Intermediate Statistics: A Modern Approach

By James P. Stevens | Go to book overview

3 Power Analysis
CONTENTS
3.1 Introduction
3.2t Test for Independent Samples
3.3 A Priori and Post Hoc Estimation of Power
3.4 Power Analysis with PASS 6.0 for t Test
3.5 Estimation of Power for One Way Analysis of Variance
3.6 A Priori Estimation of Subjects Needed for a Given Power
3.7 Power Analysis for One Way ANOVA with PASS 6.0
3.8 Ways of Improving Power
3.9 Power Estimation on SPSS MANOVA
3.10 Summary

3.1 INTRODUCTION

Recall from Chapter 2 that type I error, or the level of significance (α), is the probability of rejecting the null hypothesis when it is true, in effect saying the groups differ when they do not. The α level set by the experimenter is a subjective decision, but it is usually set at .05 or .01 by most researchers. The reason for setting α so low, of course, is to minimize the probability of making this error. In statistical inference we can never be sure we have made the correct decision; however, by setting α very low we can control quite effectively the risk of this type of error occurring. As we shall see shortly, though, it is not always wise to set α as low as .05 or .01, especially when the group sizes are less than 20.

There is another type of error that one can make in conducting a statistical test, and this is called a type II error. Type II error (denoted by β) is the probability of accepting H0 when it is false, i.e., saying the groups don't differ when they

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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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