developed by Mrs. L. Hemalatha Krishnaveni (2013) was adopted. A sample of 900 high school teachers representing all categories of high schools is selected in Andhra Pradesh by following the standardized procedures. Factorial design test were employed for analysis of the data. The findings are there is significant influence of Region at 0.01 level on the role expectation and role performance of high school teachers. There is significant interaction effect of region Vs gender at 0.01 level on the role expectation and role performance of high school teachers. There is significant interaction effect of region Vs management at 0.05 level on the role expectation and role performance of high school teachers. INTRODUCTION The task of shaping the future citizens as a noble one and so the teacher has always occupied a place of honour and reverence in the Indian Society over the ages. The preparation of teachers has changed with the passage of time and with the changes in expectations of society. The role of the teacher in a society is well known. The wellbeing of the Nation depends upon the well being of the teachers. The teacher has a powerful and abiding influence in the formation of the character of the future citizens. The teacher acts as a pivot for the transmission of intellectual and technical skills and cultural traditions from one generation to another. The role of the teacher involves two broad fields of research. On the one hand ‘role refers to behaviour, thus studies of teacher – role performance are those in which the actual behaviour of teachers is observed. On the other hand, ‘role’ refers to expectations of behaviour thus studies of teacher role expectations are those in which expectations maintained for teachers by teachers and others are investigated, in general, these are two distinct fields of research for investigation. Role expectation of teachers Expectations are learned through experience and ones they are formed, expectations will affect the behaviours of those who hold them in predictable ways (performance). Any expectations we should posses means, the activity of performance. Role performance of teachers What is expected of an individual and how well he fulfills what is expected of him are the two inseparable questions to be analyzed and understood in the study of role. The first question deals with the concept of role expectation and the second question deals with the role performance in the manner in which the individual fulfills the requirements of his positions. Review of Literature Venkateswara Rao (2002) found from a study on job satisfaction of primary schools that there is significant difference between job satisfaction and job involvement. Job involvement also influences the variables viz., gender, management, locality, type of school and some of the personality characteristics. He also found a significant influence of family satisfaction and life satisfaction on their level of job involvement. Eagly, Alice H.; Karau, Steven J.; Makhijani, Mona G (2005) found that this article presents a synthesis of research on the relative effectiveness of women and men who occupy leadership and managerial roles. Aggregated over the organizational and laboratory experimental studies in the sample, male and female leaders were equally effective. However, consistent with the assumption that the congruence of leadership roles with leaders’ gender enhances effectiveness, men were more effective than women in roles that were defined in more masculine terms, and women were more effective than men in roles that were defined in less masculine terms. Also, men were more effective than women to the extent that leader and subordinate roles were male-dominated numerically. These and other findings are discussed from the perspective of social-role theory of sex differences in social behaviour as well as from alternative perspectives. Vijayalakshmi (2005) conducted a study and the findings showed, low and positive correlation between teacher effectiveness and job satisfaction. Only the management of the school has significant impact both on teacher effectiveness and job satisfaction. The other variables included in the study viz., locality, subjects of teaching have no significant impact on both teacher effectiveness and job satisfaction. Maheswar Thalkur (2007) conducted that correlates of Job Satisfaction for the high and low groups of the management level. The obtained highest percentage value for the high group is 86.19 and the lowest percentage value is 44.19. He found that ‘management’ is the most prominent correlates of job satisfaction for the high group of Secondary school Principals. Kyla L. Wahlstrom and Karen Seashore Louis (2008) found that three types of instructional behaviours—Standard Contemporary Practice, Focused Instruction, and Flexible Grouping Practices—emerged as strong factors which operationally described effective teacher practice. The presence of shared leadership and professional community explained much of the strength among the three instructional variables. Furthermore, the effect of teachers’ trust in the principal becomes less important when shared leadership and profes-

INTRODUCTION
The task of shaping the future citizens as a noble one and so the teacher has always occupied a place of honour and reverence in the Indian Society over the ages. The preparation of teachers has changed with the passage of time and with the changes in expectations of society.
The role of the teacher in a society is well known. The wellbeing of the Nation depends upon the well being of the teachers. The teacher has a powerful and abiding influence in the formation of the character of the future citizens. The teacher acts as a pivot for the transmission of intellectual and technical skills and cultural traditions from one generation to another.
The role of the teacher involves two broad fields of research. On the one hand 'role refers to behaviour, thus studies of teacher -role performance are those in which the actual behaviour of teachers is observed. On the other hand, 'role' refers to expectations of behaviour thus studies of teacher role expectations are those in which expectations maintained for teachers by teachers and others are investigated, in general, these are two distinct fields of research for investigation.

Role expectation of teachers
Expectations are learned through experience and ones they are formed, expectations will affect the behaviours of those who hold them in predictable ways (performance). Any expectations we should posses means, the activity of performance.

Role performance of teachers
What is expected of an individual and how well he fulfills what is expected of him are the two inseparable questions to be analyzed and understood in the study of role. The first question deals with the concept of role expectation and the second question deals with the role performance in the manner in which the individual fulfills the requirements of his positions. Venkateswara Rao (2002) found from a study on job satisfaction of primary schools that there is significant difference between job satisfaction and job involvement. Job involvement also influences the variables viz., gender, management, locality, type of school and some of the personality characteristics.

Review of Literature
He also found a significant influence of family satisfaction and life satisfaction on their level of job involvement.
Eagly, Alice H.; Karau, Steven J.;Makhijani, Mona G (2005) found that this article presents a synthesis of research on the relative effectiveness of women and men who occupy leadership and managerial roles. Aggregated over the organizational and laboratory experimental studies in the sample, male and female leaders were equally effective. However, consistent with the assumption that the congruence of leadership roles with leaders' gender enhances effectiveness, men were more effective than women in roles that were defined in more masculine terms, and women were more effective than men in roles that were defined in less masculine terms. Also, men were more effective than women to the extent that leader and subordinate roles were male-dominated numerically. These and other findings are discussed from the perspective of social-role theory of sex differences in social behaviour as well as from alternative perspectives.
Vijayalakshmi (2005) conducted a study and the findings showed, low and positive correlation between teacher effectiveness and job satisfaction. Only the management of the school has significant impact both on teacher effectiveness and job satisfaction. The other variables included in the study viz., locality, subjects of teaching have no significant impact on both teacher effectiveness and job satisfaction.
Maheswar Thalkur (2007) conducted that correlates of Job Satisfaction for the high and low groups of the management level. The obtained highest percentage value for the high group is 86.19 and the lowest percentage value is 44.19. He found that 'management' is the most prominent correlates of job satisfaction for the high group of Secondary school Principals.
Kyla L. Wahlstrom and Karen Seashore Louis (2008) found that three types of instructional behaviours-Standard Contemporary Practice, Focused Instruction, and Flexible Grouping Practices-emerged as strong factors which operationally described effective teacher practice. The presence of shared leadership and professional community explained much of the strength among the three instructional variables. Furthermore, the effect of teachers' trust in the principal becomes less important when shared leadership and profes-sional community are present. Self-efficacy strongly predicts Focused Instruction, but it has less predictive value for the other measures of instructional behaviour. Individual teacher characteristics of gender and years of experience have clear impact on instructional practice, but there are no discernible patterns that suggest that the level of the principal (elementary vs. secondary) have more or less influence on teacher instructional behaviours.
Anit Somech (2010) investigated that the increasing emergence of Participation in Decision Making (PDM) in schools reflects the widely shared belief that flatter management and decentralized authority structures carry the potential for promoting school effectiveness. However, the literature indicates a discrepancy between the intuitive appeal of PDM and empirical evidence in respect of its sweeping advantages. The purpose of this theoretical article is to develop a comprehensive model for understanding the distinct impacts of PDM on school and teachers' outcomes. The proposed analytical framework is set within contingency theory and is aimed to predict the distinct impacts of PDM on school outcomes: innovation, organizational citizenship behaviour (OCB), and productivity; and on teacher outcomes: job satisfaction and strain. It contains mediator-moderator components, where the mediator factors explain the relationship between PDM and school and teacher outcomes and the moderator factors influence the strength and/or the direction of these relationships. Specifically, the framework suggests that two mechanisms, one motivational and one cognitive, serve as mediators in the PDM-outcomes relationship. Then, by taking a multilevel perspective, the author posits moderators that may facilitate or inhibit the PDM effect: teacher personality (the Big Five personality characteristics) at the individual level, principal-teacher exchange (leader-member exchange; LMX) at the dyadic level, structure (bureaucratic/ organic) at the school level, and culture (individualism/collectivism) at the environmental level.

Scope of the Study
The main intention of the study is to find the influence of region, gender and management on the role expectation and role performance of high school teachers.

Objective of the Study
To study the influence of region, gender and management on the role expectation and role performance of high school teachers.
Hypothesis of the study Region, gender and management do not have significant influence on the role expectation and role performance of high school teachers.

RESULTS AND DISCUSSION
The influence of the variables region, gender and management and their interactions on the role expectations and role performance of High school teachers is studied with the help of Factorial designs.
1. Factorial design for role expectation score There are three divisions in the region, two divisions in the gender and three divisions in the management. The influence of region, gender and management on the role expectation scores of High school teachers is investigated through 3X2X3 factorial design.
To examine whether there exists any significant difference on role expectation scores among the high school teachers belonging to region, gender and management; and to probe into the effect of interaction between these variables, the role expectation scores are analyzed by applying analysis of variance (ANOVA) technique using 3X2X3 factorial design.
The following hypotheses are framed.
Hypothesis -1: There would be no significant influence of main effects namely, region, gender and management on the role expectation scores of the High school teachers.
Hypothesis -2: There would be no significant influence of interaction effects namely, region, gender and management on the role expectation scores of the High school teachers.
In order to test the proposed hypotheses, the analysis of variance technique is applied using 3X2X3 factorial design and the results are presented in Table -1.
It is observed from Table -1 that the computed value of 'F' for the main effect region is 7.870 which is significant at 0.01 level. Hence Hypothesis -1 is rejected. It is concluded that region has significant influence on the role expectation.

RESEARCH PAPER
The It is evident from Table -1 that the computed values of 'F' for the two factor interaction effect namely, region Vs gender is 6.328 which is significant at 0.01 level and region Vs management is 2.687 which is significant at 0.05 level. Hence Hypothesis -2 is rejected. It is concluded that the two factor interaction effect namely region Vs gender and region Vs management have significant influence on the role expectation.
It is seen from Table -1 that the computed values of 'F' for the three factor interaction effect namely, region Vs gender Vs management is 2.237 which is not significant at 0.05 level. Hence Hypothesis -2 is accepted. It is concluded that the three interaction effect namely, region Vs gender Vs management has not significant influence on the role expectation.

Factorial design for role performance score
There are three divisions in the region, two divisions in the gender and three divisions in the management. The influence of region, gender and management on the role performance scores of High school teachers is investigated through 3X2X3 factorial design.
To examine whether there exists any significant difference on role performance scores among the high school teachers belonging to region, gender and management; and to probe into the effect of interaction between these variables, the role performance scores are analyzed by applying analysis of variance (ANOVA) technique using 3X2X3 factorial design.
The following hypotheses are framed.
Hypothesis -3: There would be no significant influence of main effects namely, region, gender and management on the role performance scores of the High school teachers.
Hypothesis -4: There would be no significant influence of interaction effects namely, region, gender and management on the role performance scores of the High school teachers.
In order to test the proposed hypotheses, the analysis of variance technique is applied using 3X2X3 factorial design and the results are presented in Table -2.  Findings: There is significant influence of Region at 0.01 level on the role expectation and role performance of high school teachers. There is significant interaction effect of region Vs gender at 0.01 level on the role expectation and role performance of high school teachers. There is significant interaction effect of region Vs management at 0.05 level on the role expectation and role performance of high school teachers.

Conclusions:
In the light of the findings, the following conclusions are drawn. Region has significant influence on the role expectation and role performance of high school teachers. Region Vs gender has significant influence on the role expectation and role performance of high school teachers. Region Vs Management has significant influence on the role expectation and role performance of high school teachers.

EDUCATIONAL IMPLICATIONS
On the basis of the results of the present investigation the following recommendations are suggested: Region has influence on the role expectation and role performance of high school teachers. It is observed that Rayalaseema high school teachers have better than Coastal Andhra high school teachers. It is advised to provide good amenities for Coastal Andhra high school teachers.
Since good library facilities are associated with the positive role expectation and role performance, school managements are advised to equip their libraries with the books that are liked by the teachers.
Teacher's dairy and student's dairy should be maintained for the smooth work of daily activities.


A School Library in Sub-Saharan Africa

This paper reports on the success and suitability of a Western-donated school library in furthering literacy and reader development in Malawi.

A qualitative, case study approach was taken using semi-structured interviews with teachers and a library assistant at a primary school in Malawi.

The research reveals positive attitudes towards reading and literacy in a predominantly oral culture. Limitations include a lack of attention to reader development and inappropriateness of materials for the local context.

The study reveals that the book donation model commonly supported by international donors and non-governmental organisations (NGOs) falls short in its ability to contribute to global literacy and education targets. Recommendations to improve impact are given.

This research is original in representing the voices of school teachers in the debate over the suitability of libraries and the overseas book donation model to the sub-Saharan African context.

Introduction
Access to free, universal primary education for all is a basic human right, the attainment of which is one of the eight Millennium Development Goals (MDGs) agreed upon by the United Nations in 2000, to be met by 2015 (United Nations Development Programme, 2000).
Literacy is recognised by The United Nations Educational, Scientific and Cultural Organization (Unesco) as a fundamental human right which has a central role to play in tackling global poverty (Unesco, 2005).
For most people in sub-Saharan Africa, primary school provides the first opportunity to acquire literacy skills but pupil to teacher ratios is typically very high and if there are any books available in the school they are often just a few _______________________________________________________________________________ _______________________________________________________________________________ J. Anderson 4 government text books which have to be shared between six or more pupils at a time (Makotsi, 2004, 6). There are rarely the resources available to create a literate environment.
Non-governmental organisations (NGOs) and donors have traditionally attempted to address the lack of resources through the donation of surplus Western books and educational material. While much current research focuses on how information and communication technologies (ICT) can facilitate access to information in developing countries, lack of electricity, computer access and internet connection (World Economic Forum, 2009) still mean that book donation has a large role to play and libraries are ideally suited to fill the resource gap.
With sufficient investment and support, libraries will have a major positive impact on the achievement of Education for All and the Millennium Development Goals. (Krolak, 2005, 13) Book donations come in two forms, the solicited and the unsolicited. Unsolicited book donations are the easiest to obtain, and therefore the most common. Donors who provide solicited material generally insist on proof that the resources will be used effectively before assistance is secured. This requires skill and patience from the requester because impact and effectiveness are difficult to measure and competition for the resources is great. Unsolicited donations rarely have provisos attached. There is concern that where the unsolicited book donation approach is used, professional needs assessments are seldom undertaken and continuing monitoring and evaluation procedures, with active community participation, are rarely implemented (Krolak, 2005). The result is the provision of information services that are based upon assumptions and not on actual need.
Since the 1960s there has been much scrutiny of library aid; the tone of which has changed little. However, many of the theories and conclusions presented by the literature have been arrived at via desk-based research and there is a lack of first hand data available. This paper reports the findings of a research project that was designed, using a largely qualitative approach, to investigate library aid from the recipient's perspective so that library aid donors can be better informed about the people they are serving. The intention was to inform future practice and research.
The research questions posed in the study were:  5 alongside internal documentation collected, which included exam statistics and diary-like reports written by the library assistant since the library was installed.
The voice of library aid recipients in Sub-Saharan Africa is very poorly represented in existing literature so a largely participatory approach was considered the most appropriate method to use as this "enhanced the opportunity to reveal aspects of social worlds that are important to the participants that might not otherwise cross the mind of the unacquainted researcher" (Bryman, 2001, 280), thus allowing the researcher to establish the opinions and needs of the library aid recipients in depth.
Twelve of the thirteen teachers at the school, including the head teacher, agreed to be interviewed as did the library assistant. The questions were designed to encourage the interviewee to think in depth about many aspects of the library, such as patterns of usage, the relevance of the stock, and the role of reading in Malawian culture.
The interviews were recorded and transcribed verbatim and then analysed alongside the internal documents that had been collected, using data management and analysis software NVivo.

Context for the research
Malawi is culturally and economically representative of many sub-Saharan African countries. It is landlocked, has few natural resources, is one of the least developed countries in the world, and despite its rich cultural diversity, has an oral culture that features many similarities to other sub-Saharan African societies. Malawi used to be an English protectorate and its official language is English despite its people predominantly speaking Chichewa, their local language, as a first language.
The Malawian government abolished primary school education fees in 1994 (UNDP, 2003, 4), however there were not the materials to support the increase of student numbers that this resulted in. A small NGO based in Bristol, United Kingdom (UK) is attempting to address this need for educational material by shipping unsolicited donated English material to schools in Malawi and setting up libraries.
The NGO installed a library in rural Malawi at Cape Maclear Primary School in 2005 with the intention of setting up more in the future. Since its installation they have funded a library assistant, selected by them, to work in the library at the primary school. The library assistant received no training and has not completed secondary education himself. The teachers and library assistant at the school had no knowledge of the stock selection before it reached them.
The NGO rely on book donations from Western publishers, British schools that donate surplus or unwanted stock, and other private donations. The stock selection policy is informal and the recipient schools are left to run the library as they see fit.

The literature
Before discussing the findings of the primary research conducted in Malawi, key ideas from the available literature are presented, which suggest that cultural traits, teaching methods and language barriers are all major obstacles that need to be tackled if the low levels of literacy in sub-Saharan Africa are to be addressed.

Culture and literacy
Commentators often state that sub-Saharan Africa lacks a reading culture (Totemeyer, 1994;Sturges and Neill, 1998;Rosenberg, 2003;Krolak, 2005). Totemeyer (1994,413), suggests that this is because sub-Saharan Africa's oral culture renders reading redundant -people stop reading once they complete their schooling as they "derive more pleasure from the oral and performing arts". As most adults in sub-Saharan Africa are non-literate they do not read at home, and if reading does not take place at home then a reading culture will not develop. The non-literate majority affect the literate minority and as such oral modes of communication remain prevalent. Sturges and Neill (1998, 68) posit that the act of reading is not only superfluous to oral traditions but it is in discord with traditional values. In oral traditions trusted sources of information are community chiefs and not the written word in a foreign book. What is more, "both the content of the books and the solitude required to read them conflict with traditional values, making them at once less comprehensible and less acceptable" (Sturges and Neill, 1998, 150).
Similar conclusions regarding cultural preferences and traits feature throughout the discourse on libraries and literacy in sub-Saharan Africa, suggesting a limited role or cultural ceiling for reading. However, these claims are contradicted in the few qualitative studies that have been undertaken. When assessing the information needs of a rural sub Saharan African community (Sturges and Chimseu 1996) observed that print material is widely valued and that some traits of an oral culture actually facilitate access to the written word. For example it is "shared by the literate (often school children) with the non-literate". A South African initiative called "Born to Read" (Mtshweni, 2003, 9), which encouraged non-literate mothers to become library members and read with their children by using the pictures in books to tell a story, found that this was welcomed as it promoted traditional storytelling. Instead of the reading culture being stifled by an oral tradition where some may say it had no place, the mothers could identify similarities of storytelling in their own culture with the storytelling using books, thus enabling them to use their experience to introduce their children to reading in a way that they were comfortable with. By gaining an understanding of the local culture and what was important to the participants it was possible to take an approach that exploited synergies between oral and literate cultures.

Teaching and Reader Development
Reader development focuses on fostering a reading habit by developing positive attitudes towards reading, which in turn creates positive attitudes towards the development of reading skills. It is active intervention to sell: ..the reading experience and what it can do for you [. . .] recognizing that reading has a crucial role to play in creating independent learners, underpinning literacy skills and educational attainment, and helping people understand themselves and others better. It starts with librarians introducing very young babies to books and carries on throughout the ages. (Rosenberg, 2003, 4) Many commentators lament the fact that teachers in sub-Saharan Africa do not have the knowledge or experience to encourage reader development so that when they are given access to books the resources are not used to their full potential. Sturges and Neill (1998, 163) claim that it is hard to convince teachers in sub-Saharan African schools the value of libraries due, not only to a previous lack of access to books, but also to the difficulty of persuading teachers to use teaching methods other than the ones with which they are familiar. Williams (1998, 14) observed reading classes in primary schools in Malawi and Zambia and found that the predominant method of teaching is the drilling of words and sentences through repetition. This method of teaching merely serves to reinforce structural patterns and does little to attend to meaning.
It is no guarantee of understanding and at worst is simply a performance which masks a lack of real competence. (Williams, 1998, 14) These teaching methods are not suitable for teaching children in a second language and they are not conducive to reader development and the raising of literacy standards.
The active support of reader development is vital to the growth of a reading culture in sub-Saharan Africa. However, "it is not yet regarded as a core aspect of service provision in libraries in developing countries" Rosenberg (2003, iv) and it is an area that is rarely discussed in the literature.
In the available literature, the voice of the teachers is distinctly lacking. As teaching methods and attitudes have a pivotal role to play in reader development and the growth of a reading culture, it was hoped that by engaging the teachers in dialogue for the research project, new ideas would emerge on how reader development can be adapted to their situation.

Language
In sub-Saharan Africa, Western books donated by NGOs and 80 per cent of new titles from Africa are in ex-colonial languages, particularly English and French, despite the fact that less than 5 per cent of the continent's population is regarded as being fluent in either of them (Sturges and Neill, 1998, 26). In sub-Saharan Africa, children mainly begin their preschool and early school lives communicating only in their local language. When they reach higher classes they are taught in languages such as English or French, which to them, although they are their country's official languages, are essentially foreign languages.
A study of bilingual literacy and teaching practices in Malawi and Zambia, concluded that students in Malawi do not read English well enough to be able to use it to learn in other subjects (Williams, 1998, 58). This is of serious concern if the only books that the children have access to are written in English.

Findings
As is evident from the literature there are many perceived barriers to the development of a reading culture in Sub-Saharan Africa. The following sections detail the findings of the research project which investigated these issues from the recipient's perspective.

Culture and Literacy
The research found that the community members in Cape Maclear with an interest in reading are predominantly the newly literate, such as the recent school leavers and secondary school pupils, who frequently request to use the books.
As it is often only school children who have access to the information in books and newspapers, due to a lack of external resources coupled with adult illiteracy, information no longer just flows from the elders to the children. The books provide children with access to information, which they then share with their parents. The sharing of information from books between the literate and nonliterate encourages readers and turns the typically lone activity into a social one.
The role of reading is very much seen as educational. Contrary to the claims of Sturges and Neill (1998, 150), the teachers say the attitudes of the community towards reading are positive. Books are associated with knowledge and wealth and to be seen with one gives prestige so some members of the community request to use the library books even if they cannot read.
Malawians cannot afford to travel to learn about other countries and cultures, books are one of the few ways they can access this knowledge. Access to knowledge about the world is considered to have the potential to change Malawians' behaviour, culture and to improve their standard of living. The teachers see Western visitors and the countries they come from as economically successful, so by imitating an economically successful culture they hope to achieve economic stability also.
At Cape Maclear Primary School, the teachers credit these positive attitudes towards reading and education in Malawian society to the stance of the current government: In previous years the government introduced adult literacy schools so that they know reading [and] writing, but ten years ago [

This has had a direct impact on the community:
Our life depends in the lake because it is where we get fish; we get money after selling the fish. Because of this our old parents didn't write, they were busy catching fish in the lake, so most of them didn't go to school. . .but now people are sending their pupils to learn here. It is also encouraging parents to send their people because they are seeing now, some children, they are working after school. . .they are getting money. . . so, when they see what is happening, they are sending their pupils here.
For those interested in the development of a reading culture in Malawi this encouragement from the parents is an exciting finding if Krolak (2005, 4) is correct in her claim that "the desire to support the literacy acquisition of their children is a strong motivation for illiterate adults to become literate". She suggests that this should be seen as an opportunity to reach the adults through family literacy programmes especially as school children are more likely to be successful at school if they come from literate or semi-literate homes.
The findings indicate that reading does have a role to play in an oral culture; the barriers, which stand in the way of a reading culture taking root are poverty and lack of education rather than cultural influences.

Teaching and Reader Development
The teachers recognise that the library provides the children with the opportunity to utilise the books in a way they never could before, Children understand by seeing, touching, feeling . . .this library have really helped this school. They have really improved in their reading and learning capacity. We had not enough materials from the government so some of the children have never seen a book or taken a book to read, just, reading or hearing the teacher, so in having a library, they go in to the library, they take a book, they see the picture, they read the words . . . In so doing they add more knowledge to what they have been taught in class.
The teachers have high expectations of the library's ability to facilitate independent learning and hope that the children will obtain knowledge that they cannot access in class due to the large student numbers and a lack of individual attention from the teachers. However, the language barriers that the children face render the books inaccessible so, in practice, the teachers have to act as intermediaries. Most of the teachers do not take the library books into the classroom but they get information from the books, which they then add to their lessons.
In this school, the children are only allowed access to the books from standard 5 onwards; the age of standard 4 students can range from nine to sixteen so it is possible that a child can be as old as sixteen before having any access to the books, and at least as old as nine. As the books are written in English and the children do not begin to get taught in English until these later grades it is seen as pointless to be giving them access to books they cannot understand. However, it is not just the younger children who have problems with language barriers; the older children face difficulties also: Even these guys who are in the elder class not most of them they can understand English very well. Not most of them they can understand these bombastic words that are found in the books so they always come and ask me, "Please interpret this for us". (Library assistant) Four of the teachers "sometimes" take the children to the library during the school day but because the classes are so big and the library so small they have to take it in turns. This is both impractical and time consuming. The class sizes often reach 100 but there is only room for ten pupils at a time in the library.
This study indicates that Sturges and Neill's (1998, 163) suggestion that teachers in Africa are hard to convince of the value of libraries is incorrect. All of the teachers interviewed see the value of the library and think it is important to encourage the older children to go to the library if they have problems with their studies, to practice reading, and to expand their knowledge. Indeed, they almost see it as a substitute teacher. This approach is dependent on the child's initiative to act on this advice and on the library assistant's support once they are in the library. The children do not have access to books in the classroom, they are not given consistent, regular library time during the school day and there was little evidence to indicate that children are actively being taught independent research skills yet they are still expected to be independent learners.
The library assistant notices that the children are good at memorising information read to them from books but observes that when asked to explain what they have read, using their first language Chichewa, they are unable to do so. This corroborates Williams (1998) findings that the teaching methods used in the classroom focus on learning by rote but neglect to establish and ensure understanding.
Despite receiving no training and having not completed secondary school himself, the library assistant does much of the reading, library and book promotion work. He talks to students during assemblies and gatherings, explaining how using the books can help them in their exams and later in life. He helps the students to understand the books by explaining the meanings of words and "topics they do not understand".
Only two of the teachers read for pleasure; in contrast, the library assistant frequently mentioned leisure and the fun aspects of the library in his reports and interview, expressing a different attitude towards reading: Children come to the library because of the funny games and pictures, as you know kids are very much attracted to the pictures and they learn through that they always have great fun.
Although many of the teachers use the library for personal reading the reasons given for this always relate to how the information within these books supports their jobs. This is an important role for the library as it is the teachers' only access to books.
If I stay away from that then I will never impart knowledge to the children, because our careers as teachers, as a teacher I have to be reading continuously.

So the library is now an important part of our being encouraged in our learning as well as teaching.
It is clear from the findings that the provision of donated book stock alone will not overcome the barriers to literacy and reader development. Professional support and training is required as well as the adaptation of teaching styles and use of resources.

Implications
As is evident in this case study, thorough consultation with library aid recipients can reveal important aspects that the external donor may not have otherwise considered, aspects that will be crucial in informing the direction that a library project should take and how a service can be made relevant and effective. Library aid donors must not make assumptions about the community they wish to assist if inaccurate presumptions that undermine the aims of a project are to be avoided. Project evaluation using both qualitative and quantitative data is still lacking in the area of library aid, this study suggests that this must be addressed.
Experience from the case study suggests that donors, working alongside governments, must work with information professionals and education experts to develop innovative reader development programmes that utilize the traits of the community to engage everyone in reading. For example, in this study it was revealed that: New literates were a theme throughout the findings. New literates can slip back into illiteracy if they do not have access to reading materials post-school. This section of the community should not be overlooked by library providers. Reader development should be a lifelong, continuous process. The evident interest in learning about the outside world shown in this study and the desire for continued education is an ideal basis on which to encourage people to read.
Information from books gets shared orally from the literate to the non-literate. The sharing of stories and the experience of reading is a prime factor of reader development. How can this highly sociable trait of an oral culture be used to engage more people in reading and facilitate involvement of non-literate community members? The new enthusiasm from parents due to government influence could be harnessed to help develop a reading culture but it would need community participation and relevant resources.
Education and knowledge are associated with wealth. To be seen with a book gives one prestige. How can this be transformed into increased literacy levels and active engagement with library resources?
The teachers and library assistant place great emphasis on the value of independent study, an important aspect of reader development, yet the current situation does not enable the children to utilize the library in this way. How can the teachers and library assistant be supported in developing the children's independent study skills? Library aid projects should consider training to be as essential as the provision of relevant books; training is necessary to help the teachers and the library assistant to use the resources that are already available to them more effectively. Book donations and enthusiasm from the stakeholders alone is not sufficient; professional support is also vital.

Future research
Future research is also recommended in the following areas: The few reader development programmes that have been researched and evaluated illustrate that if managed, directed and supported appropriately cultural traits can actually facilitate access to the written word. Reader development activity in sub-Saharan Africa is a new and emerging area that requires more evaluation and research without which resources will not be used to their full potential.
Language barriers were a constant theme in this study. It is suggested that research be carried out regarding how this can be addressed. Zeleza (2002) reports that the supremacy of the English language hinders the success of local language publishing, if this is the case perhaps donors should look towards providing material used specifically for teaching English as a foreign language rather than just providing material printed in the English language.
In this study the teachers and library assistant spoke for the children and the community. A repeat of this study extended to collecting first-hand data from these library stakeholders is recommended to provide a more comprehensive picture.
No librarians, teachers, education or development experts were employed by the NGO featured in this study. It is recommended that research be carried out to establish whether this is endemic and if so, why? Philanthropic endeavours can have a vital role to play in international development. However, they must be subjected to quality insurance measures and regulation if they are to be directed effectively and appropriately. The NGO central to this study was formed on good intentions and philanthropy. However, a lack of consultation with professionals and the library users, a lack of consideration of the specialist training needed for the library assistant and no evaluation of their service in the five years since its installation, has limited the library's potential to serve its purpose despite the high expectations of the teachers.

Conclusion
One of the teachers interviewed for this study said: I think in Malawi it is the song of the government, they decide that in every part and every learning area there must be a librarian, but the libraries must grow because it is a matter of encouraging a child to read . . . now a library is most important to our lifespan of our learning, really. . . Yes this is a very serious matter.
Libraries, the library profession and the book donation model have vital contributions to make to global priorities for human development, particularly with the agreement of the Millennium Development Goals and the emphasis placed on education and literacy by African governments such as Malawi's. However, as librarians and libraries in the UK fight for funding and recognition it is likely that, as is evident in this case study, trained staff and professionals are overlooked in the consultation process by UK based NGOs and development agencies. Any short term financial savings made by not employing or consulting library professionals can only be a false economy if the resources that are shipped overseas at great cost are not properly planned and directed and do not fulfil their potential. If not matched to need and supported with capacity building the widely used book donation model will fall short in its ability to contribute to global literacy and education targets.


Charm quark system at the physical point of 2+1 flavor lattice QCD

We investigate the charm quark system using the relativistic heavy quark action on 2+1 flavor PACS-CS configurations previously generated on $32^3 \times 64$ lattice. The dynamical up-down and strange quark masses are set to the physical values by using the technique of reweighting to shift the quark hopping parameters from the values employed in the configuration generation. At the physical point, the lattice spacing equals $a^{-1}=2.194(10)$ GeV and the spatial extent $L=2.88(1)$ fm. The charm quark mass is determined by the spin-averaged mass of the 1S charmonium state, from which we obtain $m_{\rm charm}^{\msbar}(\mu = m_{\rm charm}^{\msbar}) = 1.260(1)(6)(35)$ GeV, where the errors are due to our statistics, scale determination and renormalization factor. An additional systematic error from the heavy quark is of order $\alpha_s^2 f(m_Q a)(a \Lambda_{QCD})$, which is estimated to be a percent level if the factor $f(m_Q a)$ analytic in $m_Q a$ is of order unity. Our results for the charmed and charmed-strange meson decay constants are $f_D=226(6)(1)(5)$ MeV, $f_{D_s}=257(2)(1)(5)$ MeV, again up to the heavy quark errors of order $\alpha_s^2 f(m_Q a)(a \Lambda_{QCD})$. Combined with the CLEO values for the leptonic decay widths, these values yield $|V_{cd}| = 0.205(6)(1)(5)(9)$, $|V_{cs}| = 1.00(1)(1)(3)(3)$, where the last error is on account of the experimental uncertainty of the decay widths.

I. INTRODUCTION
Precise determination of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix is an indispensable step to establish the validity range of the standard model, and to search for new physics at higher energy scales. Lattice QCD has been making steady progress in this direction. For the matrix elements such as |V ud | and |V us | in the first row which involve only light quarks, dynamical simulations including up, down and strange quarks have reached the point where the relevant pseudoscalar meson decay constants and form factors are being determined at subpercent precision. On the other hand, for |V cd | and |V cs | in the second row, the precision of lattice QCD calculation for the decay constants and form factors is still at 5 to 10% level. This is not clearly superior to non-lattice QCD determinations. Indeed, the estimate quoted in Particle Data Group (PDG) 2010, |V cd | = 0.230 (11) [1] with an accuracy of 5%, is obtained from neutrino and anti-neutrino experiments. 1 Much effort is needed on the part of lattice QCD toward a better precision in the charm sector.
One of the difficulties with the charm quark in lattice QCD simulations at a typical cutoff a −1 ≈ 2 GeV resides in significant cutoff errors due to the charm quark mass. The heavy quark mass correction is m Q a ∼ 1, and hence we must control errors to all orders of m Q a to achieve a few percent accuracy. The Fermilab action [2] and the relativistic heavy quark action [3,4] have been proposed to meet this goal. In the present work we employ the relativistic formalism of Ref. [3] to explore the charm quark system.
Another source that prevents precise evaluations in lattice QCD is the error associated with chiral extrapolations in the light quark masses. This problem has been increasingly alleviated through progress toward simulations with lighter and lighter dynamical quark masses and sophisticated application of chiral perturbation theory techniques. The acceleration of dynamical lattice QCD simulation using multi-time steps for infrared and ultraviolet modes [5,6] has made it possible to run simulations with light up, down and strange quark masses around their physical values [7]. In such simulations, uncertainties due to chiral extrapolations are drastically reduced.
In fact we can proceed one more step and reweight [8] dynamical simulations such that dynamical quark masses take exactly the physical values. A potential difficulty with dynamical lattice QCD is a large fluctuation of quark determinant ratios necessary for reweighting. We have demonstrated the feasibility of this procedure in Ref. [9] by reweighting a set of PACS-CS configurations with m π = 152(6) MeV and m K = 509(2) MeV to those with m π = 135(6) MeV and m K = 498(2) MeV. Once the reweighting is successfully made, ambiguities associated with chiral extrapolations are completely removed. In the present work we employ the reweighting factors and the set of original dynamical configurations employed in Ref. [9]. Hence our light quark masses sit at the physical point.
In this paper we present our work for the charm quark system treated with the relativistic heavy quark formalism [3] on the 2+1 dynamical flavor PACS-CS configurations of 32 3 × 64 lattice generated with the Wilson-clover quark and reweighted to the physical point for up, down and strange quark masses. The lattice spacing is estimated as a −1 = 2.194(10) GeV. We measure the masses and decay constants of charmonia, charmed mesons and charmedstrange mesons. We then calculate the charm quark mass and the CKM matrix elements.
This paper is organized as follows. Section II explains our method and simulation parameters. Section III describes our results for the charmonium spectrum and the charm quark mass. In Sec. IV, we show our charmed meson and charmed-strange meson spectrum. Section V is devoted to present our pseudoscalar decay constants and the CKM matrix elements. Our conclusions are given in Sec. VI.

II. SET UP
Our calculation is based on a set of N f = 2 + 1 flavor dynamical lattice QCD configurations generated by the PACS-CS Collaboration [9] on a 32 3 × 64 lattice using the nonperturbatively O(a)-improved Wilson quark action with c NP SW = 1.715 [10] and the Iwasaki gauge action [11] at β = 1.90. The aggregate of 2000 MD time units were generated at the hopping parameter given by (κ 0 ud , κ 0 s ) = (0.13778500, 0.13660000), and 80 configurations at every 25 MD time units were used for measurements. We then reweight those configurations to the physical point given by (κ ud , κ s ) = (0.13779625, 0.13663375). The reweighting shifts the masses of π and K mesons from m π = 152(6) MeV and m K = 509(2) MeV to m π = 135(6) MeV and m K = 498(2) MeV, with the cutoff at the physical point estimated to be a −1 = 2.194(10) GeV.
Observables at the physical point are evaluated through the formula where the reweighting factors are defined as , (II. 3) and D κq [U] is the Wilson-clover quark operator with the hopping parameter κ q . We refer to Ref. [9] for details of our evaluation of the determinant ratio. Our parameters and statistics at the physical point are collected in Table I. The relativistic heavy quark formalism [3] is designed to reduce cutoff errors of O((m Q a) n ) with arbitrary order n to O(f (m Q a)(aΛ QCD ) 2 ), once all of the parameters in the relativistic heavy quark action are determined nonperturbatively, where f (m Q a) is an analytic function around the massless point m Q a = 0. The action is given by where κ Q is the hopping parameter for the heavy quark. The parameters r t , r s , c B , c E and ν are adjusted as follows. We are allowed to choose r t = 1, and we employ a one-loop perturbative value for r s [12]. For the clover coefficients c B and c E , we include the nonperturbative contribution in the massless limit c NP SW for three flavor dynamical QCD [10], and calculate the heavy quark mass dependent contribution to one-loop order in perturbation theory [12] according to The parameter ν is determined non-perturbatively to reproduce the relativistic dispersion relation for the spin-averaged 1S states of the charmonium. Writing for | p| = 0, (2π/L), √ 2(2π/L), and demanding the effective speed of light c eff to be unity, we find ν = 1.1450511 with which we have c eff = 1.002 (4). It is noted that the remaining cutoff errors are α 2 s f (m Q a)(aΛ QCD ), instead of f (m Q a)(aΛ QCD ) 2 , due to the use of one-loop perturbative values in part for the parameters of our heavy quark action.
We tune the heavy quark hopping parameter to reproduce an experimental value of the mass for the spin-averaged 1S states of the charmonium, given by This leads to κ charm = 0.10959947 for which our lattice QCD measurement yields the value M(1S) lat = 3.067(1)(14) GeV, where the first error is statistical, and the second is a systematic from the scale determination. Our parameters for the relativistic heavy quark action are summarized in Table II. We use the following standard operators to obtain meson masses, where f, g are quark flavors and Γ = I, γ 5 , γ µ , iγ µ γ 5 , i[γ µ , γ ν ]/2. The meson correlators are calculated with a point and exponentially smeared sources and a local sink. The smearing function is given by Ψ(r) = A exp(−Br) at r = 0 and Ψ(0) = 1. We set A = 1.2, B = 0.07 for the ud quark, A = 1.2, B = 0.18 for the strange quark, and A = 1.2, B = 0.55 for the charm quark. The number of source points is quadrupled and polarization states are averaged to reduce statistical fluctuations. Statistical errors are analyzed by the jackknife method with a bin size of 100 MD time units (4 configurations), as in the light quark sector [9]. We extract meson masses by fitting correlators with a hyperbolic cosine function. For charmonium, Fig. 1 shows effective masses, from which we choose the fitting range to be [t min , t max ] = [10,32]. Similarly, Fig. 2 and Fig. 3 represent effective masses for charmed mesons and charmed-strange mesons. We employ the fitting range [t min , t max ] = [14,20] for pseudoscalar mesons, and [t min , t max ] = [10,20] for the other channels.
We calculate the decay constant f P S of the heavy-light pseudoscalar meson using the improved axial vector current A imp 4 .
if P S p µ = 0|A imp µ |P S(p) , (II.10) where |P S is the pseudoscalar meson state and ∂ ± is the lattice forward and backward derivative. For the renormalization factor Z A 4 and the improvement coefficients of the axial current c + A 4 and c − A 4 , we employ one-loop perturbation theory to evaluate the mass-dependent contributions [13], adding the nonperturbative contributions in the chiral limit by with c NP A = −0.03876106 [14] and Z NP A = 0.781(20) [15]. The bare quark mass is determined through the axial vector Ward-Takahashi identity, where P is the pseudoscalar meson operator. The renormalized quark mass in the MS scheme is given by Similar to the case of Z A 4 , the renormalization factor for the quark mass at the renormalization scale µ, Z m (µ), is nonperturbatively determined at the massless point, with Z NP m (µ = 1/a) = 1.308(35) [15]. The charm quark mass is then evolved to µ = m MS charm using N f = 3 four-loop beta function [16]. We employ N f = 3 based on the fact that our simulation includes N f = 2 + 1 dynamical quarks.

III. CHARMONIUM SPECTRUM AND CHARM QUARK MASS
Our results for the charmonium spectrum on the physical point are summarized in Fig. 4 and Table III. Within the error of 0.5-1%, the predicted spectrum is in reasonable agreement with experiment.
Let us consider the 1S states more closely. Since these states are employed to tune the charm quark mass, the central issue here is the magnitude of the hyperfine splitting. Our result m J/ψ − m ηc = 0.108(1)(0) GeV, where the first error is statistical and the second error is systematic from the scale determination, is 7% smaller than the experimental value of 0.117 GeV. In Fig. 5, we compare the present result on N f = 2 + 1 flavor dynamical configurations with previous attempts on N f = 2 dynamical and quenched configurations using the same heavy quark formalism and the Iwasaki gluon action [17]. We observe a clear trend that incorporation of dynamical light quark effects improves the agreement.
We should note that the continuum extrapolation is to be performed. A naive order counting implies that effects of O(α 2 s f (m Q a)(aΛ QCD )) from the relativistic heavy quark action is at a percent level. Another aspect is that dynamical charm quark effects and disconnected loop contributions, albeit reported to give a shift of only a few MeV [18], are not included in the present work. Additional calculations are needed to draw a definite conclusion for the hyperfine splitting of the charmonium spectrum. where the first error is statistical, the second is systematic from the scale determination, and the third from uncertainty in the renormalization factor. The systematic error due to the heavy quark of O(α 2 s f (m Q a)(aΛ QCD )) is also to be estimated. Figure 6 compares our result with a recent N f = 2 + 1 lattice QCD estimation by the HPQCD Collaboration [19] in the continuum limit, which uses the HISQ form of the staggered quark action for the heavy quark on the MILC dynamical configurations.

IV. CHARMED MESON AND CHARMED-STRANGE MESON SPECTRUM
We calculate the charmed meson and charmed-strange meson masses which are stable on our lattice with the spatial size of L = 2.88 (1)  Our results are summarized in Fig. 7 and in Table IV and V. All our values for the heavylight meson quantities are predictions, because the physical charm quark mass has already been fixed with the charmonium spectrum. The experimental spectrum are reproduced in 2σ level. The potential model predicts the D * s0 meson mass is above the DK threshold [20], which deviates from the experiment significantly. But, our result does not indicate such a large difference from the experimental value. A similar result is obtained in other lattice QCD calculations [21]. It should be noticed that our calculation does not cover DK scattering states yet. DK contamination for D * s0 and D s1 meson masses can be considerably large. Further analysis is required to validate our results for D * s0 and D s1 meson spectrum. We compare our results for the hyperfine splittings m D * − m D and m Ds − m D with experiments in Fig. 8, where we also plot our previous results for N f = 2 and quenched QCD [17]. The deviation from the experimental value is 1.2σ for charmed mesons, and 2.3σ for charmed-strange mesons. Table VI presents our estimate of the pseudoscalar decay constants for D and D s mesons. Figure 9 shows the experimental values [1] and our decay constants, as well as three recent lattice QCD results: HPQCD and UKQCD Collaboration [19] using HISQ heavy quark on the MILC staggered dynamical configurations, Fermilab lattice and MILC group [22] using the Fermilab heavy quark on the MILC configurations, and ETM Collaboration [23] who uses the twisted mass formalism. Our value for f Ds is in accordance with experiment, while that for f D is somewhat larger. Comparing four sets of lattice determinations, we observe, both for f D and f Ds , an agreement between our values and those of the Fermilab group, while there seems to be a discrepancy between our values and those by the HPQCD and UKQCD Collaboration and ETM Collaboration, though continuum extrapolation is needed on our part.

V. CHARMED MESON AND CHARMED-STRANGE MESON DECAY CON-STANTS AND CKM MATRIX ELEMENTS
We plot the ratio of f Ds to f D in Fig. 10. Uncertainties coming from the renormalization factors cancel out, and that of the lattice cutoff to some extent. Our result is slightly smaller, but still N f = 2 + 1 lattice results are mutually consistent within the errors of a few percent.

A. Estimating the CKM matrix elements
The standard model relates |V cd | to the leptonic decay width of the D meson Γ(D → lν) by where G F is the Fermi coupling constant, and m l is the lepton mass in the final state. A lattice determination of the D meson decay constant f D with the experimental value of Γ(D → lν) gives |V cd |. |V cs | can be obtained in the same way. We estimate |V cd | from our D meson mass and decay constant with the CLEO value of Γ(D → lν) [24]. Up to our heavy quark discretization error of O(α 2 s f (m Q a)(aΛ QCD )), we obtain where the first error is statistical, the second is systematic due to the scale determination, the third is uncertainty of the renormalization factor, and the forth represents the experimental error of the leptonic decay width. For comparison, the PDG value given by |V cd | = 0.230 (11) [1] is about 10% larger (see Fig. 11). Similarly, using the CLEO value of Γ(D s → lν) [25], we find as compared to |V cs | = 1.02(4) from PDG [1]. For completeness we also record the ratio |V cs |/|V cd | for which the systematic errors are partially dropped out.

VI. CONCLUSION
We have reported our study of the charm quark system in N f = 2 + 1 dynamical lattice QCD. Although carried out at a finite lattice spacing of a −1 = 2.194(10) GeV, our results for the spectra of mesons involving charm quarks are consistent with experiment at a percent level, and so are those for the decay constants within a few percent accuracy. These results indicate that the heavy quark mass correction m Q a in the charm quark system is under control by the relativistic heavy quark formalism of Ref. [3]. Of course, the continuum extrapolation and further reductions of statistical noises are required to obtain the result competitive with other approaches in the literature.
From methodological point of view, we have shown that the realistic heavy quark simulations with the light dynamical quark masses precisely tuned to the physical values are feasible. With the technique of reweighting, configuration generations are needed to be carried out approximately around the physical point, and a residual fine tuning to reach the physical point only requires a much less time consuming evaluation of the quark determinant ratios. Combined with the PACS-CS configuration generation at a smaller lattice spacing of a −1 ≈ 3 GeV underway, we hope to return to the issue of continuum extrapolation for the charm quark system in future.        FIG. 6: Comparison of the charm quark mass. The charm quark mass is obtained at µ = a −1 , and evolved to µ = m MS charm using four-loop beta function [16]. We employ N f = 3 running based on the fact that our simulation includes N f = 2 + 1 dynamical quarks, while HPQCD collaboration uses N f = 4 reflecting fictitious dynamical charm quark effects [19].


extfieldsofstudy: Psychology Medicine

text:
The Hot (Invisible?) Hand: Can Time Sequence Patterns of Success/Failure in Sports Be Modeled as Repeated Random Independent Trials?

The long lasting debate initiated by Gilovich, Vallone and Tversky in is revisited: does a “hot hand” phenomenon exist in sports? Hereby we come back to one of the cases analyzed by the original study, but with a much larger data set: all free throws taken during five regular seasons () of the National Basketball Association (NBA). Evidence supporting the existence of the “hot hand” phenomenon is provided. However, while statistical traces of this phenomenon are observed in the data, an open question still remains: are these non random patterns a result of “success breeds success” and “failure breeds failure” mechanisms or simply “better” and “worse” periods? Although free throws data is not adequate to answer this question in a definite way, we speculate based on it, that the latter is the dominant cause behind the appearance of the “hot hand” phenomenon in the data.

Introduction
Current information era, brings with it exciting opportunities for exploring old and new research fields using extensive data sets that are easily accessible nowadays. It allows scientists to explore many topics on a larger scale and in a more precise quantitative way. Sports is a great example of how one can take advantage of large data sets that are available in a digital format and address interesting questions in a variety of contexts (eg. [1][2][3][4][5][6]). Hereby, we study a large data set from the world of basketball: any person who ever watched a basketball match is likely to be familiar with terms like ''hot hand'', ''on fire'', ''in the zone'', ''on a roll'' etc. These terms are intended to describe the belief that an individual's performance temporarily increases significantly beyond his or her normal rate. The ''hot hand'' phenomenon has generated a huge interest in the past 25 years since Gilovich, Vallone and Tversky [7] published their pioneering paper in Cognitive Psychology. The original motivation of their paper was to study how human subjects misperceive random sequences and tend to attribute nonrandom patterns to completely random data. For that purpose they analyzed three types of data coming from the world of basketball. They claimed that the observed patterns could have been produced by random as well and hence the fact that people relate ''temperature'' inspired adjectives to players in different times is connected to the way human beings perceive the random world surrounding them and not to the objective features of reality. Since this provoking work many people have analyzed basketball and other sports looking for evidence of deviations from random patterns (see the reviews of [8], [9] and the website [10]).
However, since data is inconclusive in most cases [8] and evidence for clear deviations from random patterns are rare (e.g. [5,6,11]), the question of what type of deviation from the random pattern was hardly addressed. In particular, the nature of deviation from the base rate could be attributed to sequential dependence between events (''success breeds success'' and ''failure breeds failure'') or to non-stationary probability of success (''better'' and ''worse'' periods). The psychology of the player underlining each type of deviation is completely different and in principal could be a very interesting research topic by its own conditioned that such deviation exists.
Since the illuminating work of Wardrop [12], it is clear that if one is interested in the individual level one should not analyze the aggregated data because strange effects due to Simpson's paradox [13] sometimes referred to as ''the fallacy of the averages'' [14] might change the results dramatically. Later on, Wardrop [15] did find traces of deviation from the repeated independent Bernoulli hypothesis also in the individual level by analyzing 2000 shots of one player (Katie Voigt, who took 100 throws each day for 20 days); the results, however, weren't conclusive as they were based on one individual only, the nature of deviation from the null hypothesis wasn't clear (dependency or non-stationarity) and the setup was controlled and wasn't part of an ongoing basketball game. In the current paper a large amount of data is analyzed: all free-throw sequences extracted from play by play data of five regular seasons of the NBA (data is available at www.nba.com). Indeed, it is shown that there is a dramatic difference in the results if one looks at the aggregated data or the individual level data. Nevertheless, even after taking the effect caused by different individual levels properly into account, we were still able to find ''hot hand'' traces in the individual level. We argue that this finding is mainly due to time fluctuations of the probability of success and does not necessarily imply that there is a psychological process that influences the performance of a player based on his previous results.
As mentioned above, Wardrop [12] showed that the answer to the question whether a ''hot hand'' exists in free throws data might be different if one looks at the aggregated level or the individual level. He argued that since the typical basketball fan does not hold different data sets for each player, but rather one aggregated data set for all free throws he had ever seen, the ''hot hand'' phenomenon that is perceived by the typical fan is real since it is present in the aggregated data set. Wardrop concluded that since data in the individual level didn't show ''hot hand'' traces, the conclusions of [7] still hold and each individual series of results could be taken as a result of a random number generator of independent Bernoulli trials with a constant probability of success (p). Hereby, we reach a somehow different conclusion and show that the collection of individual sequences is indeed biased toward a hot hand tendency, which might explain Amos Tversky's (who initiated the hot hand research) words: ''I've been in a thousand arguments over this topic, won them all, but convinced no one'' [8].

The data
The NBA season is divided into two: regular season and playoffs. In the regular season, each of the 30 teams plays 41 home games and 41 away games, combined to a total of 1230 games in a season. For each of these games a ''play by play'' data is collected and is available through the NBA official website. This data lists all the events that have an influence on the game such as throw attempts, fouls, rebounds, assists, etc. along with the names of the players involved and the time of the event.
There are three types of free throws in a basketball game -all come after a foul was committed. The resulting penalty is a series of either 1,2 or 3 consecutive free throws. A player which is awarded a free throw, gets an uninterrupted attempt to score a basket from a predetermined distance. Since this distance is the same in all the basketball courts and the defending skills of the opposing team and players do not affect the outcome, one is lead to a conclusion that free throws outcome are a measure of the skill of the individual player at that point in time. This makes free throws an excellent candidate to find a ''hot hand'' provided that such phenomenon exists. Since we were interested only in free throws data the relevant information was extracted from the entire database of five NBA regular seasons (2005=6{2009=10). The data set used in our analysis after cleaning it for various items (see next section), is constructed of a total of 308862 free throw attempts consisting of 38441 single free throw attempts, 132917 pairs of free throw attempts taken by 712 different players and 1529 triplets of free throws attempts taken by 251 different players from a total 6150 games over 5 consecutive seasons.
Cleaning the data. The first step in analyzing the data was to clean it from all types of errors and inconsistencies: N The data of 12 games (out of the 1230 games played in season 2008=2009) was not complete on the NBA website and therefore was excluded.
N 540 records of the 267772 two throws data points had only one entry (the first or second trial). Hence were suspected to be typing errors and were moved into the single throw sets. N In some cases two players from the same team share the same last name. In most of these cases the player ID or the initial of the first name helps in telling them apart but in several individual cases the data was still ambiguous: in all of these cases we simply ignored this data for the current analysis (sums into 1693 throws out of the 310555 throws exist in the entire data set, 1398 of them were part of two throws sets).
All together, less than 1% of all data points were ignored for the current analysis. There is no reason to believe that the resulting data is biased in any sense due to the cleaning procedure. The cleaned data is available in Dataset S1.
Analyzing the data. As mentioned above there are three types of of free throws sequences: a single attempt, a sequence of two consecutive attempts and a sequence of three consecutive attempts. For all the two attempts sequences of every player, i, we measured the success rate for the first and second free throws attempts and denoted them by p i (1,) and p i (,1) respectively. Throughout this text lower case letters denote single individual properties. Then we measured the conditioned success rate in the second free throw attempt (conditioned the first throw went in/out) denoted by p i (1j0) and p i (1j1) respectively. The average of the players success rates and conditional probabilities were calculated and denoted by an upper case letter using the same notation, P(1,), P(,1), P(1j1) and P(1j0). We have also measured the success rates and conditional success rates for the entire data set aggregated over all players and denoted it by P P(1,), P P(,1), P P(1j0), and P P(1j1). An equivalent procedure was done with the data of the three consecutive free throw attempts.
The results were then tested for statistical significance for two measures: N Conditional probability (CP): the change in success rate of the second attempt for a given results of the previous attempt (for a sequence of three free throw attempts the same was done with the third attempt as well).
Both of these measures can be studied with the aid of the hypergeometric distribution. In order to test the NS one can think of hits as ''white balls'' and misses as ''black balls'' and put them all in one urn after labeling them as first or second attempt. Since the null assumption is that there is no systematic deviation in the probability of success between the first and the second attempts, one can sample, without replacement, one half of the total number of throws (first and second attempts combined) and check how many hits (white balls) are in the sample. The null assumption implies that the number of hits in the first or second attempt should be consistent with a random sample from this hypergeometric probability distribution function.
In the case of testing the change in CP one can think of putting all the second attempts as balls in the urn (hits are the ''white balls'' and misses are the ''black balls''). This time the number of balls that are drawn, without replacement, is the number of hits in the first throw. Once again, the null assumption, which states that the result of the second attempt is independent of the result of the first attempt, implies that the number of times one gets hits in both throws will agree with a random sample from this hypergeometric distribution function.
We describe the hypergeometric distribution function with the following parameters: W (number of white balls in the urn), B (number of black balls in the urn), S (sample size) and w (the number of white balls in the sample) and the data variables by N 11 ,N 10 ,N 01 ,N 00 ,N as the number of times the results Hit-Hit, Hit-Miss, Miss-Hit, Miss-Miss, and the total number pairs respectively.
Thus, the formulation of the NS hypergeometric distribution function is, while the formulation of the CP hypergeometric distribution function is, After calculating these measures, in principal, one can calculate for each individual player, the p value resulting from an exact Fisher test or an exact Bernard test. Both tests have their own disadvantages in accuracy and more importantly, since the distributions are discrete it is not so easy to analyze the collection of results for all individuals and deduce from it a resulting ''q value'' or ''p value of the p values'' [16]. Hence, we decided to take two independent approaches to estimate the probability of obtaining the observed collection of result for all individuals just by chance (''q value'').
The first, computationally faster, approach involves estimating a ''z value'' for each individual player; the z value is the distance (including sign) of the observed value, w, from the expected value, m~SW =N, for the hypergeometric distribution in units of its standard deviation, where the subscript is the notations we use to distinguish between the two measures defined above (NS for non-stationarity and CP for conditional probability). When calculating for the aggregated data the total number of free throw attempts is large enough and the distribution of Z Z can be approximated well by a normal distribution with zero mean and a variance of 1, from which the resulting p value can be extracted. In cases where we are interested in the statistical significance of the collection of z values of the N p players, one can look at their (the individual z's) mean value: from the definition (eq. 3), assuming the z's of the different players are independent, one should expect the mean value to be 0 and a variance to be 1 N p .
Following this, we define Z~mean(z) : ffiffiffiffiffiffi N p p which in turn can use the normal approximation to obtain a ''q'' value by where erf is the Gauss error function and H(x) is 1 for xw0 and 0 elsewhere. A positive value means ''hot hand'' while a negative number indicates ''cold hand''. This approach is fast but rely on a normal approximation. A more accurate, though computationally intensive, approach, is permutation approach: first, we reshuffle the second throws of each individual. After reshuffling, we calculate the z CP value for each individual for the reshuffled data and record the mean Z CP value for this reshuffled realization. Repeating this procedure many times results in a collection of mean Z CP values (one for each realization/ reshuffle), each corresponds to independent second throws from the first ones. The last step in order to estimate the correspondent q value is to rank the results of the random reshuffles and see what fraction of these show larger values than the actual observed value from the original data. This fraction times two (since we are calculating a two tailed test) is an estimate of the q value. In the current analysis we have made 10 6 such realizations for each player in each season.

Results
We start by verifying two observations already pointed out in [12], but here they are observed on a much larger data set which allows for detecting better more subtle effects: 1. Aggregation of data over different players may skew and even reverse the results. and 2. An increase in the success rate with the number of throws attempts (NS). Following these two points, we describe the main results reported here: 3. Even after taking the two previous effects properly into account there is still a statistically significance correlation between the results of consecutive free throw attempts. In our notation P(1j1)wP(1j0), an increase in the conditional probability (CP), which is usually referred to as a ''hot hand''. We take, then, yet another step and propose that: 4. The increase in the conditional probability is due to time fluctuations in the probability of success rather than a causal connection between the results of consecutive throws.

Effect of aggregation
A simple statistics artifact of aggregation, sometimes referred to as ''Simpson's Paradox'' [13,14] or the ''fallacy of the averages'' [17], can produce macroscopic biased patterns out of completely random elements. Although Robert Wardrop [12] observed this effect in a smaller data set he studied (one season of one team -the Boston Celtics), it is instructive to show the presence of this effect in the current data set as it is much more noticeable here and may serve as an intermediate step for a better understanding of the effects caused by time variations of the probability of success. In order to illustrate the effect, let us look at the throw sequences data of two individual players: Dwight Howard and Kevin Martin from the 2008=2009 NBA season (summarized in Table 1). While the individual z CP values (see eq. 3 in method section) of both players for conditional probabilities have negative values: z Howard CP~{ 1:83, z Martin CP~{ 0:9, which indicates ''anti-correlation'' for these players, the combined data and the corresponding Z Z CP value shows the opposite trend ( Z Z Combined CP~0 :49), suggesting the combined data shows ''hot hand''. According to [12], this might be the hot hand that the typical basketball fan perceives as he/she cannot remember all the individual sequences for each of the players separately but rather one long combined sequence. As is evident from the data presented above, Wardrop argued that observing a hot hand for the data aggregated over all players doesn't necessarily imply that the individual sequences themselves will present such a pattern (see also Supporting Information S1 for some examples of individual players values).
Yet another demonstration for this kind of bias due to aggregation is presented in the Supporting Information S1 where we show that if one takes a distribution of individual probabilities of success each of which produces an uncorrelated random sequence (that corresponds to the distribution of the different players success rates), the pattern of the aggregated data shows significant correlations in the data (i.e. a ''hot hand'') although each individual sequence is uncorrelated by construction.
The results for the aggregated level data are presented at the top part of Tables 2, 3 and in Figure 1 (a,b). The aggregated data is a sum of all free throw attempts by all players for each of the seasons. We see that both Z Z NS and Z Z CP (the Z values that correspond to the aggregated data), are positive, suggesting that we are observing the ''hot hand''. But, as we learned from the Simpson's Paradox, this alone is not enough to declare that there is a tendency for a player to improve with consecutive free throw attempts (NS) nor that there is a better chance to score after a success in the previous attempt (CP). In order to be able to correctly test for these features we need to look at the data at the individual level: i.e. calculate the level of non-stationarity and conditional probability for each of the players.

Monotonous increase in the probability of success
The success rates of free throws attempts are summarized in Table 1 and shown graphically in Figure 1(a,c). One can see for both the individual (a) and aggregated (c) level data how the mean probability of success increases with the order of throw attempt in the sequence. This effect is evident for the whole period and for each season whether one is looking on sequences of two or three free throw attempts. It is worth noting that the first two attempts from sequences of three free throw attempts have higher mean success rates, this is due to the fact that players who attempt a three point shot usually posses better shooting skills (the blue symbols in figure 1 represents these results). For the case of two free throws attempts, the success rate for the second attempt is increased by at least 4% for all the seasons examined with the Z NS and Z Z NS values (see Table 4) for all of the seasons above 10 (!). The probability of this happening by chance under the null hypothesis is ridiculously low (v10 {23 ) for both the individual and aggregated data, which gives these results a very high level of statistical confidence. Moreover, the fact that both Z NS and Z Z NS are very close suggests that this tendency of improving the probability for the second shot is relatively a homogeneous feature of the players. The three attempts sequences show the same tendency for the third shot as well but with less statistical significance as there are only 251 players with 4587 free throws attempts (see Supporting Information S1).
In the left panels (with the red bars) of Figure S1 we plot the histograms for the improvement in success rate for all the individual players and the corresponding z NS values for each individual player taken from the data for all seasons. The average improvement values span between the limits 7:6{12:7% and the median between 4:9{7% the positive skew from a symmetrically distribution in the individual players level is evident. The histograms of the z NS values show a similar skew as well with a means and medians values between 0:5 and 0:7, which result, once again, in a negligible q value (p value of the collection of individual p values, see methods) of *10 {24 calculated from table 4.
The reasons for this effect could be easily justified as an ''alignment gauge'' for the hand of the shooter. The time taken by the player until the second attempt also allows for rest and more concentration before the second and third shots are taken. Needless to say that this tendency cannot go on forever and it may be interesting to quantify this feature further using targeted experiments.

Increase in conditional probability (''Hot Hand'')
Panels b and d of Figure 1 show the success rate of the second free throw attempts conditioned a successful/unsuccessful first attempt for both aggregated and average of the individual players (the data is summarized in Table 3). Over all 5 seasons examined there is a 1:4{4:6% improvement in the second attempt success rate conditioned that the first attempt was good. This data is for the mean of the individual level, eliminating any skew of the results due to aggregation. The histograms for the individual players success rates and corresponding z CP values are presented in the the right blue panels of Figure S1. As for the statistical significance of this result, one is referred to table 4 to see the resulting q values calculated by the two methods (normal approximation and permutation approach) described in the methods section. One sees that in both methods similar numbers are obtained (which means that the normal distribution approximation is a decent one in this case) and that in most seasons (apart from 2008/2009) the trends we observed are statistically significant (q value v0:05=G, where G is the number of repeating tests one is performing, 5 in our case). These q values are much less significant from the aggregated level data.   This is attributed to the fact that the players probability of success distribution is broad and the ''mean'' individual is not a representative player. In three attempts sequences we observed the same trend but with a much lower level of statistical significance due to the low numbers of throws (see Supporting Information S1). The interpretation of this result is essentially that the results are unlikely to emerge from a collection of uncorrelated sequences each with a constant probability of success and no auto correlation. But statistical significance is borderline in some cases and the question about its' origin remain: does it mean that we found proofs that''success breed success'' or can something else explain the observed ''hot hand'' pattern? Recently, for the change in the conditional probability, similar results were obtained in [6], using different methodology and based on a subset of the data presented hereby (namely, the 2005=6 season). Our analysis agree with these results for that season and extend them to a larger period of time.

''better and worse'' periods rather than ''success breeds success''
In principle, ''better and worse'' periods for individual players can cause the same effect as ''success breeds success'' on the success rate of the second free throw attempt and are hard to separate apart. To illustrate the reasons for this difficulty, two of the simplest descriptions of each possibility are compared: N ''Better'' and ''worses'' periods: switching with random (or constant) periods of time spent in each of the two states where each state is a Bernoulli independent repeated trials with probability of success p good and p bad . Figure 1. The two trends observed in the data. Panels a and c(individual and aggregated levels respectively) show how the chances of hitting a free throw increase with the number of throws taken in a row (until a set of three throws). This increase is evident in both individual and aggregated levels (a and c respectively). The last two values of the x axis represent sets of two throws taken only by individuals who had at least one three throws set. These values resembles the values of the first two throws in a three throws set. Panels b and d show the success rates of the second throw in a two throws sequence following a success/failure in the first throw. These panel shows a major finding of the current paper: ''hot hand'' statistical traces -success rates in the second throw are higher when the throw attempt followed a success in the first attempt rather than a failure. In this case as well, the results are present both in the individual level and in the aggregated level (b and d respectively). doi:10.1371/journal.pone.0024532.g001 N Positive/negative one step feedback: the probability of success given the last trial was a success is p hit and p miss if the previous trial was a failure.
Both options can be viewed as a system where each player behaves essentially like two players sharing the overall sequence with different probabilities of success. This point of view connects back to the first observation (effect of aggregation) and to Supporting Information S1 where it is shown that in this case there will be a systematic deviation between p(1j0) and p(1j1) and thus a ''hot hand'' will be present in the data.
In order to distinguish between the two there is a need for an analysis of the time series of results which will help in identifying a characteristic timescale in which the probability of success changes and then to try and link it to one of the possibilities presented above (see [15] for a comparison of several methods to detect such pattern). However, the studied data set does not allow such analysis since the typical player throws only one set of two throws in a game and it would not be wise to treat free throw attempts from different days as one sequence. Moreover, the free throws happen during a game in which the players experience success and failure in several aspects not captured by the current analysis. We think there will be merit in an experiment that includes many subjects aiming to extend the results in [15] to address this interesting question. In spite of the statistical ''hostile'' environment for choosing between the two options in this data, it is still possible to come up with two different arguments that support the first possibility (better and worse periods) over the second one (success breeds success and failure breeds failure).
1. Common sense: it will be unrealistic to think that during a year players will not have temporal fluctuations in their objective skills due to various environmental conditions disregarded of their achievements. Some examples are injuries and recovering from them, unrelated psychological crises or improvement in their skills due to hard work.
2. Hard wired: the belief in the positive/negative feedback mechanism is attributed to processes related to the psychology of the player. In particular, it implies that there should be certain players who have a tendency to a ''hot hand'' and others who have tendencies to a ''cold hand'' or play neutrally. If such psychological reasons do exist and are hard wired in the players minds, they will dominant the deviation from the null hypothesis. Thus, one expects to be able to see a tendency for each individual to maintain his hot/cold tendency from one season to the other. In We conclude that these two points suggest that the observed pattern interpreted as ''hot hand'' in the analyzed data is in large part a consequence of better and worse periods.

4th quarter
It is believed that the last quarter of a basketball game is very different from the other quarters. The game is often interrupted and special tactics apply to this period. An interesting question is if and how the features we have seen so far are affected by this. For that purpose, we have divided the data into two parts: 1) quarters 1{3 and 2) 4th quarter and overtime and repeated the above analysis. Interestingly, our findings were consistent between these two periods of the game; See Supporting Information S1 for the complete analysis. One more point worth mentioning is that, indeed, as one might expect the percentage of sets of two consecutive free throws taken on the 4th quarter is significantly larger than 25% of the total number of sets in the game (except the 2009=2010 season, in which the deviation is not statistically significant). In addition, the fraction of sets of one free throw is significantly lower than 25% in all seasons. One can connect these observations to the fact that the fouls committed in this quarter are harder and chances of scoring a basket after a foul was committed on the player are lower.

Discussion
Strong evidence for the existence of a ''hot hand'' phenomenon in free shots of NBA players were found. More precisely, several statistically nontrivial features of the data were found and can be summed into one concept: heterogeneity. The heterogeneous behavior was found both in ''space'' (across players) and time (along one season). In particular it has been shown that N If one looks at the aggregated data he/she is likely to observe patterns that do not necessarily exist at the individual level. N Even if one looks at each individual sequence separately, ''hot hand'' patterns are still visible (CP): probability of success following a success is higher than the probability of success following a failure.
N These patterns could have resulted from ''better and worse'' periods and not necessarily from positive/negative feedback loops.
These statistical features per se are not so surprising when studying performance of human subjects. Nevertheless, due to the intensive debate in the last 25 years since the first paper about the ''hot hand'' phenomenon [7], they can be seen as crucial pieces of information that serve as solid evidences to rule out a stationary . The color code refers to the total number of two throws sets taken in both seasons. The numbers (in black) in each quartile are the number of observations that fall in each of them. This random pattern of the z CP (see text for more quantitative support for this statement) values across seasons suggest that the individual ''hot hand'' is not a characteristic of the player but rather something that can vary from one season to another for the same individual. This fact leads us to suggest that this phenomenon is caused by whithin-season nonstationary probability of success rather than psychological reasons which are connected to positive/negative feedback loops. doi:10.1371/journal.pone.0024532.g002 randomly independent behavior. In retrospect, it seems like a very long journey to walk through just in order to notice that human subjects have good periods and bad periods and that the time sequence results can not be produced from a binomial independent repeated trials with a constant probability of success. We hope that this work will pave the way for studying the more important questions concerning the ''hot hand'' phenomenon such as what are the physiological and psychological causes for the changes in the probabilities of success and how do the players and observers perceive these indicators for good and bad periods. In particular, it will be constructive to find new examples and/or stage new experiments that will allow one to measure the time scale in which the good and bad periods alternate. Except [15], the only supported example we have found in the literature that claims that there is a causal connection (dependency) between one trial and the following was from the world of Bowling (see the review by [8]). In that study [5], came to a conclusion that there is a dependency between trials. We re-examined their test for independence and found that the test they have used could have detected nonstationarity rather than dependency. Nevertheless, the Bowling setup seems to be a good place to perform such analysis that will address the question of timescales of good and bad periods as well as what causes the transitions between the two periods.
From the basketball fan/professional perspective, it could be beneficial if the NS result which implies that the probability of success increases with the shot number would be further exploited.
To start with, this could be added as one more statistical feature that is calculated and presented throughout basketball matches, but more importantly, one can study further the psychological and physiological reasons behind it and maybe come up with techniques that will help the player to improve the first trial(s) in a sequence of trials.
Although the phenomenon that was studied here is taken from the world of sports, the implications are much more far reaching and should bear in one's mind when analyzing data of any kind. In spite of the fact that it is known for many years that aggregated data (or mean behavior) can deviate significantly from the microscopic dynamics underlying it (e.g. [13,14,[17][18][19][20]), it tends to be forgotten in many cases; in particular when referring to time aggregation.
The current example of the ''hot hand'' phenomenon serves as a fascinating one since it is possible to trace back the fundamental reason for the deviations between the observed macro patterns and the underlying micro processes causing them to heterogeneity both in space and in time. It is demonstrated that not only different individuals may have display different characteristics which need to be treated with extra precautions, but also that the ''mean behavior'' of one individual can be non representative of it's own true time dependent dynamics.