# What do you consider to be the difference between independent t-test and dependent t-test? What non-parametric statistical analysis can you use if the data do not meet the assumptions of parametric analysis. When do you use ANOVA? If you cannot identify where the differences occur in groups,  What statistical procedure  can you apply?

The independent t-test and dependent t-test are two different types of statistical tests used to analyze the differences between group means. These tests differ in terms of the assumptions made and the types of data that they are suitable for.

The independent t-test, also known as the two-sample t-test, is used when comparing the means of two independent groups. This test assumes that the data are normally distributed and that the variances of the two groups are equal. The independent t-test is appropriate when you have two different groups of participants or subjects that are independent of each other, such as comparing the mean exam scores of two different classes.

On the other hand, the dependent t-test, also known as the paired-samples t-test, is used when comparing the means of two related or dependent groups. This test is suitable when the measurements are taken from the same set of participants or subjects under different conditions or at different time points. The dependent t-test assumes that the differences between the paired observations are normally distributed. An example of the dependent t-test would be comparing the pre- and post-test scores of individuals who underwent a specific intervention or treatment.

If the assumptions of parametric analysis, such as normality or equal variances, are not met, non-parametric statistical analyses can be used. Non-parametric tests are less reliant on assumptions about the underlying distribution of the data. One commonly used non-parametric test is the Mann-Whitney U test, which is an alternative to the independent t-test. This test can be used when comparing the medians of two independent groups when the data do not meet the assumptions of the independent t-test.

Another non-parametric test is the Wilcoxon signed-rank test, which is an alternative to the dependent t-test. This test can be used when comparing the medians of two related groups when the data do not meet the assumptions of the dependent t-test.

ANOVA, or analysis of variance, is a statistical test used to compare the means of three or more groups. ANOVA is appropriate when there are more than two independent groups and the outcome variable is continuous. ANOVA tests the null hypothesis that all group means are equal. If the null hypothesis is rejected, it indicates that there is at least one group mean that is significantly different from the others.

Furthermore, if you cannot identify where the differences occur among groups, you can apply post-hoc tests following an ANOVA. Post-hoc tests allow for pairwise comparisons between groups to determine which specific groups differ significantly from each other. Examples of post-hoc tests include Tukey’s honestly significant difference (HSD) test, Bonferroni correction, and the Scheffe test. These tests help to identify and compare the differences between groups when the null hypothesis of the ANOVA is rejected.

In summary, the independent t-test is appropriate when comparing the means of two independent groups, while the dependent t-test is used for comparing related groups. Non-parametric tests, such as the Mann-Whitney U test and the Wilcoxon signed-rank test, can be used when the assumptions of parametric analysis are not met. ANOVA is applicable for comparing the means of three or more groups, and post-hoc tests can be employed to identify specific group differences when the differences are not clear from the ANOVA results.