Intermediate Statistics: A Modern Approach

By James P. Stevens | Go to book overview

partial η2 = (k - 1) · F + (N - k)] (8)

Thus the only difference between η2 and partial η2 for one way ANOVA is N vs. (N - k) in the denominator. Since the denominator for Equation 8 will always be smaller than for Equation 7, partial will be an overestimate of effect size; however, for moderately large N (say > 50) the difference between the two is small.In discussing η2 for one way ANOVA, Cohen ( 1977) characterizes η2 = .01 as corresponding to a small effect size, η2 = .06 to a medium effect size, and 712 = .14 to a large effect size.
3.10 SUMMARY
1. Power is the probability of rejecting the null hypothesis when it is false.
2. Power for a specific statistical test is dependent on (a) level of significance, (b) sample size, and (c) effect size. It is important to realize that power is heavily dependent on sample size.
3. Small and medium effect sizes are very common in social science research.
4. Cohen has provided the following rough, but useful, guidelines for small, medium, and large effect sizes for the t test and for one way analysis of variance:

t test: d + ̂ = .20 (small), d + ̂ = .50 (medium), d + ̂ > .80 (large)

F test: f + ̂ = .10 (small), f + ̂ = .25 (medium), f + ̂ > .40 (large)

5. Post hoc estimation of power for completed studies is important in properly interpreting results. In particular, lack of significance in small sample studies may be simply due to inadequate power.
6. The following relationships exist between the t and F statistics and their corresponding effect size measures:

Using these relationships, the corresponding effect size can be easily computed for any study in the literature and then Cohen's power tables entered to determine power.

7. A priori determination of sample size required for a given power at some a level requires an estimate of the anticipated effect size. Ibis estimate can be obtained using estimated effect sizes from previous similar studies and/or from theory.
8. We illustrated the PASS 6.0 program, which is very nice for obtaining power estimates very quickly. This program can be used to try out different

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Intermediate Statistics: A Modern Approach
Table of contents

Table of contents

  • Title Page iii
  • Contents vii
  • Preface xi
  • 1 - Introduction 1
  • Appendix 1: Obtaining the Mean and Variance on the Ti-30xa and Casio Fx-300sa Calculators 52
  • Appendix 2: Obtaining the Z Scores Within Each Group for a Variable Using Split File, Descriptives Procedure, and Case Summaries in Spss 53
  • 2 - One Way Analysis of Variance 63
  • 2.1 Introduction 63
  • 2.20 Summary 110
  • Appendix 111
  • 3 - Power Analysis 121
  • 3.1 Introduction 121
  • 3.10 Summary 139
  • 4 - Factorial Analysis of Variance 145
  • 4.1 Introduction 145
  • 4.8 Summary 193
  • Appendix: Doing a Balanced Two Way Anova with a Calculator 194
  • 5 - Repeated Measures Analysis 203
  • 5.1 Introduction 203
  • 5.15 Summary 234
  • 6 - Simple and Multiple Regression 239
  • 6.1 Simple Regression 239
  • 6.18 Summary of Important Points 292
  • Appendix: the Press Statistic 294
  • 7 - Analysis of Covariance 305
  • 7.1 Introduction 305
  • 7.15 Summary 335
  • Appendix a Data Sets 341
  • Appendix B Statistical Tables 371
  • Appendix C Power Tables 383
  • References 393
  • Answers to Selected Exercises 399
  • Author Index 419
  • Subject Index 421
  • Sas Statview Supplement for Intermediate Statistics a Modern Approach Second Edition 427
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