Okay, ladies and gentlemen, thank you for your patience. I now present Honourable Wayne Girad, Minister in the Ministry of Finance and MP for Ancillary. Morning, members of the press. Good to see you again. I'm beginning to get comfortable. Yeah, so this morning I thought there's only appropriate that we update you on the work that took place on the Ancillary Bridge. As you would have noticed, there was a demolition of some of the houses in order to create the bypass for the construction of the new bridge. So that went on very, very smoothly. We took some time to get to that point because we wanted to make sure that we relocated the affected residents properly. It wasn't simply of us just throwing them out in the street. So we made sure that there was relocation in place before we went ahead and did that. I would like to also update you on the installation of the sewer treatment system. You may have heard that there was some possibility that one existed. But I think on Friday last week some members of the media did visit Ancillary and they're still apparently looking for the sewer treatment system. I'd like to remind my constituents that it's only last week that the Prime Minister approved the million dollars to put in the sewer treatment system. So at the moment, it doesn't exist. And what I said previously with regards to the sewer going into the sea was the intent. And if it was not the intent, then somebody needs to explain why it wasn't in place before the construction of the facility. I think it's also appropriate that I address you on the upcoming budget dates. On the 26th of March, at 10 a.m., the Prime Minister will lay the estimates of revenue and expenditure. And at 3 p.m. would be the Standing Finance Committee. On the 23rd of April, at 10 a.m., the Prime Minister also will lay the appropriation bill. This year, our priority, the Prime Minister's indicated, would be infrastructure. And when we say infrastructure, those simply mean roads. I mean, the Prime Minister made the point to indicate that schools are involved, the airport is involved, the port is involved. So not simply a matter of roads. It's a responsibility that the Prime Minister takes very seriously. We inherited a situation to be quite frankly where the road network was in a mess. And we've tried our very best to make sure that we keep up with the deterioration. But as you would well recognize when we came into government, this is a very significant point. The debt to GDP ratio was 101%. As of December 2021, pain in Miami got into government of July 2021. As of the check that was done by the World Bank and the IMF, as of December 2021, our debt to GDP ratio was 101%. So I think the Prime Minister has done a very sterling job to get us to where we are at the moment. And out of every confidence, he will encourage us and will support us in delivering for the commitments that we made to the people of San Jose. Thank you very much. Any questions? I will happily take them. Just one quick question. Regarding the demolition of the Alps and the Strait Bridge, do you expect a larger bridge to take a wider dimension? Yes, we expect to have a two-lane bridge. At the moment as you know, it's a one-lane bridge. So the intent is to have a two-lane bridge. So what you see built at the moment is the bypass. So we create the bypass, then we remove the existing bridge and we install a much more appropriate bridge for the community of Ansari. The days of Ansari being seen as the backward community, the community with no ambition, the community that always seemed to be interested in is other things interested in other people. But we seem to get the brunt of the focus of what we've not been able to achieve. Going forward, you see a remarkable difference in Ansari countries. I'm from Ansari countries. I'm from Jackmel. And I take personal pleasure in ensuring that I deliver on those commitments. It will be a new constituency at the time of the next general election. I read an article that spoke about a $40 million investment from the World Bank for fiscal and regional reforms. Are you able to comment on that? What does it entail and what is it for? So it is something that we inherited to be quite honest. And the former minister of finance never admitted it. Saint Lucia was born as if there was no tomorrow. So we needed to get some assistance. They needed to get some assistance to be able to finance the expenditure that they were essentially encouraging. So it is something that we did simply to ensure that there was no break in continuity, because we did inherit a very difficult situation. As I say, into 101% of debt to debris is a significant figure. Of the countries in the region and the world, I think Saint Lucia would have borrowed two and a half times more than any other country. Countries borrowed during COVID, but in our particular case, we brought two and a half times more than any other country in the world, and certainly in the Caribbean. So the $40 million is simply to assist us with budgetary support, which was an inherited program that we went through. We did have to do some refining and some better work in terms of targeting what the money will be used for, but it was something that was existing when we came into government. So we like to continue things. We're not in the business of destroying or stopping and starting. We're in the business of continuity because the people of Saint Lucia at the end of all is who we serve and who we had to serve. How long is the historic bridge expected? So we are anticipating all things being equal. I'm told nine months. So we should have this constructed and in place in nine months there. But in the interim, you'll get periodic updates as to where we are. Because as you know, rainfall, heavy rainfall would have some challenges in terms of how we proceed, but we told nine months to completion. What did you do to address crime and you've seen it in Jackmell? Now, I want to say Jackmell. We need to be careful. It's not actually Jackmell. So I know the general generalization is to say it's Jackmell. But the challenges that exist as a look for the enough of Jackmell in the constituency of Boyden, it is something that we are keeping a very close eye on as you would have noticed over the last few weeks there have been nothing happening there and as a matter of fact, last night, once I was in Jackmell, the SSU was making its regular rounds. So we recognize the challenges that exist there and we try our best to ensure that we're not a community known simply for all things negative, including crime. We have a lot more to provide to the country and to showcase ourselves than just that. I know you will be able to give more details on this, but you know it's a very concerning matter. Young people, I mean this was a rural caste list, but do you think it's outside influence and not just the kids from the air? Outside influence in bringing into this crime? I think partly, I think also we have a system where residents go overseas from a particular community. They find themselves in trouble overseas, they get trained in the things that are not lawful and when they are deported they come back to the country and create a problem. So there is an element of outside influence, but I think we all need to just redouble our efforts to do what we can to mitigate that outside influence. When I grew up in Jackmell, if I ever saw a fight, it would be very rare and very shortly because the community would separate. In this particular instance, you find everybody is paying a blind eye and saying it's not their business until it gets to their doorstep. And this is one thing we know for a fact, it may not get to you today, but at some point if we don't arrest the situation, it will get to your doorstep. And that is why the Prime Minister did the two and a half security levy. It is not simply because we are happy with the minor benefits we get in. We wanted to enhance our police force, give them access to more equipment, more technology, and that is one of the reasons, principle reasons for the two and a half levy. Because we know we could always do better, or we want to do better.  On the 26th of January, and I will come back to you to announce that officially, we are launching our fish fry and ancillary. I would like it to be a very safe environment. I would like all of you to come spend your money in the community. And I don't want you to feel harassed or threatened. It's in our interest to ensure that we have and maintain a very safe community and country. Good afternoon. How is that time of day? The year is flying. I just want to, before I open for your questions, I just want to tell you that I've always taken a pledge to speak the truth to the people of Sennusha. Even the truth is very uncomfortable. I know it's very uncomfortable for the UDP to understand that they destroyed a holding facility without making adequate preparations or adequate arrangements for housing people who were arrested. I know it's very uncomfortable for them to admit that was irresponsible. And having destroyed that facility and not creating any viable arrangement to detain arrested people, people arrested on suspicion, people arrested to be charged in the future and having been so short-sighted as to destroy that facility. Considering the fact that we are rebuilding that facility, I expect Day 9 of the Sparta to be very ashamed. But truth is there was absolutely no place, there was no holding facility in castries for the detention of arrested people and the police force apart from, and I want to commend them and thank them for having to find places to detain arrested people. Grossly, Babono, Marchand, Marigold, Anslery, sometimes as far as Souffre, when these cells were full, there was no place to put these people. This is an uncomfortable truth, the responsibility of the United Workers Party, which they are ashamed to admit. And fact is, very uncomfortable, some of these people who were arrested had to be released because there was physically no place to put them because the United Workers Party destroyed the custody suite. So I know it's very uncomfortable, but that is a fact and I want to thank the police for having to deal with that inconvenience. It caused an increase in the use of our resources, police vehicles had to be used to transport detained people and it caused quite an issue with our national security. That situation had been rectified with the construction of the custody suites, but it was highly responsible and an act of callousness on the part of the United Workers Party to destroy the custody suites. We are rebuilding the custody suites. Among other things that we are doing for the Z-Police, among other things, we are doing many other things in terms of the physical existence for the Z-Police. I want to invite you to have a talk sometime on work on the grossly, the northern headquarters for the police is situated in grossly. I want to invite you to have a talk about that at some point. Again, an act of irresponsibility that was supposed to be built from 2016. That was supposed to be built, not built, irresponsibility. Then the view for the police station, that there was a mold infestation in that police station from since 2020. Let's say 2019 was COVID again, no work done there. We're the one who started to do work on that facility.  There's several other police facilities, no workers done. We're going to be repairing them. We're going to be renovating them so ensure that the police have a better environment to work on. On bodily, the situation which inherits as far as bodily is concerned, you understand? You have to have discussions to find out what was the situation in bodily in 2021 when we won elections. So the national security situation is a situation that has many, many facets. What would happen at bodily? What was the condition of bodily when we took government in 2021? These are things we have to consider. So again, I want also to note that the homicides in this country, I'm very, very concerned about it. But fact is, for the latter part, the last half of 2023, the percentage in homicide rates decreased substantially when compared to the first half. No comfort. I take no comfort for that. I'm stating a statistical fact that in the second half of 2023, the homicide rate decreased when compared to the first half. The measures that we put in place, these measures are going to be strengthened. This year, hopefully we can continue that downward trend that we're seeing in the second half of 2023. But it's not good enough. It ought to be better. But I would thank the police for the efforts. I want to thank all the NGOs for the efforts. But we're hoping that we can continue that trend in 2024. But the last, the second half of 2023, if you look at it, there was substantial decrease in number of homicides, but not good enough. Nothing to boast about these artifacts. I also want to congratulate Miss Nina Compton, daughter of the late Prime Minister, Sir John Compton, and Lady Janice. She has a luxury vessel in the Royal Caribbean Fleet. The vessel is called Silver Nova, was named after her. She is the godmother of that vessel. It's one of the latest vessels in the Royal Caribbean Fleet. It's a luxury vessel that happened on January the 4th in Miami, in Florida. And then she was hailed as Nina Compton for human connection, cultural discovery, and honoring tradition. And it reads, Bolling St. Lucia, a resident of New Orleans, and trained at the Carolina Institute of America. Nina Compton is an award-winning chef, restaurateur, and TV personality. Her values of human connection, cultural discovery, and the honoring of heritage, tradition, and identity align with those of Silver Sea's program. The owner of two restaurants in New Orleans, Nina Compton is a leading practitioner and passionate advocate for the food of the Caribbean, and was named a culinary ambassador for a home country of Saint Lucia, where her father served as the nation's first Prime Minister. So I want to congratulate Miss Compton, and I want to congratulate Lady Janice, and the rest of the family, for the single honor that was bestowed on Miss Compton. Press. And that's why the custody switch should not be destroyed. Well, as you know, again the city police was not a construct of my government. We found it. I've asked the minister of local government to have a professional assessment of the police, which is happening now. Once that assessment is done, we will be able to tell you what we found. You see, I do not want to speak without evidence. So the assessment has been done by a professional. When the assessment is done, we'll have a conversation with the city police. I know a commissioner did address this, but we are asked about it. Yes, the commissioner has made a plea for the establishment of the K-9 unit. We had some operations, the police had some operations late last year that involved using the K-9 unit. We actually evolve in these discussions, but as I said, I mean, this is not as simple. You need trainers, it may sound like a very simple K-9 unit, but it has many things. Surprisingly, many things have to go through to get a K-9 unit going, but we are working on it, and we'll make announcements as to when and if we're going to have a K-9 unit in St. Lucia. But we continue to seek use of dogs from our friendly neighbors. The French, the Americans, our sisters, when there are several years of dogs, but we are considering actively a K-9 unit. Yes, there was, but as most things, and I always tell you, I'm not a position to make any, to opine on police operations. And I insist in that position, I'm not, I can't opine on police operations. I'm not a police officer, my father was, not one. So in terms of the training that is necessary, I have to go strictly on the advice of the police professionals, commissioner and staff. What I know is the commissioner has asked for a K-9 unit. We're going to have these discussions and I will tell her the resources that are available if they become available and for the details on training and the logistics that will be up to her. That's her job. She is a commissioner police. She is the one, she is a professional who has the responsibility for ensuring that law enforcement happens. My job is to create the policy, to create the advice and to make the resources available. And this is why we've been using the health and security levy to make these resources available to the police. Well, I'm sure that you know now the dates for our budget presentation and the dates for our estimates presentation during these presentations, particularly the policy statement. You will hear the resources that we have made available to the police, the resources. And we intend to increase that. Before the end of this year, we're going to have another batch of police recruits before the end of this year. The training will start shortly. Right now, the recruitment process is underway. That's going to happen. So I'm going to show you. We had the RSS in San Musia fighting three or three tours of duty. The money, that costs money. These things, health and security levy helped in that regard. So we're going to be outlining all the things that we did. The work at Baudelais, Baudelais is part of the security apparatus. The work at Baudelais was done. All that work, the health and security levy is used to fund all these things. In regards to statements for the 2023 position, I'm pretty curious to respond in regards to the large amount of candidates that were confiscated. You are saying that right now, even if the police are basically wasting their resources because there's so much on candidates, whereas there are other states that have little amounts of participation in other companies? I know in terms of cannabis, I know that the minister is preparing a complete policy to strengthen what exists. As you know, it is our government that decriminalize the use of small quantities of cannabis. It is our government that said that if you get arrested and you have a record, you expunge from the records. Our government that did that is our government who is looking into use. Some work was started by the last government, while our government is continuing that work and enforcing it and strengthening it. The work to do the eventual decision as well as cannabis is going to be legalized or not. Right now cannabis is not legalized. What's legalized is small quantities for personal use and for the planting of four trees per household. This is what's legalized. This is the law. We're looking into that law. It's been looked into, but again, that's the function of law enforcement. If that is the opinion of Mr. DeCarras, I can't fault him for his opinion. The fact is, the trafficking of cannabis is still an offense. That's where I think that the police face. Until these laws are changed, and I can tell you, we are actively looking at these laws. Actively pursuing these laws, the minister has formed her commission, and these have been looked into, and I'm sure, very shortly, we'll have a statement, so the police now would know what is trafficking and what is personal use. Right now, they've defined what is personal use and what is trafficking. So Mr. DeCarras' opinion is well understood, coming from his point of view. I've mentioned that to the police commissioner, and she has assured me that if there are any deficiencies in this regard, she's going to make sure they happen. Can you give us an update on how many people are in prison? I can find a lot for you. I can find a lot for you. I'll ask my people to find a lot for you. Because again, that doesn't come to me, that goes through the process. You see, our government is a government of processes, and this is what we...   And that's a problem, you understand? And this is why we find ourselves in the situation that we find ourselves. Because we do not allow professionals to do their work. Of course we have issues, but professionals must be accountable. So what has happened is politicians have tried their best to pretend that they have the answers to all the questions in St. Lucia and St. Lucia did not. So our government, the government of processes, this year we are going to be calling for an increase in the implementation rate. So the people responsible directly, because you know, the job, and this is why it's so difficult for some politicians to understand when they have lost power. They haven't understood that this job is a job that's temporary. It's not a permanent job. You sit at the dictates of the people of the country. So you can't take it all for yourself. You've got to let processes continue. When I'm no longer the minister of finance, the finance ministry will continue. It's not mine. I'm just going for somebody, you understand? And it is hard to understand. And it's why you have all that bitterness and all that calmy. Because people haven't understood that their job is temporary. And I want to tell to all budding politicians. Those in my government, those want to see government, that being in government, especially as a politician is a temporary phenomenon. When you're in your father's business, you can inherit that. But you don't inherit government. Governments are not left for you because you believe that it's your place. People elect you. And I've been very fortunate. People have elected me six times to represent them. I will slang them profusely for that. I will never not have gratitude for the people of Cassusies who've elected me six times. My single greatest achievement in life was to be elected six times by the people of Cassusies. But I know and no one needs to remind me that the job of prime minister is temporary. It's a temporary job. And I think people should think of that. And if they think of that, then they're thinking will be more focused. They will understand it's for the good of the country and not for their own personal aggrandisement. It's not an I, it's not a me, me, me. It's a country. And this is what I try to do. I try to involve all my ministers. This morning you heard the Honorable Wyn Girad, who is in the minister of finance. He's out there working on the budget with me, doing what he has to do, seeing about his constituency. We have to develop this thing holistically. It can be a one-man show. And I will not lead a one-man government. I have confidence in my cabinet. Each man and woman have their responsibilities which you have to follow. It's not a one-man show. Mr Girad about this, I also want to comment on a different article about the 40 billion dollar investment from the World Bank. No, it's not an investment. Go ahead, sorry. I think it's a loan. A policy-based loan. You can correct me. A PBL loan, yes. A whole fiscal loan and free reforms. Yes. Sure, sure. It's a policy-based loan from the World Bank to help. We have two policy-based loans. One from the World Bank and one from the Caribbean Development Bank. These loans had some pre-disbursement conditions which we had to do. We had some changes in legislation which we've done. We actually have done it with the process of finalizing it. These conditions were met and the World Bank were convinced that in the trajectory of our economy and the work we have been doing, it was okay for us to get a policy-based loan for 40 million dollars. That loan is going to be used to do a few things. In fact, both of these loans, the Caribbean Development Bank and the World Bank, these loans are going to be used to modernize the inner revenue department. They make it to modernize it to get up-to-date with modern technology. Some of it is going to be used for land administrative matters. Some of it is going to be used for budgetary support. The remainder is going to be used for the growth development of Saint Lucia's economy. These were two loans, policy-based loans. You heard more about it at the policy address. We actually passed all the tests from the World Bank to get these loans. Both the World Bank and the CDB were satisfied that the economy of Saint Lucia was being managed in a way that they could make these two loans available for us on the concessionary financing. Without direct interference in the ruin of the economy, we met the conditions. That's what we are doing. According to your report, they expect food prices to be generally high in 2024. Is there anything that the government is doing to help out of that? Is there anything the government can do to help out of that? I just heard that the U.S. cargo ship was attacked in the waters by the U.T. Revers. And your issues in the Panama Canal. What Saint Lucia needs? And we had a discussion on inflation. And the comments from the opposition on inflation on the consultation were childish and immature. I also heard a discourse on inflation. There was a comedian called Paul King Douglas. And that was typical of Paul King Douglas. But if it was the country we were running, that would be the cause for amusement. But the country we were running, inflation last year was 6.5% to 10%. That was a range. Inflation before that. There was deflation after COVID. The highest level of inflation was 2.5%. Most of the food and the stuff we buy using Saint Lucia is imported. We do not control the cost of goods. We control the price. Saint Lucia is a free enterprise system. The government only imports a few commodities. In these commodities, the government has removed service charge. The government has subsidized it to keep the price down for the products that the government imports. The rest of the importation is done by the private sector. This government has said that the supermarket business is open for anyone. Anyone who wants to go into the supermarket business, the government thinks it's free enterprise. Anyone can enter into this market. There are factors. You just spoke about shipping. There are factors that the government, the prime minister has no control over. What is the solution? What we have control over? We've removed the service charge on all the goods that are in the baskets. Saint Lucia has the highest number of non-vattable and exempt goods in the region. There is no vat on electricity. There is no vat on water. There is no vat on these two items, again in Saint Lucia. We continue to subsidize LPG, cooking gas, the 20-point and the 22-point cylinder. We continue to subsidize it. We continue to encourage people to use locally produced goods. We are enhancing the resources at the major agriculture so we can plant more food so we can use it. When the minister of finance tries to emphasize the use of local products, his adversaries try to take it as if it's a joke. Instead of looking at the message, they try to attack the messenger. The messenger is temporary. The fact is, even if you attack the messenger, the reality is inflation is ravaging the world. That's the reality. Attacking the messenger doesn't change that reality. It doesn't change it. The fact is, you can attack the messenger but when the shipping costs go up, it's going to impact on Saint Lucia even though you attack the messenger. So all we're saying is that the whole phenomenon of inflation is a worldwide, the ministry of finance or if this prime minister could have done anything more. And we are continuing to explore what we can do more. We have a discussion with the Chamber of Commerce as to say that exempt goods and non-vattable goods. We have a discussion with them as to how we can deal with that list. We have cushioned the impact on inflation by removing the vats on building materials. We have cushioned the impact of inflation by removing the vats on equipment bought by doctors and medical people so the cost of use services can decrease. We continue to subsidize LPG. The government gets its revenue from duties, import duties, etc. This is what runs the country. We've continued to give income tax exemptions. We've continued to have amnesty for income tax due. All kinds of tax including vats. We've increased the threshold from which people pay no tax. We've increased our social support to almost double. We've removed facility fees to ease the strain on people. So the government is cognizant of the fact that the price that inflation is ravaging the countries, even in Cohen St. Lucia. But we hoped that there would be a decrease in shipping costs. Now, because of what is happening, these shipping costs, it is not sure whether they are going to come down as results. Because of what is happening now in the world. As far as the world maritime situation is concerned. Which we have no control over. So what we must do as a country is to have a mature discussion on inflation as we did before. I'm going to instruct the Minister of Commerce to continue that discussion. Continue it. Because many ideas came out of that discussion. A mature discussion on inflation. Which is our concern. Which is the government's concern. But attacking the messenger will not help. Because in attacking the messenger, no one has come with a viable option as to how you will reduce the impact, further reduce the impact of inflation on the people of St. Lucia. Establishing trade links with the south. Brazil. We are actively pursuing that for long. But again, there are psychoscientary things you have to deal with. You know, it's not isolated. You know, it's holistic. Now, in important things, some other parts, you have to deal with psychoscientary situations. So we should have to ensure that that is done. But we are actively pursuing that. Actively pursuing that. Because of the important goods, one aspect of the primary sector, some of the goods that are important, they stay on the top, so they stay in the ship. Very good question. That is why, you understand how it's coming together. That's why we're taking the cruise away from Slasper. That's why Slasper bought a new... That is why Slasper bought a new crane. You see, I'm very happy with the way you... I'm very pleased with you. Who are you looking for? Choice. I'm very pleased with the way you are analyzing the analysis. Very good. That is why we, Slasper, just bought a new crane so that the processes at Slasper can increase. We've taken cruise away completely from Slasper. Because whereas Slasper only got 10% of his ready from cruise, and they had to put so much... They had a loan of $20 million for cruise. So we said we didn't have to be completely from Slasper. So Slasper can concentrate on cargo, can concentrate on making the processes easier. They've just bought a new crane. They're going to buy some more equipment to make it... So your question is perfect. These are all parts of the puzzle of the cost of goals in this country. Any more questions? Go ahead. We have a lot of respect for the President of the National Consumer Association. And then her call is being considered. I have not been advised on that. Thank you very much.


Welcome to the first lecture of our basic statistics course. We hope you have as much fun with this as we did. I'm going to start with some key terms. The first term you must know is population. A population is the entire category under consideration. Thus, it could be every lawyer in the United States, if that's what you're studying. Or it could be every single woman, or it could be every adult in the United States. But the entire category under consideration is the population. The way we represent the population size is with a capital N. So when you see a capital N, N for number, we're talking about the population. Now of course it's very expensive to contact everyone in the population. Imagine if you had to contact every single lawyer in the United States. So what do we do? The whole course is based on the idea that we take a sample, which is essentially a portion of the population. A good sample should be representative, or it's worthless. You want a representative sample, and that's why we're going to learn a little bit about probability samples and how they provide assurance that a sample is indeed representative. Now when we're talking about a sample size, remember it's a portion of the population, the sample size is shown with a lowercase N. Capital N, population, lowercase N, sample. So for example, let's say a company manufactures a million laptops. They don't want to test a million laptops. Of course a fortune. So what they'll probably do is take a representative sample of say 500 laptops. So the population size, that's the capital N, is a million. The lowercase N, that's the sample. N is 500, lowercase N. So we're going to test the 500, and that's usually what we do in something called quality control. Now you know about a population and a sample. Any kind of measure that comes out of a population, in other words a characteristic of the population, we call that a parameter. Generally we use a Greek letter. For the population mean, for example, we use the Greek letter mu. You'll see the mu on the slide, that's a mu. It looks a little bit like a U, it's a Greek letter, we call it mu. The population standard deviation, again we use a Greek letter, and that's called sigma. Those are two very good examples of population parameters. Again, a population parameter, these are measurements that come from a population. You take a census, and that's essentially the only way you're going to get a population parameter. You must take a census, and we know that it costs a lot of money to take a census. You've got to contact every single member of the population, so that's very rarely done. The government does it every 10 years, but corporations are not doing it. Normally we work with statistics, in fact that's the name of the course. We don't call the course parameters, we call it statistics, because that's what we usually work with. We work with statistics. These are measurements that come from the sample. Any measurement that comes out of a sample, remember the sample is the lowercase n, small n, not a capital n. So we're not going to look at mu for working with a sample. We actually examine the sample mean called X bar. X bar is a sample mean, and the sample standard deviation we call S. S is the sample standard deviation, and those are called statistics. Those are estimates. We use them to estimate the parameters. So again, the way it works is we're going to take a small sample, a percentage of the population, and we're going to use lowercase n. From that we're going to get statistics such as X bar, the sample mean, S, the sample standard deviation. These in turn are then used to estimate the parameters which we don't know. Remember the parameters are going to be mu and sigma. We're going to estimate those parameters from the sample statistics. Now we're going to talk about statistical inference. What is statistical inference? You know the English word infer to infer something? This is the process of using sample statistics to draw conclusions about population parameters. So we'll give an example. Suppose you take a sample of a thousand. Now the whole population is 330 million. You took a sample of a thousand people, let's say. You got the sample mean X bar. You're going to use that X bar. You're not so interested in X bar on its own merits. It's not so important to do that X bar. You'll see in a moment why it's not so important. But it's a good tool. That X bar will be a tool to infer something about the population mean mu. Now you have to also realize your X bar is nothing special. So I could take a sample of a thousand out of the 330 million. I might get an X bar that's somewhat different. And I'll use that as a tool. We call X bar an estimator of mu. It's used as an estimate of mu. So X bar is, that's called inference. Using X bar to learn about the population from mu. But keep in mind that your X bar is not that special. Somebody else may get X bars a bit different. You know that pollsters, they don't bother contacting. It's too costly except when we took a census. But the pollster doesn't work with a census. The pollster will take a sample of one or two thousand people to determine who they will vote for for president. So rather than contacting everybody, which should be a fortune, they take a representative sample of maybe a thousand people, sometimes more. They will get a sample statistic from that sample. We call it the sample proportion. That is a statistic. And they're going to try to estimate who's going to win the election. That's the population proportion. So notice how we use the sample proportion as a tool to try to predict the population proportion, which is really the measure of interest. This example is from quality control. Try to imagine General Electric has a plant on Staten Island and they're manufacturing LED bulbs. They won't have an idea of how many of these bulbs are defective. Now suppose this plant manufactures one million bulbs a year. So they have a million bulbs and they hire you. Now you're not going to test the whole million bulbs. If you're smart, you might take randomly 500 bulbs to estimate the proportion of defectives. So capital N, that's the population size of a million, you took a random sample of 500. Lowercase N is 500. Now out of the 500, suppose you test them and then a machine, you find 5 out of 500 are defective. 5 out of 500 bulbs are defective. So we call that the sample proportion. Your sample proportion is 1%. So 1% of defective, 5 out of 500. That's called your sample proportion and that's a statistic. You're going to use that statistic using inference tools to estimate the true proportion of defective bulbs and that's called the population proportion. We're going to show that we generally don't use the Greek letter. We're going to use a big capital P because the Greek letter would be pi. So we use P usually for the population proportion. And back to me. Descriptive statistics as opposed to inferential statistics summarize a sample of numerical data, maybe in summary statistics, maybe in the form of pretty pictures, images, graphs, charts, and in that case, we're only interested in turning that data into information about that particular sample. With descriptive statistics, we're not interested in any larger population. We're only interested in the data in front of us and in understanding that data and producing some summaries so that it's easier to talk about the data. Sometimes your data set can be quite large. So for example, if I give an exam to a class of, say, 35 students, ha, when was the last time our class had 35 students? And, you know, suppose I want to use descriptive statistics so I can assess the performance of the class, which we do. Every time we get an exam, you can look at the summary statistics on block board. We could get the median. We can get the average, the standard deviation, the mode, the max, the min. But one thing we're not going to do is look to take these measurements and draw inferences about the larger population. What larger population could we possibly be interested in? Throughout our college, all the sections of STAT 2000, through the whole CUNY system, through all of New York State universities, through colleges across the world, what's the population that my class comes from? It really doesn't make much sense to do that and we don't want to do that. That's not what we're getting descriptive statistics for. We just want to describe the performance of the class on this particular test. That's what descriptive statistics are all about. Where does data come from? It'll come from primary sources or secondary sources. Primary data is data that the researcher collects on his own or on her own. How do we get primary data? Field experiments, observations, in-depth interviews, focus groups, and for the most part, surveys. There's all kinds of surveys. Many of them yourself. Mail surveys in the actual mail and snail mail sent to you by the USPS hardly get any of those anymore. Used to be very, very popular, very low cost, very fast, but you're not going to see that anymore. You're more likely to see email. Your survey can come in email and in the email it could link to a web page so that it's actually a web survey. We have personally administered surveys where you have an actual interviewer and the interviewer has to be trained. That's the human being there and it's the most costly type of survey. But there are advantages because you have a human being. The interview can last longer and can be more in-depth based on the answers to an early question the interviewer could probe and try to understand the situation better and ask follow-up questions. What depends on the point and the kind of data that you're trying to collect? When you need something fast, telephone is probably the fastest because you get immediate response as long as somebody is in and picks up the phone and we all know we hate it and they're fast becoming very problematic because a lot of people don't pick up. But if you're not that concerned about how representative your sample is, telephone will be the fastest. And email is kind of next. It's not too far behind. So basically you've got different types of surveys. You've got advantages. You've got disadvantages. And it's like everything else. You want to look at the objective of your study and figure out which way you're going to go. Secondary data is data that already exists that was collected by somebody else, not the researcher who's working on this project currently. It might be in a library. It might be available for purchase from a corporation or a professional association. It might be census data from the government that you're working with. It might be hospital data. Again, the various ways that hospital data might be available. Secondary data, even though you might think it's difficult to find exactly what you need and that's true, still if you can manage to use what's out there, it's there. You can skip the whole process of collecting data which could be very, very long and involved. It often is cheaper than collecting your own data, of course, as well. What are some of the problems? The data is very easily outdated. It was collected for some other purpose. The variables may not quite be the variables that you're thinking of in your project, the units of measurement, the accuracy. Basically, you're not in control of your data, but there's a lot to be gained. In fact, there are some studies that you can only do using secondary data. Let's take a look. Some of the types of research studies that work very well with secondary data. One is fact finding. You're exactly interested in the secondary data. Maybe the amount spent by different industries or by different corporations inside an industry on advertising. Maybe related to market share. Maybe things having to do with technology, laptops, iPads, cell phones in different countries, Wi-Fi availability in different locations. A fact finding study is a perfect example of when you need secondary data rather than going out and collecting it on your own. Model building. When you have large data sets, one of the things you can do is look for relationships among variables, quantifying the relationship, creating a model, a linear model, or a non-linear model, but basically a mathematical model of these relationships and learning something about it. That's something that you can do with primary data, but you'd have to collect a lot of data in order to accomplish it. And finally, one thing you can do with secondary data, longitudinal studies. A longitudinal study is one where we're not just looking at data we collected this moment. We're looking at data over the long term, like in a time series. And if you have data that's secondary in the library, in institutions, in associations, in the government, generally this data is collected regularly every year, every quarter, every 10 years. And so you can do a longitudinal study without waiting for data collection to be done over the long term.  Can errors creep into your survey data? Well, you better believe it. There are basically two major sources of error in survey data, either from the responses or from not getting responses, and we'll see that in a moment. Response errors come from different types of errors that arise in the responses themselves. Now, in this course, we assume that the data we're working with is accurate. We have no other way of doing it, but in real life, obviously, you can't do that. You would like to have your data as error-free as possible. Where would the errors come from in the responses? All kinds of reasons. Some malicious, some not so. So for example, you know subjects have been known to lie, right? It happens. People aren't always totally honest, especially in certain situations. That's why sometimes we go to great lengths to make sure that our survey is completely anonymous and obviously anonymous, to take away the necessity for lying. We want as much as possible to get honest responses. Sometimes the subject isn't really trying to lie, but people make mistakes they don't remember. They think something happened in a certain way when it didn't happen that way. We're human. We're not angels. People make mistakes. Sometimes people want to give an answer even if they don't know the answer, because everyone wants to be nice and helpful. And they think they know what the researcher is looking for. So they try to give the right answer. People want to give the right answer. They want to give the socially acceptable answer. Sometimes it's the interviewer that makes a mistake. When there's an interviewer doing a telephone interview, let's say, the subject says the answer and the interviewer has to write it down. How easy is it to make a mistake in that case? Very easy. An honest mistake. And now how about the dishonest mistake? Interviewer cheating. Yes, I'm sorry to say that has been known to happen. When an interviewer, let's say, is supposed to go door to door and ask people questions, people who are home, and maybe if they're not home, has to go there again and try to get the answer at least twice or three times. Well, sometimes you'll find the interviewer at the local coffee shop filling out the surveys because it's a lot easier. People, as we know, have been known to take the easy way out. Finally, though, the most interesting of these is something called interviewer effects. That's where there's nothing malicious. Everyone's trying to do a good job. Everyone's trying to do what they're supposed to do. But it's inadvertent. Everybody has inadvertent biases. Don't forget, some biases are good biases. And sometimes, for example, certain characteristics about the interviewer could influence a subject's response.  There certainly might be bias creeping into your survey. And it may not be so bad as long as you know about it and you take it into account, but you really have to at least know what you're doing. The bias creeps in sometimes, and we don't know about it, and if we don't know about it, we can't correct for it. Okay, now we're going to talk about a different kind of error that can creep into survey data. It's not that the responses weren't accurate. It was a non-response. People have not responded to your survey, and that's not unusual. We get a low rate of response to a survey. Now what happens if the rate of response is low? See, if it be a random thing, and let's say only 30% of the people you survey respond, it was random, wouldn't be an issue. The problem is, it's generally not random. The people who respond usually are overly interested in the subject of the survey, or they could be more educated, and if only 20-30% respond, you may have a bias. You may have a bias study. That's why you try to do the best you can to achieve what's called a high rate of response. There's a time the government wanted you to get at least 60%. It's getting harder and harder to get 60% of people to respond to a survey. But you can if you try lots of follow-ups and there are ways it can be done. Look at sample 1 and 2. Look at the slide. Sample 1 is with the researcher, the sample size, notice lower case N was 2,000. 2,000 people. But the researcher was successful and got 90% of them to respond. Sample 2 is a much bigger number, dealing with a million people. Notice N is a million, but only 20% responded. There's a lot of non-response. 80% didn't respond. Most people think, well, sample 2, you got 20% of a million. It's a lot of people, right? And they think, oh, it's much better. 20% of a million is 200,000 people. 90% of 2,000 is 1,800. But the reality is that to a researcher, sample 1 is more effective and more reliable. Why? Because you have a high rate of response. So the chance of all your sample is still representative. Actually, like 100%. You're not getting 100%. You got 90%. So this is probably a representative sample and represents the population. So you can make the inference about the population. With sample 2 and only 20% respond, you may not be able to make that inference. Because it could be the 20% that responded do not represent everyone. They could be atypical. So it's of no value to you, possibly. That's why there are all kinds of problems when you get a low rate of response. Let's talk about the different types of samples. Now, let's talk about non-probability samples, which are based on convenience or judgment. Here's some quick examples of non-probability samples. Something called a convenience sample. You basically just take what's convenient.  You just take students in a classroom. Say, well, I'll go to five classes. I'll get 200 students. I'm fine. That's convenience. You don't know, really, if you have a representative sample, or a judgment sample. Use your own judgment. This is more like, I'll look at these 20 stores because I believe it's my judgment that these 20 stores represent the whole chain. Because they're typical of what I have in my chain of stores, of 1,000 stores. That's a judgment sample or a quota sample. Sometimes that's done at malls. You tell the interviewer, oh, come back with 100 subjects. 50 must be male and 50 must be female. Another 50 males. 10 should be non-white and 40 white, et cetera. That's called a quota sample. Again, it's kind of a judgment sample. The problem with any kind of non-probability sample is you really don't know how representative your sample is of the population. It's essentially your guessing. You think it's okay, but it may not be okay. Let's talk about probability samples. That's where you collect the sample in a way that every element in the population has a known chance of being selected. You don't advance what the probabilities are of selecting certain people. Let's talk about the most common one that we talk about in statistics, the simple random sample. That's where every element in the population has an equal chance of being selected. You're not responsible for this, because you have to understand what it is. You can do this. If you want to collect a simple random sample, generally we work with random numbers or random number generator. All you have to know is that let's say I have 100,000 employees and I take a simple random sample, everyone had an equal chance of being selected. Let's say the sample size was 1,000 out of the 100,000. Everybody has the same chance, which is 1,000 over 100,000, which is basically 1%. Everybody has a 1% chance of being selected. That's called a simple random sample. Let's talk about other kinds of probability samples. Just briefly. There's something called a systematic random sample. Essentially it's very much like a simple random sample, but you might just take every 50th element. Basically you figure it out. You take capital N, the population size over the sample size, whatever that happens to be. Again, try to imagine we have 100,000 employees in your computer system. You tell the computer, just choose every 20th employee. That'll be called a systematic random sample and probably most cases it's going to be just as effective as a simple random sample. Sometimes you want to stratify. That's when you subdivide the population based on some kind of characteristic. Then you take a simple random sample from each stratum. Stratum is like a group. For example, I want to look at my students. I have freshman, sophomore, junior and senior. Let's say a certain number of freshmen and a certain number of sophomores. That would be called a stratum. It's a reason for doing that. Statistics, again, beyond the scope of this course. A third kind of probability sample is called a cluster sample. You might actually do this by, for example, zip codes. It's kind of a cluster. It's like a certain number of students from this cluster, from this subcode, a certain number from this zip code. Again, there are advanced reasons for doing this in statistics. That's called a cluster sample. You may learn this in another course. It's beyond the scope of this course. What you have to know is that these are examples of probability samples. Remember a probability sample? A known, you know the probability that everything will be selected. Hey, you know it. You purposely weigh it in a way. So it's not equal necessarily. The reasons for doing this in statistics. But these are, again, probability samples. They're not based on judgment or convenience. Now we finally get a chance to look at the data itself. We want to classify the data. We want to know what kinds of data do we have to work with. And one reason we want to do this classification is because depending on the type of data, that's going to determine what kind of analysis we could do with it. For now, let's break things up into qualitative and quantitative data. Qualitative data is categorical. It's also called nominal. And it's data that results in categories. For example, the example listed there, what's your student status? Are you a grad student or an undergrad? You can't get a mean for that. A numerical analysis is not numerical data. One thing you could do is count. You could say, here's the number of grad students in the college. Here's the number of undergrad students in the college. And maybe you could even get a proportion. On the other hand, quantitative data you could do a lot more with. And with quantitative data we're going to be talking about whether the data is discrete or continuous. And we will be talking about that a lot in the course. Discrete data arises from accounting process. How many courses have you taken at the college? That's a number. It's an integer. You're not going to split that up and have a decimal component there. There's no fractions. If I ask you, how many siblings do you have? You're not going to say 1.273. You're going to say you have 1.273, whatever.  That's accounting process. Continuous data, on the other hand, arises from a measuring process. Instead of asking how many we're asking how much. How much do you weigh? Now, you may think you weigh 127 pounds. But the reality is that there's no such thing as weighing exactly 127 pounds. 127 could mean 127 with 8 million zeros after it, if you really are exactly 127. It could mean 127.4532 pounds. Basically, the data is continuous and it's we're going to have a continuous value even if the decimal portion is zero. You can't do that with children. You can't say and I'll get back to the example on the slide now. You can't say well, I have two children but it's really 2.3217638. No, of course not. So with the question about children, that's discrete data. The question about weight, that's continuous data. We're going to spend a little time now talking about levels of data. Sometimes it's called levels of measurement. Same thing. And we're looking at the data in terms of whether it is a nominal, ordinal interval or ratio. And you can see how the arrow points up. Nominal is the lowest level of data. Ordinal is the next interval is the next and ratio is the highest form of data. We're going to look at each one of these in more detail in the next slide. Nominal data is qualitative data. You get classifications or categories. You don't really get something that you can measure even though we call it a measurement but it's all we get is frequencies really. We can ask are you a CIS student or a psychology student? We can ask what's your ethnicity? Are you white or non-white? We can ask what's your occupation? But you don't get any numeric data out of this unless you code it and then it's meaningless. You can code undergraduate 0 and graduate 1 and there's still not numbers. All you have is categories and all you can do is count. It's a, what can you get out of it? Let's see what we have here. We can get a frequency. How many in each category? We can get a percentage for each category, the percentage of the total. We can get a mode which is the most frequent category. But what we can't do is anything more higher than that. We can't get averages. We can't get anything that requires numerical analysis.  We can't get a standard deviation. We don't even have a median. We don't have a middle point because we can't order these. If the categories had some sort of ordering, it would be ordinal data which we'll see in a moment. Suppose we have in a class, let's say 30 females and suppose at the moment that those are the only two categories. These are frequencies. What's the percentage? We have 60% female. What's the mode? The mode is female. Even if you code the data, it's meaningless. You can't force an average. You can't force numeric responses in nominal data. Let's talk about ordinal data. Ordinal data rises from a ranking. And then think to remember that ordinal data is that the intervals between the points are not equal. We don't do not have equal intervals. But what we can do is, let's say we check the top box. You have more of some kind of characteristic than somebody checks the next box. You see that, for example, with category of hurricanes. Category 5 is a worse hurricane than category 4. Category 4 is worse than Category 3, etc. Or this from class standing. A senior has more credits than a junior. A junior has more credits than a sophomore. A sophomore has more credits than a freshman. Those of you who took geology know this with hardness of minerals. There's a scale there. The hottest mineral is diamonds and talc is the softest. It's very rank. General is more than a kernel which is more than a major. What do we mean by unequal intervals? Look at the example. We have three people who checked these boxes for income. John Smith is earning under 20,000. Jane Doe checked the box for 20,000 to 49,999. Bill Gates checked the third box. He's making more than 50,000. Again, you know that the intervals are not equal. Jane Doe is making $3,000 more than John Smith. Bill Gates makes $50,000,000,000 more than Jane Doe. The intervals are clearly not equal. The appropriate statistics when something is measured on an ordinal scale, when you have ordinal data, you definitely can do the same stuff with nominal data. You can use the median, but you really technically can't use a mean. Using an average, a mean when you have unequal interval sizes. More on ordinal data. Ranking scales are obviously ordinal. Take something you've seen so many times, strongly agree, agree, neither agree, no disagree, disagree, strongly disagree. You know the intervals are not equal, but you know that if you strongly agree, it's more than agree. Another problem with ordinal scales, look at this example here. We ask you to rank for four scenarios.  Okay, now we ask you to rank it. And you can rank it, one, two, three, four, but doesn't mean you like any of those choices. Presumably it's not one of those four choices is something you want. So ranking doesn't tell you that just because I ranked something one that is something I like. It may be better, I'd rather be failed the course than being buried up to my neck in common ore perhaps. Now we have a higher level of measurement, interval data. An interval level of measurement. We have equal intervals, the intervals are now equal. But the zero, you don't have to really have a true zero. For example, let's talk about temperature or IQ, most test scores there's not a real zero. With temperature, you know the zero is arbitrary. Okay, but you could say let's say we're looking at Fahrenheit. The difference between 40 degrees and 50 degrees, that's 10 degrees, is the same as 1780, 10 degrees or 90 and 100. The number, or same with the test score, the zero doesn't mean you have complete absence of all knowledge. But if somebody gets a 30 and another person gets a 40 beaten by 10 points, well a 90 is 10 points better than an 80, but the zero does not mean the complete absence of what is being measured. You can't really speak about ratio, so that's why if the temperature in New York is 40 degrees and the temperature in Buffalo is 20 degrees, it'll be wrong to say that it's twice as cold. First of all, as you can tell, if you're doing in Fahrenheit once you change the centigrade, it's going to be different numbers and the ratio will be different. Now why can't you do ratios? I told you why, because it's not a true zero. If you want to speak in ratios you need a real zero, a true zero which is the absence of what's being measured. So this is good news, if you get a zero on the stat test it doesn't mean you have absolutely no knowledge of statistics. That's not what the zero means. Now what are the appropriate statistics for an interval scale? Well, you can do everything you can do with a nominal order, you can do the mode, you can do the median, but now you can do the mean, that's important. That's why when something is on an interval scale, you're allowed to do a mean, compute the mean. Okay, now we're going to talk about a ratio scale, that's the highest form of measurement in a sense because you have equal intervals, you have a true zero, real zero, and that you have with weight, length, height, unit sold. That's why you could say, if some rock weighs 400 pounds and another rock weighs 200 pounds you can say, oh the 400 pound rock weighs double the 200 pound rock and it's going to be true in any units. Switch the kilograms, guess what? It still weighs twice as much, or a line. This line is let's say 5 feet long and you compare that to a line that's 2.5 feet long. You can say, well this line is twice as long as the other line. 5 feet is double 2.5 feet and it's going to be the same with the switch to other units to inches, it doesn't matter what unit you use, it'll still be twice as long and that's because you have a true zero. Once you have a true zero, you can talk about ratios like double, triple and again, 100 pounds is double 50 pounds. $100, if you have $100 in your bank account and somebody else has 200, guess what? They've doubled the amount of money and if you both convert to Frank's, guess what? The one person that had $200 now had double the Frank's as the person that had the $100. What kind of data do you want to collect? The goal of a good researcher, you try to use the highest level of measurement. Remember the lowest level measurement is nominal you can't do means all you can do is mold. So you try to get the best measurement possible. For example, if I wanted to know about your smoking behavior you can see you have a choice here. A or B, A is a nominal scale. Do you smoke? Yes or no? I can count. I can say I did this at Brooklyn College or Baruch College and I found out of a thousand students 300 said yes to smoking 700 said no. I have a count, a percentage if you want 30% smoke. But if I do it in the B format how many cigarettes did you smoke in the last three days? Now remember that becomes a ratio scale because the zero is real. If I smoke zero cigarettes in the last three days, that's a real zero and we know what that means. For somebody who says 50 cigarettes that's going to be double 25 cigarettes. B gives you a ratio scale so you want the best measurements. For the one question you're going to ask it's always better to ask it in a way you get a more powerful kind of measurement.  We're going to talk about what type of data to collect again. A and B, comparing soft drinks. Now which question is better? In A we ask rank. Rank the following soft drinks from one to five. One is the best. If you like coke the best that will be a one. Pepsi the best that becomes a two. The one you like least that gets the five. So that's basically you get an ordinal scale. You have rankings. But B gives you a more powerful measurement. Look what you're doing with B. You're asking them to rate each of those soft drinks. Each one has to be rated on a one to seven scale. The scale is on the side there. The one is excellent. Two is very good. Three is good. Four is fair. Five is poor. Six is very poor. Seven is awful. Now it's very hard to say that's equal intervals. You can't really prove it so easily to show that the intervals are equal. But it's close. It's darn close to an equal interval scale. And we assume such that it's equal interval. But even if it's not it's certainly better than the ordinal scale. It's closer to interval and it's almost interval and now we can do the mean on each one. We can say the average for coke was and now we know what these numbers mean. Let's say we get an average for coke of 1.6. That's between excellent and very good. Let's say it's a 3.5. That's between good and fair. It's a better measurement. And that's why researchers will do it that way. Rather just ask people to rank five beverages. Let's talk about the objectives of this course. First of all, you'll learn how to summarize data, descriptive statistics. You're also going to learn how to use sample data to make inferences about population parameters. We call that statistical inference. And basically, and this may be the most important thing, we want you to be an informed user of statistics learning to think for yourself. You have to realize we're going to leave what's called a post truth world. And we've seen so many lies about everything. Fake news has now become very very popular. There's a lot of fake news. A lot of junk science. They invented a term called alternative facts. The goal of this course is that you should actually know how to make a distinction between something that's junk science and real science or fake news and real news. One thing, one way to do this is to ask for the statistics. Look at the data. Try to look at the data and make judgments. And this course will help you. Like many of your professors will be teaching you nonsense. They'll be teaching you, we call these indoctrination courses. They want to indoctrinate you. This course will teach you to ask a simple question. Let me see the data. Where is the data that says X causes Y? As you all know there's no relationship between vaccines and autism. There's absolutely no relationship. So anyone who tells you that vaccines cause autism, where's the data? There's no data. It's all baloney. I have no time to go into it. But if you ever look into it you'll find out why it's nonsense. Or some of your professors might even tell you something like how wonderful communism or Marxism is. Well, good news. You can look at the data. 18 countries have tried Marxism slash socialism communism. Guess what? 18 failures. I think you're smart enough to know if they're 18 out of 18 failures maybe we shouldn't test Marxism. Maybe it's not a good idea. I don't care what my professor tells me. If you strike out 18 times out of 18 at bats maybe it's not such a good idea. This course will teach you about looking at evidence, thinking for yourself. And again, professors of statistics make mistakes too. But look at the data. Look at the numbers and make sure you're looking at accurate numbers. And that's what this course is all about. Appreciating facts. Real facts. Real data. Looking at numbers. And don't say things that are not based on evidence. You can ask to see the evidence. There's so much data out there you just have to know where to go and nowadays it's easy with Google. Make sure you look at actual data. Good luck with the course. I hope you enjoy the course.