# 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:Click for a larger versionUsing 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

• 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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