Effect Size

The magnitude of difference between two groups

Authors
Affiliations

Doctor of Physical Therapy

B.S. in Kinesiology

Doctor of Physical Therapy

B.A. in Neuroscience

Overview

  • Effect size is a measure of the difference between sample means.
  • Effect size could be considered “How much something changes after a specific intervention”.
  • Effect size measures the extent to which two samples do not overlap.
  • Often Abbreviated “d” (Cohen’s d)

Types of Effect Size

Raw Score Effect Size

Raw score effect size provides the literal mean difference between mean group scores.

Symbol Meaning
μ1 Sample 1 mean
μ2 Sample 2 mean

Raw Score Effect Size=μ1μ2

Standardized Effect Size

The standardized effect size is the raw score effect size divided by the standard deviation of its respective population.

Symbol Meaning
d Cohen’s D (Effect Size)
μ1 Sample 1 mean
μ2 Sample 2 mean
σ Standard Deviation of the Population

d=μ1μ2σ

Standardized Effect size allows one to compare effect sizes between different measures. For example, standardized effect size allows a researcher to compare a pain scale from 0-43 to another pain scale which ranges from 0-10.

Note
  • Notice that you are using standard deviation of the population (σ) not standard deviation of the distribution of means (σM)
  • In addition you are only concerned with one population’s standard deviation.
  • In hypothesis testing, all of your participants should be from the same overall population.

Example

Experiment A results:

  • Control group mean: 200
  • Experimental group mean: 220
  • Raw Score Effect size: 220200=20
  • Standardized Effect size: d=μ1μ2σ=22020048=0.416

Experiment B Results

  • Control group mean: 200
  • Experimental group mean: 210
  • Raw Score Effect size: 210200=10
  • Standardized Effect size: d=μ1μ2σ=21020048=0.208

Experiment A Effect size compares the means of the control group (200) with the experimental group (220)

Experiment A Effect size compares the means of the control group (200) with the experimental group (220)

Experiment B Effect size compares the means of the control group (200) with the experimental group (210)

Experiment B Effect size compares the means of the control group (200) with the experimental group (210)

When comparing these two experiments, we can visually see that Experiment A has a much larger effect size.

References

1.
Aron A, Coups EJ, Aron E. Statistics for Psychology. 6th ed. Pearson; 2013.

Citation

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