Podcast
Questions and Answers
Which test is recommended for checking equal variances in t-test and ANOVA?
Which test is recommended for checking equal variances in t-test and ANOVA?
- Kolmogorov-Smirnov Test
- Levene’s Test (correct)
- Q-Q Plot
- Shapiro-Wilk Test
What does a boxplot indicate when no dots are present?
What does a boxplot indicate when no dots are present?
- There are no outliers present. (correct)
- The data follows a uniform distribution.
- There are significant outliers present.
- The data is normally distributed.
What characterizes heteroscedasticity in correlation data?
What characterizes heteroscedasticity in correlation data?
- The data points 'fan out' across the graph. (correct)
- The data points are all clustered closely together.
- The data points show a consistent spread.
- The data points maintain a linear relationship.
Which method is primarily used to visually check for outliers in correlation data?
Which method is primarily used to visually check for outliers in correlation data?
When using the Shapiro-Wilk Test, what does a p-value less than .05 imply?
When using the Shapiro-Wilk Test, what does a p-value less than .05 imply?
In the context of the Kolmogorov-Smirnov Test, what does a sample size of n ≥ 50 indicate?
In the context of the Kolmogorov-Smirnov Test, what does a sample size of n ≥ 50 indicate?
What is an indication of no significant outliers in the context of a scatterplot?
What is an indication of no significant outliers in the context of a scatterplot?
Which plot helps to visually assess if a dataset follows a normal distribution in large samples?
Which plot helps to visually assess if a dataset follows a normal distribution in large samples?
Which assumption must be checked before using One-Way ANOVA?
Which assumption must be checked before using One-Way ANOVA?
What should be used if the assumptions of the t-Test for Independent Samples are violated?
What should be used if the assumptions of the t-Test for Independent Samples are violated?
What is a requirement for using Tukey’s HSD test?
What is a requirement for using Tukey’s HSD test?
Which test is appropriate when there is a significant variability in group variances?
Which test is appropriate when there is a significant variability in group variances?
When using the Kruskal-Wallis H Test for nonparametric data, what should follow if significant differences are found?
When using the Kruskal-Wallis H Test for nonparametric data, what should follow if significant differences are found?
What is NOT an assumption for the t-Test for Independent Samples?
What is NOT an assumption for the t-Test for Independent Samples?
If the assumptions of One-Way ANOVA are met except for homogeneity of variance, which approach is recommended?
If the assumptions of One-Way ANOVA are met except for homogeneity of variance, which approach is recommended?
Which test is the nonparametric counterpart of the paired t-Test?
Which test is the nonparametric counterpart of the paired t-Test?
Which test is more robust when the assumptions of correlation are violated?
Which test is more robust when the assumptions of correlation are violated?
What is a prerequisite for conducting the Chi-Square Test for Goodness of Fit?
What is a prerequisite for conducting the Chi-Square Test for Goodness of Fit?
Which of the following assumptions must be met when conducting a Pearson’s r correlation?
Which of the following assumptions must be met when conducting a Pearson’s r correlation?
Which of the following is NOT an assumption of the Chi-Square Test for Independence?
Which of the following is NOT an assumption of the Chi-Square Test for Independence?
What does the term 'homoscedasticity' refer to in correlation analysis?
What does the term 'homoscedasticity' refer to in correlation analysis?
What is the primary focus of a Two-Way ANOVA?
What is the primary focus of a Two-Way ANOVA?
In the context of ANOVA, what does ANCOVA control for?
In the context of ANOVA, what does ANCOVA control for?
What must be ensured when using multiple dependent variables in MANCOVA?
What must be ensured when using multiple dependent variables in MANCOVA?
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Study Notes
Assumptions Checks Overview
- Assumptions checks determine the appropriateness of hypothesis-testing procedures for data.
- Conduct various methods to assess assumptions and identify violations.
Normality Assumption
- Shapiro-Wilk Test: Ideal for n < 50; assesses normality.
- p-value < .05 indicates non-normality.
- p-value ≥ .05 indicates normality.
- Kolmogorov-Smirnov Test: Suitable for n ≥ 50; similar decision criteria as Shapiro-Wilk.
- Histogram: Use for large sample sizes (e.g., n = 300); visually assess normality.
- Q-Q Plot: Complement histogram for large samples; normal distribution indicated if dots align along the straight line.
No Significant Outliers Assumption
- Boxplot: Identifies outliers.
- Absence of dots indicates no outliers.
- Presence of dots indicates outliers.
- Scatterplot: For correlation, visually check for data points deviating from the pattern indicating significant outliers.
Equal Variances Assumption
- Homogeneity of Variance: Critical for t-tests and ANOVA.
- Levene’s Test: p < .05 indicates unequal variance; p ≥ .05 indicates equal variance.
- Homoscedasticity: Assessed with scatterplot for correlation; data should “fan out” evenly.
Tests for Differences
- Wilcoxon-Signed Rank Test: Nonparametric alternative to Paired t-Test when assumptions are violated.
- t-Test for Independent Samples: Compares two datasets from different groups.
- Assumptions include continuous dependent variable, two categorical groups, independent observations, normal distribution, no outliers, and homogeneity of variance.
- Mann-Whitney U Test: Nonparametric alternative if assumptions are violated.
One-Way ANOVA
- Used for comparing three or more groups.
- Assumptions involve continuous dependent variables, independent categorical groups, independent observations, no significant outliers, normal distribution across groups, and homogeneity of variances.
- If assumptions are met, use Student’s ANOVA.
- Post hoc comparisons for significant ANOVA results:
- Tukey’s HSD for equal sample sizes.
- Tukey-Kramer for unequal sample sizes.
- Scheffé test for unequal sample sizes.
- To address violation of homogeneity of variance, use Welch’s ANOVA and Games-Howell post hoc test.
- Kruskal-Wallis H Test: Used when assumptions are violated, followed by Dunn’s test or Bonferroni Procedure for post hoc testing.
Variations of ANOVA
- Repeated-Measures ANOVA: Analyzes three or more scores from the same respondents.
- Two-Way ANOVA: Assesses effects of two factors (e.g., coffee and music on memory).
- ANCOVA: ANOVA controlling for other influencing variables.
- MANOVA: Simultaneous ANOVA for multiple dependent variables.
- MANCOVA: Like ANCOVA but for multiple dependent variables.
Pearson’s r Correlation
- Examines the relationship between two continuous variables.
- Assumptions include both variables being continuous, paired observations, independence, linear relationship, bivariate normal distribution, no outliers, and homoscedasticity.
- If assumptions are violated, use Kendall’s tau-B or Spearman’s rho for correlation analysis.
Chi-Square Tests
- Chi-Square Test for Goodness of Fit: Determines if actual proportions align with expected proportions (e.g., gender representation in crime statistics).
- Assumptions include one categorical variable, independence of observations, mutually exclusive groups, and at least 5 expected frequencies per group.
- Chi-Square Test for Independence: Assesses whether categories are related (e.g., color preference and personality traits).
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