Module_3_Flashcards_ANOVA_Non_Parametric_Tests
What is ANOVA?
ANOVA (Analysis of Variance) is a statistical test used to compare the means of three or more groups.
Why is ANOVA used instead of multiple t-tests?
ANOVA controls for Type I error that increases when performing multiple t-tests.
When is a one-way independent-measures ANOVA used?
It is used when comparing the means of three or more independent groups on one factor.
What are the assumptions of ANOVA?
ANOVA assumes normality, homogeneity of variances, and independent observations.
What does the F-ratio represent in ANOVA?
The F-ratio compares between-group variance to within-group variance. A higher F-ratio suggests significant differences between groups.
What does a significant p-value (<0.05) in ANOVA mean?
A significant p-value means there is a statistically significant difference between at least two group means.
What is the effect size in ANOVA and why is it important?
Effect size (e.g., η²) shows the magnitude of the difference between groups. It is important to interpret practical significance, not just statistical significance.
How do you handle violations of homogeneity of variance in ANOVA?
If the assumption of homogeneity is violated, you can use a Welch ANOVA or transform the data.
What are post-hoc tests?
Post-hoc tests are conducted after a significant ANOVA to determine which specific group means are different.
Why are post-hoc tests necessary after ANOVA?
Post-hoc tests control for Type I error when making multiple comparisons between group means.
Give an example of a post-hoc test.
Examples include Tukey’s HSD, Bonferroni correction, and Scheffé test.
How do you interpret post-hoc test results?
Look for pairwise comparisons with p-values less than 0.05 to identify which groups differ significantly.
What are planned comparisons in ANOVA?
Planned comparisons test specific hypotheses developed before data collection about group differences.
When would you use planned comparisons?
Use them when you have specific predictions about the differences between certain group means.
How are contrast weights used in planned comparisons?
Contrast weights assign values to group means based on hypothesized relationships, focusing the comparison on specific groups.
How do you interpret planned comparisons?
Interpret planned comparisons by looking at the contrast weights, F-ratio, p-value, and effect size.
What is trend analysis in ANOVA?
Trend analysis examines patterns of change (e.g., linear or quadratic trends) across levels of the independent variable.
Why would a researcher perform a trend analysis?
Trend analysis helps identify systematic increases or decreases in the dependent variable across different groups.
When is trend analysis appropriate?
It is appropriate when you expect a specific pattern or trend across ordered levels of a variable (e.g., time, dosage).
How do you interpret trend analysis results?
You interpret significant trends by looking for systematic patterns in the data (e.g., a linear or quadratic trend).
What is the Mann-Whitney U test?
The Mann-Whitney U test is a non-parametric test used to compare two independent groups when the data are not normally distributed.
When should the Mann-Whitney U test be used?
It should be used when data are ordinal or not normally distributed and the assumptions of the independent t-test are violated.
How do you interpret the results of a Mann-Whitney U test?
If the p-value is less than 0.05, there is a significant difference in the ranks of the two groups.
What is the Wilcoxon Signed-Ranks test?
The Wilcoxon Signed-Ranks test is a non-parametric test used to compare two related groups (e.g., pre-test vs post-test) when data are not normally distributed.
When should the Wilcoxon Signed-Ranks test be used?
It should be used when comparing two related groups and the assumptions of the paired-samples t-test are violated.
How do you interpret the results of the Wilcoxon Signed-Ranks test?
A significant p-value (<0.05) indicates a significant difference between the two paired samples.
What is the Kruskal-Wallis test?
The Kruskal-Wallis test is a non-parametric test used to compare three or more independent groups when the assumptions of ANOVA are violated.
When should the Kruskal-Wallis test be used?
It should be used when comparing three or more independent groups with ordinal or non-normally distributed data.
How do you interpret the Kruskal-Wallis test results?
A significant p-value (<0.05) means that at least one group differs from the others. Post-hoc tests can then be performed.
What are confidence intervals, and why are they important?
Confidence intervals provide a range of values within which the true population parameter is likely to fall. They show the precision of an estimate.
How do sample size and confidence intervals relate?
Larger sample sizes lead to narrower confidence intervals, indicating more precise estimates of the population parameter.
What is statistical power, and why is it important?
Statistical power is the probability of detecting a true effect. High power reduces the likelihood of a Type II error.
How can researchers increase statistical power?
Researchers can increase power by increasing sample size, using stronger manipulations, or setting a higher alpha level.
What is the relationship between sample size and statistical power?
Larger sample sizes increase statistical power, making it more likely to detect a significant effect if it exists.
