Cover
Contents
Guided tour
Introduction
Acknowledgements
1 Why statistics?
Overview
1.1 Introduction
1.2 Research on learning statistics
1.3 What makes learning statistics difficult?
1.4 Positive about statistics
1.5 What statistics doesnโt do
1.6 Easing the way
1.7 What do I need to know to be an effective user of statistics?
1.8 A few words about SPSS
Key points
PART 1 Descriptive statistics
2 Some basics: Variability and measurement
Overview
2.1 Introduction
2.2 Variables and measurement
2.3 Major types of measurement
Key points
Computer analysis
3 Describing variables: Tables and diagrams
Overview
3.1 Introduction
3.2 Choosing tables and diagrams
3.3 Errors to avoid
Key points
Computer analysis
4 Describing variables numerically: Averages, variation and spread
Overview
4.1 Introduction
4.2 Typical scores: mean, median and mode
4.3 Comparison of mean, median and mode
4.4 The spread of scores: variability
Key points
Computer analysis
5 Shapes of distributions of scores
Overview
5.1 Introduction
5.2 Histograms and frequency curves
5.3 The normal curve
5.4 Distorted curves
5.5 Other frequency curves
Key points
Computer analysis
6 Standard deviation and z-scores: The standard unit of measurement in statistics
Overview
6.1 Introduction
6.2 Theoretical background
6.3 Measuring the number of standard deviations โ the z -score
6.4 A use of z -scores
6.5 The standard normal distribution
6.6 An important feature of z-scores
Key points
Computer analysis
7 Relationships between two or more variables: Diagrams and tables
Overview
7.1 Introduction
7.2 The principles of diagrammatic and tabular presentation
7.3 Type A: both variables numerical scores
7.4 Type B: both variables nominal categories
7.5 Type C: one variable nominal categories, the other numerical scores
Key points
Computer analysis
8 Correlation coefficients: Pearson correlation and Spearmanโs rho
Overview
8.1 Introduction
8.2 Principles of the correlation coefficient
8.3 Some rules to check out
8.4 Coefficient of determination
8.5 Significance testing
8.6 Spearmanโs rho โ another correlation coefficient
8.7 An example from the literature
Key points
Computer analysis
9 Regression: Prediction with precision
Overview
9.1 Introduction
9.2 Theoretical background and regression equations
9.3 Standard error: how accurate are the predicted score and the regression equations?
Key points
Compu ter analysis
PART 2 Significance testing
10 Samples and populations: Generalising and inferring
Overview
10.1 Introduction
10.2 Theoretical considerations
10.3 The characteristics of random samples
10.4 Confidence intervals
Key points
Computer analysis
11 Statistical significance for the correlation coefficient: A practical introduction to statistical inference
Overview
11.1 Introduction
11.2 Theoretical considerations
11.3 Back to the real world: the null hypothesis
11.4 Pearsonโs correlation coefficient again
11.5 The Spearmanโs rho correlation coefficient
Key points
Computer analysis
12 Standard error: The standard deviation of the means of samples
Overview
12.1 Introduction
12.2 Theoretical considerations
12.3 Estimated standard deviation and standard error
Key points
Computer analysis
13 The t-test: Comparing two samples of correlated/related/paired scores
Overview
13.1 Introduction
13.2 Dependent and independent variables
13.3 Some basic revision
13.4 Theoretical considerations underlying the computer analysis
13.5 Cautionary note
Key points
Computer analysis
14 The t-test: Comparing two samples of unrelated/uncorrelated scores
Overview
14.1 Introduction
14.2 Theoretical considerations
14.3 Standard deviation and standard error
14.4 Cautionary note
Key points
Computer analysis
15 Chi-square: Differences between samples of frequency data
Overview
15.1 Introduction
15.2 Theoretical issues
15.3 Partitioning chi-square
15.4 Important warnings
15.5 Alternatives to chi-square
15.6 Chi-square and known populations
15.7 Chi-square for related samples โ the McNemar test
15.8 Example from the literature
Key points
Computer analysis
Recommended further reading
16 Probability
Overview
16.1 Introduction
16.2 The principles of probability
16.3 Implications
Key points
17 Reporting significance levels succinctly
Overview
17.1 Introduction
17.2 Shortened forms
17.3 Examples from the published literature
Key points
Computer analysis
18 One-tailed versus two-tailedsignificance testing
Overview
18.1 Introduction
18.2 Theoretical considerations
18.3 Further requirements
Key points
Computer analysis
19 Ranking tests: Nonparametric statistics
Overview
19.1 Introduction
19.2 Theoretical considerations
19.3 Nonparametric statistical tests
19.4 Three or more groups of scores
Key points
Computer analysis
PART 3 Introduction to analysis of variance
20 The variance ratio test: The F-ratio to compare two variances
Overview
20.1 Introduction
20.2 Theoretical issues and an application
Key points
Computer analysis
21 Analysis of variance (ANOVA): Introduction to the one-way unrelated or uncorrelated ANOVA
Overview
21.1 Introduction
21.2 Some revision and some new material
21.3 Theoretical considerations
21.4 Degrees of freedom
21.5 The analysis of variance summary table
Key points
Computer analysis
22 Analysis of variance for correlated scores or repeated measures
Overview
22.1 Introduction
22.2 Theoretical considerations underlying the computer analysis
22.3 Examples
Key points
Computer analysis
23 Two-way analysis of variance for unrelated/uncorrelated scores: Two studies for the price of one?
Overview
23.1 Introduction
23.2 Theoretical considerations
23.3 Steps in the analysis
23.4 More on interactions
23.5 Three or more independent variables
Key points
Computer analysis
24 Multiple comparisons in ANOVA: Just where do the differences lie?
Overview
24.1 Introduction
24.2 Methods
24.3 Planned versus a posteriori (post hoc) comparisons
24.4 The Scheffรฉ test for one-way ANOVA
24.5 Multiple comparisons for multifactorial ANOVA
Key points
Computer analysis
Recommended further reading
25 Mixed-design ANOVA: Related and unrelated variables together
Overview
25.1 Introduction
25.2 Mixed designs and repeated measures
Key points
Computer analysis
Recommended further reading
26 Analysis of covariance (ANCOVA): Controlling for additional variables
Overview
26.1 Introduction
26.2 Analysis of covariance
Key points
Computer analysis
Recommended further reading
27 Multivariate analysis of variance (MANOVA)
Overview
27.1 Introduction
27.2 MANOVAโs two stages
27.3 Doing MANOVA
27.4 Reporting your findings
Key points
Computer analysis
Recommended further reading
28 Discriminant (function) analysis โ especially in MANOVA
Overview
28.1 Introduction
28.2 Doing the discriminant function analysis
28.3 Reporting your findings
Key points
Computer analysis
Recommended further reading
29 Statistics and the analysis of experiments
Overview
29.1 Introduction
29.2 The Patent Stats Pack
29.3 Checklist
29.4 Special cases
Key points
PART 4 More advanced correlational statistics
30 Partial correlation: Spurious correlation, third or confounding variables, suppressor variables
Overview
30.1 Introduction
30.2 Theoretical considerations
30.3 Doing partial correlation
30.4 Interpretation
30.5 Multiple control variables
30.6 Suppressor variables
30.7 An example from the research literature
30.8 An example from a studentโs work
Key points
Computer analysis
31 Factor analysis: Simplifying complex data
Overview
31.1 Introduction
31.2 A bit of history
31.3 Concepts in factor analysis
31.4 Decisions, decisions, decisions
31.5 Exploratory and confirmatory factor analysis
31.6 An example of factor analysis from the literature
31.7 Reporting the results
Key points
Computer analysis
Recommended further reading
32 Multiple regression and multiple correlation
Overview
32.1 Introduction
32.2 Theoretical considerations
32.3 Stepwise multiple regression example
32.4 Reporting the results
32.5 An example from the published literature
Key points
Computer analysis
Recommended further reading
33 Path analysis
Overview
33.1 Introduction
33.2 Theoretical considerations
33.3 An example from published research
33.4 Reporting the results
Key points
Computer analysis
Recommended further reading
34 The analysis of a questionnaire/survey project
Overview
34.1 Introduction
34.2 The research project
34.3 The research hypothesis
34.4 Initial variable classification
34.5 Further coding of data
34.6 Data cleaning
34.7 Data analysis
Key points
Part 5 Assorted advanced techniques
35 The size of effects in statistical analysis: Do my findings matter?
Overview
35.1 Introduction
35.2 Statistical significance
35.3 Method and statistical efficiency
35.4 Size of the effect in studies
35.5 An approximation for nonparametric tests
35.6 Analysis of variance (ANOVA)
Key points
36 Meta-analysis: Combining and exploring statistical findings from previous research
Overview
36.1 Introduction
36.2 The Pearson correlation coefficient as the effect size
36.3 Other measures of effect size
36.4 Effects of different characteristics of studies
36.5 First steps in meta-analysis
36.6 Illustrative example
36.7 Comparing a study with a previous study
36.8 Reporting the results
Key points
Computer analysis
Recommended further reading
37 Reliability in scales and measurement: Consistency and agreement
Overview
37.1 Introduction
37.2 Item-analysis using itemโtotal correlation
37.3 Split-half reliability
37.4 Alpha reliability
37.5 Agreement among raters
Key points
Computer analysis
Recommended further reading
38 Confidence intervals
Overview
38.1 Introduction
38.2 The relationship between significance and confidence intervals
38.3 Regression
38.4 Other confidence intervals
Key points
Computer analysis
39 The influence of moderator variables on relationships between two variables
Overview
39.1 Introduction
39.2 Statistical approaches to finding moderator effects
39.3 The hierarchical multiple regression approach to identifying moderator effects (or interactions)
39.4 The ANOVA approach to identifying moderator effects (i.e. interactions)
Key points
Computer analysis
Recommended further reading
40 Statistical power analysis: Getting the sample size right
Overview
40.1 Introduction
40.2 Types of statistical power analysis and their limitations
40.3 Doing power analysis
40.4 Calculating power
40.5 Reporting the results
Key points
Computer analysis
PART 6 Advanced qualitative or nominal techniques
41 Log-linear methods: The analysis of complex contingency tables
Overview
41.1 Introduction
41.2 A two-variable example
41.3 A three-variable example
41.4 Reporting the results
Key points
Computer analysis
Recommended further reading
42 Multinomial logistic regression: Distinguishing between several different categories or groups
Overview
42.1 Introduction
42.2 Dummy variables
42.3 What can multinomial logistic regression do?
42.4 Worked example
42.5 Accuracy of the prediction
42.6 How good are the predictors?
42.7 The prediction
42.8 Interpreting the results
42.9 Reporting the results
Key points
Computer analysis
43 Binomial logistic regression
Overview
43.1 Introduction
43.2 Typical example
43.3 Applying the logistic regression procedure
43.4 The regression formula
43.5 Reporting the results
Key points
Computer analysis
Appendix A Testing for excessively skewed distributions
Appendix B1 Large-sample formulae for the nonparametric tests
Appendix B2 Nonparametric tests for three or more groups
Appendix C Extended table of significance for the Pearson correlation coefficient
Appendix D Table of significance for the Spearman correlation coefficient
Appendix E Extended table of significance for the t-test
Appendix F Table of significancefor chi-square
Appendix G Extended table of significance for the sign test
Appendix H Table of significance for the Wilcoxon matched pairs test
Appendix I Table of significance for the MannโWhitney U-test
Appendix J Table of significance values for the F-distribution
Appendix K Table of significant values of t when making multiple t-tests
GLOSSARY
References
Index