Group Means


Missing values in a continuous variable will be replaced with the group mean derived from a grouping variable. The grouping variable must be a categorical variablethat has no missing data. Of course if no grouping variable is specified, missing values in the variable to be imputed will be replaced with its overall mean. All such points are covered Statistic homework help and assignment help at

When the variable needs to be imputed it is categorical, with different frequencies in two or more categories (providing a unique mode), then the modal value will be used to replace missing values in that variable. Note that if there is no unique mode, i.e. if there are equal frequencies in two or more categories, then if the variable is nominal, a value will be randomly selected from the categories with the highest frequency.

If the variable is ordinal, then the ‘middle’ category will be imputed. If the variable has an even number of categories, a value is randomly chosen from the middle two.

Comparison of variances between groups

Comparisons between means, particularly when the sample size is small, assume that the data is normally distributed, and that the group comes from the same underlying population. The assumption therefore is that the variances (standard deviation squared SD2) of the groups are similar. All these points are taken care of by the experts providing Statistichomework help and assignment help at

Three common tests are available to estimate whether variances in a study is heterogeneous.

  • The Levine’s F Test provides the best estimates, but requires the original data for calculation.
  • The Bartlett’s chi square test can be calculated from n, mean, and standard deviations from the summary data, consequently it is much more commonly used.
  • The F ratio, dividing the larger variance by the smaller one produces the F value, and the probability of F is known and easily accessible.

StatTools calculates Bartlett’s Chi Squares in all cases, Levine's F only when primary raw data is used. The F ratio is not presented as this can be easily calculated (F = SDlarger2 / SDsmaller2. The significance (probability of Type I error α) of F can then be obtained from the F table.

Difference between 2 means

The difference between the mean of group 1 and 2 (d = mean1 - mean2) is used to compare two groups of parametric measurements (continuous measurements that are normally distributed). As this difference is calculated from a sample, the standard error of the difference is also estimated. Assuming a small sample size, t instead of z value is used to calculate confidence interval. The t value that will exclude 0.05 of the area under the t curve for the degrees of freedom in the data can be estimated, and the 95% confidence interval of the difference is d ± t x SE.

An alternative presentation is to use the standardized difference and standard error. The whole dataset is transformed by its own overall mean and standard deviation so that it has a mean of 0 and standard deviation of 1.

If the variances of the two groups are significantly different, adjustments to the standard error and degrees of freedom are necessary, so the results will be different.

Differences between 3 or more means

Where 3 or more groups of parametric measurements are being compared, the one way analysis of variance is usually used. The total variance in the dataset is partitioned into those related to variations from group to group, and the residual which is considered random error. The two variances are then compared using the F ratio (F = Variancegroups / Varianceresidual. F is then evaluated to obtain the probability of Type I error (α) using the table of critical F values.

If significant differences can be found between multiple groups, then post hoc comparisons between combinations of two groups can be carried out. 



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