Support your answers with the literature and provide citations and references(2016-2021) in APA format. Answer 1-What do you consider to be the difference between independent t-test and dependent t-test? 2-What non-parametric statistical analysis can you use if the data do not meet the assumptions of parametric analysis. 3-When do you use ANOVA? 4-If you cannot identify where the differences occur in groups, What statistical procedure can you apply?
1. The independent t-test and dependent t-test are two statistical tests used to analyze different types of data and make inferences about population means. The main difference between these tests lies in the nature of the data being analyzed.
The independent t-test is used when comparing the means of two independent groups in a study. It assumes that the two groups being compared are unrelated and that the observations in each group are independent of each other. For example, it could be used to compare the mean scores of two different treatment groups in a clinical trial or to compare the mean scores of males and females on a certain variable.
In contrast, the dependent t-test (also known as the paired t-test) is used when comparing the means of two related groups or when analyzing repeated measures data. It assumes that the observations in each group are paired or matched in some way, such as when each individual is measured before and after a treatment. For example, it could be used to compare the mean scores of participants before and after an intervention or to compare the mean scores of a group of twins on a certain variable.
The choice between the independent t-test and dependent t-test depends on the study design and the nature of the data being analyzed. If the groups being compared are independent and the observations are not paired or related in any way, the independent t-test is appropriate. On the other hand, if the groups being compared are related or if the observations are paired in some way, the dependent t-test should be used.
2. When the data do not meet the assumptions of parametric analysis, non-parametric statistical tests can be used as alternative methods. Non-parametric tests are distribution-free and make fewer assumptions about the underlying distribution of the data. They are robust to violations of assumptions such as normality and equal variances.
One commonly used non-parametric test is the Mann-Whitney U test, which is an alternative to the independent t-test. It compares the medians of two independent groups instead of their means. The Mann-Whitney U test is used when the data are ordinal or when the assumptions of the independent t-test are violated.
Another non-parametric test, the Wilcoxon signed-rank test, is an alternative to the dependent t-test. It compares the medians of paired or related groups instead of their means. The Wilcoxon signed-rank test is used when the data are ordinal or when the assumptions of the dependent t-test are violated.
Other non-parametric tests include the Kruskal-Wallis test (an alternative to one-way ANOVA), the Friedman test (an alternative to repeated measures ANOVA), and the Spearman’s rank correlation coefficient (an alternative to Pearson’s correlation coefficient).
The choice of non-parametric test depends on the study design and the specific research question being addressed. It is important to select the appropriate non-parametric test based on the characteristics of the data and the assumptions being violated.
3. ANOVA (Analysis of Variance) is a statistical test used to analyze the differences between three or more groups. It compares the means of multiple groups to determine if they are significantly different from each other. ANOVA is used when the dependent variable is continuous and the independent variable has three or more categories or levels.
ANOVA partition the total variance in the observed data into two components: the variance between groups and the variance within groups. If the variance between groups is significantly larger than the variance within groups, it provides evidence that there are systematic differences between the groups.
ANOVA can be applied in different scenarios, such as comparing the means of different treatment groups in a clinical trial, assessing the effect of different levels of a factor on an outcome variable, or examining group differences in experimental or observational studies.
4. If the differences between groups cannot be identified, statistical procedures such as post hoc tests, pairwise comparisons, or multiple comparisons can be applied to further investigate where the differences occur. These tests are used to compare specific group means after obtaining a significant result in the initial analysis (e.g., ANOVA or t-test).
Post hoc tests are used to analyze all possible pairwise comparisons among the groups. Common post hoc tests include the Tukey’s Honestly Significant Difference (HSD) test, the Bonferroni correction, and the Scheffe’s method. These tests control the overall Type I error rate when multiple comparisons are made.
Pairwise comparisons involve comparing specific pairs of groups to identify the differences between them. These comparisons are typically conducted using t-tests or non-parametric tests, depending on the nature of the data.
Multiple comparisons refer to procedures that involve comparing more than two groups or comparing multiple pairs of groups simultaneously. Examples of multiple comparison procedures include the Dunnett’s test, the Dunnett’s T3 test, and the Games-Howell test.
The choice of the appropriate statistical procedure depends on the specific research question, the study design, and the nature of the data being analyzed. It is important to select a method that is suitable for the research context and that takes into account the assumptions and requirements of the analysis.