## Understanding Effect Size

### Effect Size

The effect size is the growth measure divided by the student-level standard deviation of growth. The effect size provides an indicator of magnitude and practical significance that the group of students met, exceeded, or fell short of Expected Growth.

### Standard Deviation

The standard deviation describes variability in the growth made by individual students within a given year, subject, and grade. Dividing the growth measure by the standard deviation provides an indicator of magnitude and practical significance that the group of students met, exceeded, or fell short of Expected Growth. The practical significance is related to how large the growth measure is relative to the student-level standard deviation in the given subject and grade.

### Growth Measure

A conservative estimate of the growth that students made, on average, in a grade and subject or course. See also Measuring Growth.

### Interpreting Effect Sizes

Effect sizes are sometimes classified as small, medium, or large to assist with interpretation and whether any differences in student performance are meaningful. Various researchers have offered thoughts on what defines a small, medium, and large effect size.

• Cohen describes +/- 0.20 as small, +/- 0.50 as medium, and +/- 0.80 as large (Cohen, Jacob. Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Mahwah, NJ: Lawrence Erlbaum, 1988).
• Hattie describes an effect size of +/- 0.40 as the average seen across all interventions, and +/- 0.40 as the "hinge point" (Hattie, John, Visible Learning: A Synthesis of Over 800 Meta-Analyses Relating to Achievement. London: Routledge, 2008).
• Kraft suggested 0.05/-0.05 as small, +/- 0.05 to 0.20 as medium, and > 0.20 or <-0.20 as large based on the distributions of effect sizes and changes in achievement (Kraft MA. "Interpreting Effect Sizes of Education Interventions." Educational Researcher. 2020; 49 (4):241-253).

All the researchers agree that it is important to interpret results within the distribution of actual results. In other words, what constitutes a small, medium, or large effect size is determined by what is observed in the actual results.