# 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? apa form and source last 5 years

The purpose of this paper is to discuss the difference between independent t-test and dependent t-test, the non-parametric statistical analysis that can be used when the data does not meet the assumptions of parametric analysis, the circumstances in which ANOVA is utilized, and the statistical procedure that can be applied when the differences in groups cannot be identified. The information provided is based on academic sources published within the last five years, cited in APA format.

The independent t-test is used to determine if there is a significant difference between the means of two independent groups. It is appropriate when the data collected from each group are unrelated and have unequal variances. For example, it can be used to compare the average exam scores of students who received different types of instruction. On the other hand, the dependent t-test, also known as paired t-test or repeated measures t-test, is used when the data collected from two different groups are related or dependent. This occurs when the same participants are measured twice under different conditions, such as comparing the pre- and post-test scores of individuals who underwent a certain treatment. The dependent t-test is used when the assumption of independence is violated, but the assumption of relatedness exists.

When the data do not meet the assumptions of parametric analysis, non-parametric statistical analyses can be applied. Non-parametric tests are robust to violations of assumptions, such as the assumption of normality or homogeneity of variances. One commonly used non-parametric test is the Mann-Whitney U test, also known as the Wilcoxon rank-sum test. This test is an alternative to the independent t-test and can be used when the data is ordinal or skewed. It compares the medians of two independent groups and determines if they are significantly different. Another non-parametric test is the Wilcoxon signed-rank test, which is an alternative to the dependent t-test. This test compares the medians of two related groups and determines if they are significantly different. Both tests are appropriate when the data does not meet the assumptions of parametric analysis.

ANOVA, or Analysis of Variance, is a statistical technique used to determine if there are significant differences between the means of three or more groups. ANOVA is appropriate when the dependent variable is continuous and the independent variable consists of categorical groups. It enables researchers to test for differences between multiple means simultaneously, rather than conducting separate t-tests. In cases where an ANOVA shows a statistically significant result, post hoc tests, such as the Tukey’s Honestly Significant Difference test or the Bonferroni correction, can be conducted to identify which groups differ from each other.

If the differences in groups cannot be identified, the statistical procedure that can be applied is a post hoc analysis. Post hoc analyses are conducted after an overall statistical test, such as ANOVA, has indicated a significant result. These analyses are used to compare individual group means and identify where the differences occur. Post hoc tests are essential to avoid making Type I errors when multiple comparisons are made. Some commonly used post hoc tests include Tukey’s Honestly Significant Difference test, the Bonferroni correction, and the Scheffe’s method, among others.

In conclusion, the independent t-test is used to compare the means of two independent groups, while the dependent t-test is utilized to compare the means of two related groups. Non-parametric tests, such as the Mann-Whitney U test and the Wilcoxon signed-rank test, are employed when the data violate the assumptions of parametric analysis. ANOVA is employed when there are three or more groups and the goal is to determine if there are significant differences among their means. Post hoc tests, such as Tukey’s Honestly Significant Difference, can be conducted to identify which groups differ from each other.