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Effect Sizes

Summary

Effect sizes estimate the magnitude and direction of a difference or association. PyFLASH reports them next to p-values in group comparisons and some summary plots so that a result can be interpreted as more than significant or not significant.

Where PyFLASH Uses It

  • group_comparison writes Hedges g, rank-biserial correlation, confidence intervals, and interpretation labels where applicable.
  • plot_mean_bars can include effect-size text in statistics outputs when effect sizes are enabled.
  • plot_effect_forest visualizes group effect estimates.
  • plot_group_matrix visualizes group-wise effect patterns.
  • data_overview uses detectable-effect calculations when estimating power and measurement sensitivity.

Inputs

Effect-size functions use the same cleaned numeric samples as the corresponding test. For pairwise group comparisons, direction is computed from the ordered comparison: the group value is contrasted against the reference value. In pipeline tables, reference and group show the direction that was used.

Bootstrap confidence intervals require enough independent sample values to resample. If the interval cannot be estimated reliably, PyFLASH leaves the interval as missing rather than inventing a bound.

Outputs

PyFLASH can report:

  • cohen_d: standardized mean difference for two groups (computed by the cohens_d() helper).
  • hedges_g: small-sample corrected standardized mean difference.
  • rank_biserial: nonparametric pairwise effect size for rank-based tests.
  • eta_squared and omega_squared: ANOVA-style omnibus effect sizes.
  • epsilon_squared: Kruskal-Wallis omnibus effect size.
  • ci_low and ci_high: bootstrap confidence interval bounds where available.
  • interpretation: a magnitude label such as negligible, small, medium, or large.

Magnitude labels use conventional numeric bands. For standardized differences and correlations, values below 0.2 are negligible, below 0.5 are small, below 0.8 are medium, and 0.8 or above is large. For omnibus variance-style effects, values below 0.06 are small, below 0.14 are medium, and 0.14 or above is large.

Interpretation

The sign describes direction; the absolute value describes magnitude. For planned pairwise comparisons, a positive Hedges g means the named group is higher than the reference group after PyFLASH's filtering and aggregation. A negative value means it is lower.

Effect sizes should be interpreted with the confidence interval, group sizes, and measurement scale. A small p-value with a small effect can be statistically detectable but practically modest. A large effect with a wide interval can be uncertain, especially in small samples.

Limitations

Effect-size labels are generic thresholds. They are not biological thresholds and do not define importance for a particular marker or experiment. Effect sizes also inherit the assumptions of the measurement table: missing rows, repeated ROI rows, non-independent subjects, or strong outliers can change the estimate.

Bootstrap confidence intervals are data-driven intervals. They can be unstable when sample sizes are small, values are tied, or groups have little variation.

See Also