Table 5.
The most commonly used coefficients for effect size, based on publications.
| Coefficients | Small | Medium | Large | What is/When to Use | |
|---|---|---|---|---|---|
| Cliff’s δ | 0.15 | 0.33 | 0.47 | It is a measure that compares two groups in the case of ordinal or ranked variables. It is used to assess the difference in distribution between two groups, but unlike many other effect measures, it is more robust to sample imbalance, data skewness and non-linear relationships. | |
| Cohen’s d | 0.20 | 0.50 | 0.80 | This measure works best for comparisons between two groups, for example, an experimental group and a control group (comparison of two groups or differences between averages). | |
| Cohen’s d | 0.15 | 0.40 | 0.75 | Brydges’ recommendation in gerontology [220]. | |
| Cohen’s d | 0.25 | 0.55 | 0.95 | Gaeta and Brydges’ recommendation in audiology and speech-language pathology [221]. | |
| Cohen’s d | 0.15 | 0.36 | 0.65 | Lovakov and Agadullina’s recommendation in social psychology and sub-disciplines within social psychology [222]. | |
| Cohen’s g | 0.05 | 0.15 | 0.25 | Cohen’s g is a less common variant of Cohen’s d and is used to measure the difference between 2 groups (for example in McNemar’s test). | |
| Cohen’s f | 0.10 | 0.25 | 0.40 | It is used when there is a comparative analysis of more than two groups. | |
| Cohen’s ω | 0.10 | 0.30 | 0.50 | Cohen’s ω is used in regression analyses, particularly for linear regression, to measure how strongly factors are related. | |
| Cramér’s V and phi (φ) |
df |
Cramér’s V—it is used to assess the strength of the relationship between 2 or more categorical factors in tables of different sizes, allowing comparison across different contingency table sizes. It s a more general measure applicable to tables of different dimensions (different numbers of rows and columns). phi (φ)—specifically used for 2 × 2 contingency tables, ϕ measures the strength of the connection between categorical variables in contingency tables. It focuses on tables of a fixed size, making it suitable for more specific contexts like two-factor analysis in medical studies or qualitative research. |
|||
| 0.1 | 0.3 | 0.5 | 1 | ||
| 0.07 | 0.21 | 0.35 | 2 | ||
| 0.06 | 0.17 | 0.29 | 3 | ||
| 0.05 | 0.15 | 0.25 | 4 | ||
| 0.04 | 0.13 | 0.22 | 5 | ||
| Glass’s | 0.20 | 0.50 | 0.80 | It is used in the context of experimental analysis, where one group is treated as the control group and the other as the experimental group. | |
| Hedges’ g | 0.20 | 0.50 | 0.80 | This coefficient is a measure of ES similar to Cohen’s d, but with a correction for SS. Used for intergroup analyses with small samples. | |
| Hedges’ g | 0.15 | 0.40 | 0.75 | Brydges recommendation in gerontology [220]. | |
| Hedges’ g | 0.25 | 0.55 | 0.95 | Gaeta and Brydges’ recommendation in audiology and speech-language pathology [221]. | |
| Pearson’s r | 0.10 | 0.30 | 0.50 | It is used to measure the strength and direction of a relationship between 2 continuous factors. It is employed to quantify the intensity and orientation of a connection between 2 continuous variables. | |
| Pearson’s r | 0.10 | 0.20 | 0.30 | Brydges’ recommendation in gerontology [220]. | |
| Pearson’s r | 0.25 | 0.40 | 0.65 | Gaeta and Brydges’ recommendation in audiology and speech-language pathology [221]. | |
| Pearson’s r | 0.12 | 0.24 | 0.41 | Lovakov and Agadullina’s recommendation in social psychology and related disciplines [222]. | |
| Pearson’s r | 0.10 | 0.20 | 0.30 | Gignac and Szodorai’s recommendation [223]. | |
| Odds Ratio | 1.44 | 2.48 | 4.27 | Odds ratio is a measure used in statistics, especially in epidemiology and other areas of medical research, to determine the strength of the relationship between 2 variables, usually in the context of a case–control study. | |
| Odds Ratio | 1.68 | 3.47 | 6.71 | Recommended by Chen et al. [224]. | |
| η2 | 0.01 | 0.06 | 0.14 | It is a measure of ES used mainly in the analysis of variance (ANOVA). It is used to assess the strength of the connection between the independent and dependent variables when we have more than two groups of data. | |
| ω2 | 0.01 | 0.06 | 0.14 | It is a measure of ES in the analysis of variance (ANOVA). This is a more sophisticated measure that takes into account the number of groups and the number of observations in each group. It is considered to be a more accurate and less biased measure of effect size in ANOVA than η2. | |