IPR Term 2 Week 8 - Bringing it all together: types of tests

• Inferential statistics tests are consolidated to understand the key differences between them
• Key assumptions for each test must be understood to determine when to use parametric vs non-parametric versions
• Experiencing and interpreting tests using JASP software.

Tests Covered

• Chi-square: Includes the Goodness of Fit test and the Test of Association (both non-parametric)
• Correlation: Includes Pearson’s (parametric) and Spearman’s (non-parametric) tests
• T-tests: Includes One samples, Paired samples, Wilcoxon-signed rank, Independent samples, and Mann-Whitney U tests

Measurement Levels of Data

• Nominal Data: Frequency/count and the mode are measured, non-parametric tests are used, e.g., Chi-square test

• Ordinal Data: Frequency/Count, mode or median are measured, non-parametric tests are used, e.g., Mann-Whitney U or Wilcoxon signed-rank test

• Interval Data: Mean, median, mode, and standard deviation are measured, parametric and non-parametric tests are used, e.g., t-tests, correlation, ANOVA

• Ratio Data: Mean, median, mode, and standard deviation are measured, parametric and non-parametric tests are used, e.g., T-tests, correlation, ANOVA

Types of Research Designs

• Experimental Design (Quantitative): Variables are manipulated and controlled to find cause and effect, e.g., T-tests, chi-square tests

• Longitudinal Design (Quantitative): Measuring repeatedly over time to examine health outcomes, e.g., T-tests

• Correlational Design (Quantitative): Establishes relation between variables with no causality; without manipulation, e.g., Correlation

• Descriptive Methods (Quantitative): Studies behavior or experience using self-reporting, surveys, and questionnaires, e.g., Chi-square, correlation

Chi-Square Tests

• Purpose: To test if nominal (categorical) data aligns with expected frequencies; experimental (manipulate variables) or non-experimental and non-parametric data

• Goodness of Fit Test: Data is compared to an expected/predicted sample or distribution with one variable

• Test of Association (or Test of Independence): Determine whether two variables are independent from each other

Chi-Square Tests Assumptions:

• Data type: nominal/categorical
• Mutual exclusive variables or categories
• Independent observations (data points)
• Random Sampling
• Expected frequencies should be 5 or more
• Assumptions Violated: Results can lead to inaccurate results
• Note it, Transform data/combine categories
• Large sample size
• Alternative Fisher’s Exact Test

Correlation Tests

• Purpose: Assess the relationship between two variables; no variable manipulation (no IV or DV); parametric and non-parametric versions are used

• Pearson's: Interval or ratio using parametric version

• Spearman's: Interval, ratio, or ordinal using non-parametric version

Correlation Test Assumptions:

• Data type: interval or ratio (continuous)

• Normality (and no/minimal outliers)

• Linearity (relationship follows a straight line)

• Homoscedasticity (equal variance)

• Use Spearman’s if assumptions are violated:

• Violate Linearity: Use Spearman’s

• Linearity Violations: Pearson’s can be used if approx. normal and minimal outliers

• Large sample size, if violated

T-Tests

• Purpose: Compare the means of two groups/conditions if there is a significant difference; parametric and non-parametric versions are used

• One-Sample T-Test: Compares a single sample mean to a known population mean using Interval or ratio data

• Paired Samples T-Test: Compares the means of two related/matched groups (same participants) using interval or ratio data

• Independent Samples T-Test: Compares the means of two independent groups (different participants) with interval or ratio data

• Wilcoxon Signed-Rank Test: Non-parametric version that compares single sample value to a known population using ordinal, interval, or ratio data

• Mann-Whitney U Test: Non-parametric version of the Independent Samples T-Test comparisons on differences (ranks) between two independent groups using ordinal, interval, or ratio data

T-Tests Assumptions:

• Data type: interval or ratio (DV)

• Normality (and no/minimal outliers)

• Homoscedasticity (equal variance)

• Independent observations

• Use non-parametric equivalents if assumptions are violated (especially if independent observations are violated)

• Parametric tests still available if there is a large sample ( >30 per group), approx. normal results, and homogeneity of variance (Welch's t-test)