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Effectsizepresentation 110118093101-phpapp01-130629114308-phpapp02

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Karen Southerland McMahen
Karen Southerland McMahen

This document provides information on calculating effect sizes when comparing two means. It defines effect size as the extent to which a phenomenon is present in a population or how false the null hypothesis is. It lists several common effect size measures for comparing two independent groups (Cohen's d, Hedges' g, Glass' Delta), correlations (r, 2), and analysis of variance (eta squared, omega squared, interclass correlation). Formulas are provided for Cohen's d when using a t-test for independent means. An example is given of comparing study habits between public and private school students using a t-test and reporting statistical output.

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Calculating Effect Size Comparison of Two Means
1 X 2 X n df SD1 SD2 t p value 30 28 4.6 4.1 2.3 2.3 0.60 0.56 60 58 4.6 4.1 2.3 2.3 0.84 0.4 100 98 4.6 4.1 2.3 2.3 1.09 0.28 500 498 4.6 4.1 2.3 2.3 2.43 0.02* 1000 998 4.6 4.1 2.3 2.3 3.44 0.00*
Criticism on NHST 1. NHST does not provide the information which the researcher wants to obtain 2. Logical problems derived from the probabilistic nature of NHST. 3. NHST does not enable psychological theories to be tested. 4. The fallacy of replication. 5. NHST fails to provide useful information because H0 is always false. 6. Problems associated with the dichotomous decision to reject/not reject the H0. 7. NHST impedes the advance of knowledge.
Effect Size Cohen (1988) defines the effect size as the extent to which the phenomenon is found within the population or, in the context of statistical significance testing, the degree to which the H0 is false. Snyder and Lawson (1993) argue that the effect size indicates the extent to which the dependent variable can be controlled, predicted and explained by the independent variable(s).
Effect Size Measures Effect size measures of Two In/dependent Groups Cohens d Hedges g Glass Delta Correlation Measure of Effect Size r 2 採; t r; F r; d r Effect size for Analysis of Variance Eta Squared Omega Square Index of Strength Intercalss correlation
2 2 2 1 2 21 ss MMd + = 2 2 2 1 1 2 21 n s n s MMt + = Cohens d Formula t-test for independent Means Formula
Computation A research compared first year public and private school students in their study habits. Study habits was measured using the Survey of Study Habits. The t-test for two independent samples was used to determine the significant difference between the students in the public and private school in the four factors of study habits. The following statistical output was obtained:
Effectsizepresentation 110118093101-phpapp01-130629114308-phpapp02
Effectsizepresentation 110118093101-phpapp01-130629114308-phpapp02
Effectsizepresentation 110118093101-phpapp01-130629114308-phpapp02
Effectsizepresentation 110118093101-phpapp01-130629114308-phpapp02
Effectsizepresentation 110118093101-phpapp01-130629114308-phpapp02
Effectsizepresentation 110118093101-phpapp01-130629114308-phpapp02
Effectsizepresentation 110118093101-phpapp01-130629114308-phpapp02
Effectsizepresentation 110118093101-phpapp01-130629114308-phpapp02

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Effectsizepresentation 110118093101-phpapp01-130629114308-phpapp02

  • 2. 1 X 2 X n df SD1 SD2 t p value 30 28 4.6 4.1 2.3 2.3 0.60 0.56 60 58 4.6 4.1 2.3 2.3 0.84 0.4 100 98 4.6 4.1 2.3 2.3 1.09 0.28 500 498 4.6 4.1 2.3 2.3 2.43 0.02* 1000 998 4.6 4.1 2.3 2.3 3.44 0.00*
  • 3. Criticism on NHST 1. NHST does not provide the information which the researcher wants to obtain 2. Logical problems derived from the probabilistic nature of NHST. 3. NHST does not enable psychological theories to be tested. 4. The fallacy of replication. 5. NHST fails to provide useful information because H0 is always false. 6. Problems associated with the dichotomous decision to reject/not reject the H0. 7. NHST impedes the advance of knowledge.
  • 4. Effect Size Cohen (1988) defines the effect size as the extent to which the phenomenon is found within the population or, in the context of statistical significance testing, the degree to which the H0 is false. Snyder and Lawson (1993) argue that the effect size indicates the extent to which the dependent variable can be controlled, predicted and explained by the independent variable(s).
  • 5. Effect Size Measures Effect size measures of Two In/dependent Groups Cohens d Hedges g Glass Delta Correlation Measure of Effect Size r 2 採; t r; F r; d r Effect size for Analysis of Variance Eta Squared Omega Square Index of Strength Intercalss correlation
  • 7. Computation A research compared first year public and private school students in their study habits. Study habits was measured using the Survey of Study Habits. The t-test for two independent samples was used to determine the significant difference between the students in the public and private school in the four factors of study habits. The following statistical output was obtained: