[MMW] Parametric Tests & Nonparametric Tests definitions and purpose

Z-test for one sample mean

• Definition: Tests if the sample mean differs from a known population mean when variance is known. In short, it checks if the sample average is close to or far from the population average.

Z-test for one sample mean

• Purpose: For large samples, to check differences from population mean.

• Example: Testing if the average height of 200 students differs

T-test for one sample mean

• Definition: Same as Z-test, but used when variance is unknown and sample is small. It is used when we only have a small group and don’t know the population’s spread.

T-test for one sample mean

• Purpose: Compares sample mean with a known/hypothesized mean.

• Example: Checking if the mean exam score of 20 students differs from a passing score of 75.

Paired t-test

• Definition: Compares means of the same group at two different times. It checks if the “before” and “after” results of the same people are different.

Paired t-test

• Purpose: Tests for significant change in related samples.

• Example: Measuring blood pressure before and after taking a new drug on the same patients.

Independent t-test

• Definition: Compares means of two independent groups. It checks if two separate groups are significantly different.

Independent t-test

• Purpose: Determines if two groups differ significantly.

• Example: Comparing test scores of male vs. female students.

Pearson product moment correlation coefficient (Pearson’s r)

• Definition: Measures strength and direction of linear relationship between two continuous variables. It shows how strongly two things are related.

Pearson product moment correlation coefficient (Pearson’s r)

• Purpose: To assess correlation.

• Example: Studying the relationship between study hours and exam scores.

Analysis of Variance (ANOVA)

• Definition: Compares means of three or more groups. It checks if at least one group is different from the others.

Analysis of Variance (ANOVA)

• Purpose: Tests whether at least one group mean differs.

• Example: Comparing the average yields of three different fertilizer treatments.

Linear regression

• Definition: Models relationship between dependent and independent variable(s). It is used to predict one value based on another.

Linear regression

• Purpose: To predict or explain variations.

• Example: Predicting house prices based on lot size.

Chi-square test

• Definition: Tests association between categorical variables. It checks if two categories are related or independent.

Chi-square test

• Purpose: Compares observed vs. expected frequencies.

• Example: Testing if gender is related to voting preference.

Spearman rank correlation

• Definition: Measures strength and direction of monotonic relationship using ranks. It shows if two sets of ranks move in the same or opposite way.

Spearman rank correlation

• Purpose: To check correlation when data are ordinal or not normally distributed.

• Example: Relationship between class rank and extracurricular involvement.

Wilcoxon sign-rank test

• Definition: Nonparametric alternative to paired t-test. It checks before-and-after changes without needing normal data.

Wilcoxon sign-rank test

• Purpose: Compares two related samples without assuming normality.

• Example: Comparing pain levels before and after therapy in the same patients.

Sign test

• Definition: Uses signs (+/–) of differences between pairs instead of magnitudes. It only counts whether changes are positive or negative.

Sign test

• Purpose: Tests if median difference is zero.

• Example: Testing if a new teaching method leads to higher or lower scores compared to old method, using paired student results.