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Effect Size

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Eta squared (η²)

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Calculated by dividing the sum of squares between groups by the total sum of squares. It indicates the proportion of variance in the dependent variable associated with the independent variable.

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Partial Eta Squared (η²_partial)

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Similar to eta squared but it accounts for the variance explained by other variables in the model. It's the ratio of the variance explained by a specific factor to the variance of all the factors and error.

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Odds Ratio (OR)

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Calculated as the ratio of the odds of an event occurring in one group to the odds of it occurring in another group. Values greater than 1 indicate greater odds of the event in the first group.

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Cramer's V

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Calculated based on a chi-square statistic from a contingency table. Reflects the strength of association between two nominal variables and ranges from 0 to 1.

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Phi Coefficient

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A measure of association for two binary variables. Calculated similarly to Pearson's r but specifically for 2x2 contingency tables.

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Hedges' g

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Similar to Cohen's d but includes a correction factor for small sample sizes. It estimates the standardized mean difference between two groups.

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Glass's Δ

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Calculated as the difference between the experimental group mean and the control group mean, divided by the standard deviation of the control group. Used when control group variance is assumed to be more representative.

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Cohen's d

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Calculated as the difference between two means divided by the pooled standard deviation. Interpreted as small (~0.2), medium (~0.5), or large (~0.8) effect sizes.

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Point-Biserial Correlation Coefficient

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Used to measure the association between one dichotomous variable and one continuous variable. It's calculated similarly to Pearson's r.

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Pearson's r

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Calculated as the covariance of two variables divided by the product of their standard deviations. Values range from -1 to 1, indicating the strength and direction of a linear relationship.

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Cohen's f²

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Calculated as the ratio of the variance explained by the model to the variance not explained. Used to measure the effect size in the context of multiple regression.

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Cliff's Delta

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A non-parametric effect size measure that quantifies the probability that a randomly chosen value from one group will be larger than a randomly chosen value from another group minus the reverse probability.

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Vargha and Delaney's A

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A non-parametric effect size measure that tells how often values from one group are likely to be larger than values from another group, on average.

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Risk Ratio (RR)

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Calculated as the ratio of the probability of an event occurring in the exposed group to the probability in the unexposed group. Values above 1 indicate higher risk for the exposed group.

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Common Language Effect Size (CLES)

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Indicates the probability that a score picked at random from one distribution will be greater than a score picked from another distribution. Interprets the magnitude of the effect in a probabilistic context.

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