Intermediate Statistics: A Modern Approach

By James P. Stevens | Go to book overview
For disproportional cell size the sums of squares are correlated (confounded). Several methods have been suggested in the literature for analyzing such designs. There is now a consensus that generally the regression approach, where the unique contribution of each effect is obtained, should be used. If, however, an a priori ordering of the effects can be established, then the sequential sum of squares approach makes sense.
The regression approach, which yields the unique variation due to each effect, is denoted by type III sum of squares in SAS and SPSS for Windows 7.5 and 8.0.
Aptitude x treatment interaction (ATI) is a broad area of research that uses factorial designs, and is concerned with the possible moderating effect any individual difference characteristic (sex, age, locus of control, etc.) of subjects may have on their response to treatments.
In a three way ANOVA there are 7 hypotheses that are tested. The 3 main effects test whether the population level means are equal. The nature of the two way interactions is ascertained by examining the means for each pair of factors lumped over the third factor. The three way interaction indicates whether the patterns of means (profiles) for any two factors are different for the levels of the third factor.
Power estimation for two and three way ANOVA was discussed using Cohen's approach. The PASS 6.0 program was used to obtain power estimates quickly for different sample sizes and different alpha levels.
An improved Bonferroni type procedure, which makes use of p values, is discussed and illustrated.
A comprehensive computer example, using real data, is used to illustrate and integrate several important concepts from the chapter, as well as indicating some aspects of practical data analysis.
For 3 and 4 way ANOVA there are many hypotheses being tested (7 for three way and 15 for four way). It is important to note that if the .05 level is used for each effect, then the overall α level becomes quite high. Thus, I or 2 significant results from such a design, if not hypothesized a priori, could well be spurious.
The distinction between fixed and random factors is illustrated with some examples.

APPENDIX: DOING A BALANCED TWO WAY
ANOVA WITH A CALCULATOR
1. Obtain the mean and variance for each cell.
2. Obtain the row, column, and grand means.
3. Obtain the error term (MSw) as the average of the cell variances.

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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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