29 Questions
What does a correlation coefficient of -1.00 indicate?
Perfect negative correlation
Which test does not rely on the normality assumption?
Nonparametric tests
What does the Spearman Rank Correlation assess?
Independence of variables
In regression, what is the coefficient of determination (r^2) used for?
Explaining the percentage of variance explained by the independent variable
What is a core assumption for Simple Linear Regression?
Homogeneity of variances
When two variables move in opposite directions, this is known as:
Perfect negative correlation
Which statement about nonparametric tests is true?
They are less powerful than parametric tests
What type of data is suitable for the Mann-Whitney U test?
Ordinal
In what situation would you use the Wilcoxon Signed-Rank Test?
Evaluating ranks for paired measurements
When conducting the Kruskal-Wallis test, how many groups are being compared?
3 groups
What is a key assumption for the Chi-Square test?
Independent and categorical data
Under what condition should Fisher's Exact test be used?
When more than 20% of cells have expected counts less than 5 in the Chi-Square test
Which test is suitable for comparing medians between two independent groups?
Mann-Whitney U test
What assumption is common between the Kruskal-Wallis and Mann-Whitney U tests?
Random samples
Which correlation coefficient indicates the weakest relationship between two variables?
0.25
What is the primary difference between Pearson and Spearman correlation coefficients?
Pearson requires normality and interval/ratio data, while Spearman does not.
Which of the following indicates the percentage of variance in the dependent variable that can be explained by the independent variable?
Coefficient of determination (r^2)
What is a disadvantage of nonparametric tests compared to parametric tests?
Nonparametric tests are less powerful.
Which of the following best describes the difference between correlation and regression?
Correlation examines the relationship between variables, while regression uses the relationship for prediction.
Under which condition would simple linear regression be appropriate for analyzing a dataset?
When variables are interval/ratio level data, independent, and linearly correlated.
Which of the following is an assumption of both Pearson and Spearman correlation coefficients?
Independence
What is a key difference between the Mann-Whitney U test and the Wilcoxon Signed-Rank Test?
The Wilcoxon Signed-Rank Test evaluates ranks for differences in measurements while the Mann-Whitney U test evaluates medians.
What distinguishes Kruskal-Wallis test from Mann-Whitney U test?
Mann-Whitney U test evaluates differences between two groups while Kruskal-Wallis test compares three or more groups.
Which assumption is unique to the Chi-Square test compared to other nonparametric tests?
Chi-Square needs expected counts to be greater than 1 and no more than 20% of cells less than 5.
When would you use Fisher's Exact test instead of the Chi-Square test?
When expected counts are not met for Chi-Square assumptions.
What distinguishes the Wilcoxon Signed-Rank Test from the Mann-Whitney U test in terms of data requirements?
Wilcoxon Signed-Rank Test requires ordinal/interval/ratio data while Mann-Whitney U does not have this requirement.
What assumption differentiates the Kruskal-Wallis test from the Chi-Square test?
Kruskal-Wallis requires ordinal/interval/ratio level data, unlike Chi-Square.
What makes Fisher's Exact test unique compared to other nonparametric tests?
Fisher's Exact test can be used with very small sample sizes where Chi-Square assumptions are violated.
What distinguishes the Wilcoxon Signed-Rank Test from the Kruskal-Wallis test in terms of their application?
Wilcoxon Signed-Rank Test compares ranks within a group, while Kruskal-Wallis compares ranks between groups.
Study Notes
Correlation
- Evaluates the relationship between variables and direction of relationship
- Positively related: both move in the same direction
- Negatively related: move in opposite directions
- Correlation does not equal causation
- Correlation Coefficient: describes the strength and direction of a relationship, ranges from -1.00 to +1.00
- -1.00 = perfect negative correlation
- +1.00 = perfect positive correlation
Pearson Correlation Coefficient
- Assumptions: independence, normality, variables are interval/ratio level data
Spearman Rank Correlation
- Assumptions: independence
Regression
- Uses the relationship between variables as a basis for prediction
- Takes correlation a step further
- Simple Linear Regression: examines two variables that are linearly correlated
- Simple Linear Regression assumptions: normality, homogeneity of variances (Levene's test), and dependent variable is interval/ratio level data
- Regression Line formula: Y = a + bX
- Y = dependent variable
- a and b = constants
- X = independent variable
- r = correlation coefficient
- r2 = coefficient of determination (percentage of the variance in the dependent variable that can be explained by the independent variable)
Nonparametric Tests
- Do not rely on probability distribution (normality assumption)
- Do not have homogeneity of variances
- Can be used to examine nominal or ordinal level data
- Less powerful than parametric tests
Mann-Whitney U Test
- Evaluates whether medians differ significantly between two groups
- Assumptions: random samples, independence, and dependent variable is ordinal/interval/ratio level
Wilcoxon Signed-Rank Test
- Evaluates ranks for the difference between the measurements (use a before and after score and subtract to find rank)
- Cannot be used with ordinal data
- Assumptions: random samples and dependent variable is interval/ratio level
Kruskal-Wallis Test
- Evaluates whether medians differ significantly between 3+ groups
- Assumptions: random samples, independence, and dependent variable is ordinal/interval/ratio level data
Chi-Square Test
- Evaluates expected frequencies and observed frequencies of categorical (ordinal and nominal) data
- Assumptions: independence, expected counts are greater than 1 and no more than 20% of cells are less than 5
Fisher's Exact Test
- Used if Chi-Square assumptions are not met
Test your knowledge on correlation, correlation coefficient, and the evaluation of relationships between variables. Understand the concepts of positive and negative correlation, and learn that correlation does not imply causation.
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