Conceptual Statistics for Beginners

Now in its third edition, Conceptual Statistics for Beginners emphasizes and facilitates the conceptual understanding of statistics and statistical concepts for the purpose of reading and accurately interpreting research literature. The last two chapters of the book introduce two new concepts. The first concept is type VI error, which is the inconsistency between the statistical procedure and the research question. The final chapter introduces the importance of the concept of "Replicability" vs. statistical significance and effect size.

Carole Newman is a Professor in the Department of Curricular and Instructional Studies at the University of Akron.

Introduction

1

(2)

CHAPTER I Introduction to Statistics

Objectives

3

(2)

Subjects

5

(2)

Measures of Central Tendency

7

(3)

Mean Score

7

(1)

Median

8

(1)

Mode

9

(1)

Appropriate use of Central Tendency

10

(1)

What is data?

10

(1)

Normal Distribution of Data

10

(2)

Skewed Distribution of Data

12

(2)

Variability

14

(1)

Range

15

(1)

Quartile Deviation

15

(1)

Variance and Standard Deviation

15

(2)

Normal Distribution

17

(2)

Standard Scores

19

(10)

Z Scores

19

(4)

Z Scores Table

20

(3)

T Scores

23

(1)

Stanines

23

(2)

Percentile and Percentile Rank

25

(1)

Grade Equivalence

26

(3)

Age Equivalence

29

(1)

Chapter Summary

29

(2)

CHAPTER II Correlation, Reliability and Validity

Correlation

Objectives

31

(1)

Correlation Coefficient

32

(3)

Scattergram

35

(5)

Interpretation of r

40

(2)

r²

42

(1)

Rho

42

(1)

Reliability

43

(4)

Methods for Estimating Reliability

44

(1)

Test-Retest

44

(1)

Equivalent Form

45

(1)

Internal Consistency

45

(1)

Aspects that Affect Reliability

46

(1)

Validity

47

(4)

Face Validity

47

(1)

Content Validity

48

(1)

Concurrent Validity

48

(1)

Predictive Validity

49

(1)

Construct Validity

49

(1)

Usefulness of Validity

50

(1)

Chapter Summary

51

(2)

CHAPTER III The Meaning of Statistical Significance

Objectives

53

(2)

Hypothesis

55

(1)

Type I Error

56

(1)

Type II Error

56

(1)

One-Tailed and Two-Tailed Tests

57

(1)

Tests of Significance

58

(9)

t-tests

59

(2)

How to Use a t-Table

59

(2)

Chi Square (χ²)

61

(3)

How to Use a χ² Table

61

(3)

F-Tests

64

How to Use an F-Table

64

Similarities and Differences between the F-test and the t-test 66

How to Use a Table to determine if r is Significant

67

(1)

Chapter Summary

68

(3)

CHAPTER IV Introduction to the Concept of Interaction

Objectives

71

(1)

Definition of Interaction

72

(1)

Example of Plotting Interaction Data

72

(2)

What Can be Interpreted When There is Significant Interaction

74

(2)

Ordinal and Disordinal Interaction

76

(2)

Plotting Interaction for Three Treatments Across Gender

78

(2)

Dotted and Solid Lines

80

(1)

Chapter Summary

81

(2)

CHAPTER V Introduction to Factorial Design and Its Interpretation

Objectives

83

(1)

Purpose of Research Design

84

(1)

One-way Analysis of Variance Design

85

(1)

Example of a 2 x 2 Factorial Design

86

(2)

Calculating Degrees of Freedom

88

(2)

Example of a 2 x 3 Factorial Design

90

(2)

Example of a 2 x 2 x 2 Factorial Design

92

(2)

Important Considerations

94

(1)

Chapter Summary

95

(2)

CHAPTER VI Introduction to Research Design: Internal & External Validity

Objectives

97

(1)

Pre-Experimental Designs

98

(1)

Quasi-Experimental Designs

99

(1)

Ex Post Facto Research

99

(5)

Chapter Summary

104

(3)

CHAPTER VII Further Discussions on Research Designs

Objectives

107

(5)

Design # 1 The One Shot Case Study

112

(1)

Design # 2 The Pre-test, Post-test Case Study

113

(1)

Design # 3 The Simulated Before-After Design

114

(1)

Design # 4 Two Groups - Non-Equivalence

115

(2)

Design # 5 Experimental Control, Pre- and Post- test Design

117

(1)

Design # 6 The Longitudinal Time Design

118

(2)

Design # 7 Experimental and Control Groups Randomized Subjects

120

(2)

Design # 8 Experimental and Control Groups Matched Subjects

122

(1)

Design # 9 Before and After, with Control Groups

123

(1)

Design #10 The Solomon

124

(3)

CHAPTER VIII Type VI Error: Inconsistency Between the Statistical Procedure and the Research Question

127

(16)

Suggested Approach for Conducting Research

137

(2)

In Retrospect

139

(1)

Chapter Summary

140

(3)

CHAPTER IX Two Method of Estimating a Study's Replicability

143

(15)

Statistically Significant Exact Replications of a Study

144

(3)

Replication in a Different System

147

(5)

Implications

152

(6)

REFERENCES

158

(6)

APPENDICES

A. Table of Tests of Significance

164

(1)

B. Computation of Correlation Coefficient

165

(5)

C. Computation of Chi Square (χ²)

170

(3)

D. Computation of an Independent t-Test

173

(2)

E. Computation of a Dependent t-Test

175

(1)

F. Computation of a One-Way Analysis of Variance

176

(2)

G. Computation of a 3 x 3 Factorial Analysis

178

(5)

H. Example of an SAS Computer Setup for a Correlational Problem

183

(2)

I. Example of an SAS Computer Setup for an Independent t-Test

185

(6)

J. Example of an SAS Computer Setup for an ANOVA

191

(2)

K. Example of an SAS Computer Setup for a 3 x 3 Factorial Analysis

193

(2)

L. Example of an SAS Computer Setup for a Chi Square

195

(3)

M. Example of a SAS Computer Setup for a Descriptive Program on Frequencies

198

(5)

N. Example of an SPSSX Computer Setup for a Correlational Problem

203

(2)

O. Example of an SPSSX Computer Setup for a Chi Square

205

(2)

P. Example of and SPSSX Computer Setup for a dependent t-Test

207

(3)

Q. Example of an SPSSX Computer Setup for a Two-Way (3 x 3) Analysis of Variance

210

(2)

R. Example of Corrections of Multiple

212

(2)

S. SPSS Analysis of the One-Way ANOVA Example in Appendix F

214

(2)

T. SPSS Analysis of the Two-Way ANOVA Example in Appendix G

216

(3)

GLOSSARY

219

(14)

INDEX

233

(8)

ABOUT THE AUTHORS

241

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Conceptual Statistics for Beginners

Summary

Author Biography

Table of Contents

Supplemental Materials