Module 13 assignment part 3 discussion forum. This assignment is to be completed on your own. It is not a team assignment. 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 difference between an independent t-test and a dependent t-test lies in the type of data being analyzed. An independent t-test is used when comparing the means of two independent groups, whereas a dependent t-test is used when comparing the means of paired or related samples. In other words, an independent t-test compares two separate groups of participants or subjects, while a dependent t-test compares the same participants or subjects under different conditions or at different time points.
The independent t-test assumes that the two groups being compared are independent of each other, meaning that the values in one group do not depend on or influence the values in the other group. In contrast, the dependent t-test assumes that the two sets of measurements are related or paired in some way.
To illustrate this distinction, let’s consider a study comparing the effectiveness of two different teaching methods on student performance. In an independent t-test, we would have two separate groups of students, with one group taught using Method A and the other group taught using Method B. The independent t-test would then compare the means of the two groups to determine if there is a statistically significant difference in student performance between the two methods.
On the other hand, in a dependent t-test, we would have a single group of students who are taught using both Method A and Method B. Each student’s performance would be measured under both methods, and the dependent t-test would compare the mean differences in student performance between the two methods.
In cases where the data does not meet the assumptions of parametric analysis, non-parametric statistical analyses can be used. Non-parametric tests do not require the same assumptions about the underlying distribution of the data as parametric tests do. They are often used when the data is categorical, ordinal, or does not meet the assumptions of normality or homogeneity of variance.
Some common non-parametric tests include the Mann-Whitney U test, also known as the Wilcoxon rank-sum test, which is the non-parametric equivalent of the independent t-test. This test is used to compare the medians of two independent groups.
Another commonly used non-parametric test is the Wilcoxon signed-rank test, which is the non-parametric equivalent of the dependent t-test. This test is used to compare the medians of paired or related samples.
In cases where there are more than two groups being compared, or when there are multiple independent variables being considered, analysis of variance (ANOVA) is typically used. ANOVA compares the means of two or more groups to determine if there are significant differences among them.
When ANOVA indicates that there are significant differences among the groups, post-hoc tests can be conducted to identify which specific groups differ from each other. One commonly used post-hoc test is the Tukey’s honestly significant difference (HSD) test, which compares all pairwise differences between groups.
If it is not possible to identify where the differences occur in groups, a more exploratory statistical procedure, such as cluster analysis or principal component analysis, can be applied. These techniques are used to uncover patterns or relationships within the data, without making specific hypotheses about group differences.