T-Test vs. Wilcoxon-Mann-Whitney Test

Two Independent Samples T-Test

• This test compares the means of a normally distributed interval dependent variable for two independent groups.
• The dependent variable should be normally distributed within each group.
• The two groups must be independent.
• The dependent variable must be measured at an interval or ratio scale.
• There must be homogeneity of variance, meaning equal variances in both groups.
• As an example, Math scores by gender or NAT results between two locations can be compared using this test.

Wilcoxon-Mann-Whitney Test

• This test is used when the dependent variable is not assumed to be normally distributed, but at least ordinal.
• This is a non-parametric alternative to the independent samples t-test
• The two groups must be independent of each other.
• The distributions of the two groups should have a similar shape - facilitates meaningful interpretation.
• It works for movie ratings between Hollywood and Bollywood, or cloth sizes between Asian and American populations.

One-Way ANOVA

• A one-way analysis of variance is suitable with a categorical independent variable that contains two or more categories.
• Requires a normally distributed interval dependent variable.
• Determines differences in the means of the dependent variable across levels of the independent variable.
• The dependent variable should be normally distributed within each group.
• The independent variable must consist of two or more categorical, independent groups.
• The dependent variable must be measured at an interval or ratio scale.
• Homogeneity of variance across groups is assumed, which can be checked using Levene’s test.
• Observations must be independent.
• An example is comparing science scores among student grade levels.

Kruskal-Wallis Test

• Useful if there is one independent variable with two or more levels and an ordinal dependent variable.
• It is a non-parametric version of ANOVA
• It is a generalized form of the Mann-Whitney test method, allowing for 2 or more groups.
• The dependent variable must be at least ordinal.
• The independent variable must consist of two or more independent groups.
• The distributions of the groups should have a similar shape for meaningful interpretation.

Paired T-Test

• A paired t-test is used with has two related observations (i.e. two observations per subject).
• Determines if the means on two normally distributed interval variables differ from one another.
• The dependent variable should be normally distributed.
• The observations must be dependent, i.e paired or matched.
• The dependent variable must be measured at an interval or ratio scale.
• Differences between paired observations should be normally distributed. Reading score before and after can be analysed using this test.

Wilcoxon Signed Rank Sum Test

• A non-parametric alternative to the paired samples t-test.
• Used when one does not wish to assume that the difference between the two variables is interval and normally distributed.
• It is assumed the difference is ordinal
• The dependent variable must be at least ordinal.
• The observations must be dependent, or paired or matched.
• The distribution of the differences should be symmetrical.
• This can be used to assess movie ratings before and after watching a movie

One-Way Repeated Measures ANOVA

• It requires one categorical independent variable.
• Requires a normally distributed interval dependent variable that is repeated at least twice for each subject.
• The equivalent of the paired samples t-test but allows for two or more levels of the categorical variable.
• It tests whether the mean of the dependent variable differs by the categorical variable.
• The dependent variable should be normally distributed within each group.
• The independent variable must consist of two or more categorical, related groups.
• The dependent variable must be measured at an interval or ratio scale.
• Sphericity applies, meaning the variance of differences between all pairs of groups should be equal.
• Used to compare NAT Scores during the year 2020-2023

Factorial ANOVA

• Factorial ANOVA contains two or more categorical independent variables (with or without interactions).
• It requires a single normally distributed interval dependent variable.
• The dependent variable should be normally distributed within each group.
• The independent variables must consist of two or more categorical variables.
• The dependent variable must be measured at an interval or ratio scale.
• Assumes Homogeneity of variance across groups.
• Observations must be independent.
• Example cases include analysing writing scores as a dependent variable with gender and socio-economic status as independent variables.

Chi-Square Test for Association

• Indicates whether there is a relationship between two categorical variables.
• The test assumes that the expected value of each cell is five or higher.
• The variables must be categorical.
• The observations must be independent.
• The expected frequency in each cell should be at least 5; if not, use Fisher's exact test.
• Used to assess relationships between gender and civil status or between school type and gender.

Fisher's Exact Test

• Suitable when conducting a chi-square test but one or more cells has an expected frequency of five or less.
• Fisher's exact test does not assume that each cell has an expected frequency of five or more.
• The variables must be categorical.
• The observations must be independent.
• It is used when the expected frequency in one or more cells is less than 5.

Correlation (Pearson's r)

• This measures the linear relationship between two or more normally distributed interval variables.
• The two variables should be normally distributed.
• The variables must be measured at an interval or ratio scale.
• The relationship between the variables must be linear.
• No significant outliers present in the data.
• This test can be used for reading score and writing score

Non-Parametric Correlation (Spearman Rho)

• This is used when one or both variables do not meet assumptions of normal distribution and interval data.
• values are ordinal
• The values of the variables are converted in ranks and then correlated.
• The variables are at least ordinal.
• The relationship between the variables is monotonic, either increasing or decreasing.
• It is used to compare movie ratings and monthly sales.

Simple Linear Regression

• This looks at the linear relationship between one normally distributed interval predictor and one normally distributed interval outcome variable.
• The dependent variable should be normally distributed.
• The predictor variable should be normally distributed.
• There is a linear relationship between the predictor and the dependent variable.
• Constant variance of residuals (homoscedasticity).
• Absence of significant outliers or influential data points.
• Looking at the relationship between writing and reading scores, predicting writing from reading can be assessed by this test.

Multiple Regression

• Similar to simple regression, but includes more than one predictor variable in the equation.
• The dependent variable should be normally distributed.
• The predictor variable should be normally distributed.
• There is a linear relationship between the predictor and the dependent variable.
• Homoscedasticity is assumed.
• No multicollinearity.
• No significant outliers or influential data points.
• Writing score can be predicated form reading, math, science, and social studies scores.