Psych Stat Correlational Analysis

Pearson’s R

Measures the strength and direction of the linear relationship between two continuous variables.

-1 to 1
-1
0
1

Range of Pearson’s R?

Spearman’s Rho

Measures the strength of a monotonic relationship (increasing or decreasing) between two ordinal or continuous variables.

Spearman’s Rho

Example: Checking the correlation between students’ ranks in math and physics exams.

Phi Coefficient

Measures the correlation between two binary (dichotomous) variables.

Phi Coefficient

Useful for analyzing 2×2 contingency tables.

-1 to 1

Range of Phi Coefficient?

Phi Coefficient

Determining correlation between gender (Male/Female) and preference for a product (Yes/No).

Tetrachoric Correlation

Estimates correlation between two dichotomous variables assumed to be normally distributed.

Tetrachoric Correlation

Only applicable to artificially dichotomized variables.

Tetrachoric Correlation

Converting continuous height (tall/short) and weight (heavy/light) into binary variables and estimating correlation.

Cramer’s V

Measures association between two categorical variables.

0 (no association) to 1 (strong association)

Cramer’s V Range?

Cramer’s V

Checking association between different movie genres and favorite actors.

Theta Coefficient

Measures association between two categorical variables like Cramer’s V but is less common.

Goodman-Kruskal’s Gamma Coefficient

Measures the strength of association between ordinal variables. (Ordinal with many ties)

-1 (strong negative association) to 1 (strong positive association)

Range of Goodman-Kruskal Gamma Coefficient?

Goodman-Kruskal’s Gamma Coefficient

Analyzing relationship between education level and job satisfaction.

Somer’s D

Measures ordinal association similar to Gamma but accounts for tied ranks.

Somer’s D

Comparing rankings of candidates by multiple judges.

Natural

Point Biserial Correlation has ______ Dichotomous??

Point-Biserial Correlation

Measures association between one binary variable and one continuous variable.

Point Biserial Correlation

Relationship between gender (binary) and test scores (continuous).

Biserial Correlation

imilar to Point-Biserial Correlation, but assumes the binary variable is artificially dichotomized.

Kendall’s Tau

Similar to Spearman’s Rho but less sensitive to outliers.

Kendall’s Tau

Measures ordinal association between two variables, robust to ties.

Linear Correlation

Correlation use of Pearson R?

Monotonic Correlation

Correlation use of Spearman’s Rho?

Binary Correlation

Correlation use of Phi Coefficient?

Latent Normal Variables

Correlation use of Tetrachoric?

Categorical Association

Correlation use of Cramer’s V?

Categorical Association

Correlation Use of Theta Coefficient?

Ordinal Association

Correlation use of Goodman-Kruskal’s Gamma?

Ordinal Association

Correlation use of Somers’ D

Binary-Continuous Correlation (Naturally Dichotomized)

Correlation use of Point Biserial?

Artificially Dichotomize

Correlation use of Biserial?

Rank Correlation

Correlation use of Kendall’s Tau

Continuous-Continuous

Variables of Pearson R?

Continuous-Continuous/Ordinal

Variables of Spearman’s Rho?

Binary-Binary

Phi Coefficient variable?

Binary-Binary (Artificial)

Tetrachoric variable?

Categorical - Categorical

Cramaer’s V Variable?

Categorical - Categorical

Theta Coefficient

Ordinal - Ordinal

Goodman-Kruskal’s Gamma Variable?

Ordinal - Ordinal

Somers’ D Variable?

Binary - Continuous

Point Biserial variable?

Ordinal-Ordinal

Kendall’s Tau Variable?

Perfect Correlation

Correlation : ± 1.0

Correlation : ± 1.0

Perfect Correlation?

Correlation : ± 0.91 - ±0.99

Very High Correlation

Very High Correlation

Correlation : ± 0.91 - ±0.99

Correlation : ± 0.71 - ± 0.90

High Correlation

High Correlation

Correlation : ± 0.71 - ± 0.90

Moderate Correlation

± 0.51 - ± 0.70

± 0.51 - ± 0.70

Moderate Correlation

Low Correlation

±0.31 - ±0.50

±0.31 - ±0.50

Low Correlation

Negligible Correlation

±0.01 - ±0.30

±0.01 - ±0.30

Negligible Correlation

±0.00

No Correlation