# 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

• 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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