Introduction and Reader’s Guide
Intended Audience and Setting
Interactive Content
Disclaimer
Acknowledgements
1
Sampling Distribution: How Different Could My Sample Have Been?
Summary
1.1
Statistical Inference: Making the Most of Your Data
1.2
A Discrete Random Variable: How Many Yellow Candies in My Bag?
1.2.1
Sample statistic
1.2.2
Sampling distribution
1.2.3
Probability and probability distribution
1.2.4
Expected value or expectation
1.2.5
Unbiased estimator
1.2.6
Representative sample
1.3
A Continuous Random Variable: Overweight And Underweight.
1.3.1
Continuous variable
1.3.2
Continuous sample statistic
1.3.3
Probability density
1.3.4
Probabilities always sum to 1
1.4
Concluding Remarks
1.4.1
Sample characteristics as observations
1.4.2
Means at three levels
1.5
Take-Home Points
2
Probability Models: How Do I Get a Sampling Distribution?
Summary
2.1
Exact Approaches to the Sampling Distribution
2.1.1
Exact approaches for categorical data
2.1.2
Computer-intensive
2.2
Exact Approaches in SPSS
2.2.1
Instructions
2.3
Theoretical Approximations of the Sampling Distribution
2.3.1
Reasons for a bell-shaped probability distribution
2.3.2
Conditions for the use of theoretical probability distributions
2.3.3
Checking conditions
2.3.4
More complicated sample statistics: differences
2.3.5
Independent samples
2.3.6
Dependent samples
2.4
SPSS and Theoretical Approximation of the Sampling Distribution
2.5
The Bootstrap Approximation of the Sampling Distribution
2.5.1
Sampling with and without replacement
2.5.2
Limitations to bootstrapping
2.5.3
Any sample statistic can be bootstrapped
2.6
Bootstrapping in SPSS
2.6.1
Instructions
2.7
When Do We Use Which Approach to the Sampling Distribution?
2.8
Take-Home Points
3
Estimating a Parameter: Which Population Values Are Plausible?
Summary
3.1
Point Estimate
3.2
Interval Estimate for the Sample Statistic
3.3
Precision, Standard Error, and Sample Size
3.3.1
Sample size
3.3.2
Standard error
3.4
Critical Values
3.4.1
Standardization and
z
scores
3.4.2
Interval estimates from critical values and standard errors
3.5
Confidence Interval for a Parameter
3.5.1
Reverse reasoning from one sample mean
3.5.2
One confidence interval does not say anything
3.5.3
Confidence intervals with bootstrapping
3.6
Confidence Intervals in SPSS
3.6.1
Instruction
3.7
Take-Home Points
4
Hypothesis testing
Summary
4.1
A Binary Decision
4.2
Null Hypothesis Significance Testing
4.2.1
Null hypothesis
4.2.2
Alternative hypothesis
4.2.3
True effect size
4.2.4
Alpha
4.2.5
1 - Alpha
4.2.6
Power
4.2.7
Beta
4.2.8
Test statistic
4.2.9
P-value
4.2.10
Observed effect size
4.2.11
Post hoc power
4.2.12
Meta analysis
4.2.13
Sample size
4.2.14
One-Sided and Two-Sided Tests
4.3
Confidence Intervals to test hypotheses
4.3.1
Estimation instead of hypothesis testing
4.3.2
Bootstrapped confidence intervals
4.4
Bayesian hypothesis testing
4.5
Statistical test selection
4.6
Reporting test results
4.6.1
Reporting to fellow scientists
4.6.2
Reporting to the general reader
4.7
Critical reflection
4.7.1
Criticisms of Null Hypothesis Significance Testing
4.7.2
Statistical significance is not a measure of effect size
4.7.3
Capitalization on Chance
4.7.4
Specifying hypotheses afterwards
4.8
Take home points
5
Critical Discussion of Null Hypothesis Significance Testing
Summary
5.0.1
Knocking down straw men (over and over again)
5.1
Alternatives for Null Hypothesis Significance Testing
5.1.1
Replication
5.2
What If I Do Not Have a Random Sample?
5.2.1
Theoretical population
5.2.2
Data generating process
5.3
Take-Home Points
6
Moderation with Analysis of Variance (ANOVA)
Summary
6.1
Different Means for Three or More Groups
6.1.1
Mean differences as effects
6.1.2
Between-groups variance and within-groups variance
6.1.3
F
test on the model
6.1.4
Assumptions for the
F
test in analysis of variance
6.1.5
Which groups have different average scores?
6.2
One-Way Analysis of Variance in SPSS
6.2.1
Instructions
6.3
Different Means for Two Factors
6.3.1
Two-way analysis of variance
6.3.2
Balanced design
6.3.3
Main effects in two-way analysis of variance
6.4
Moderation: Group-Level Differences that Depend on Context
6.4.1
Types of moderation
6.4.2
Testing main and interaction effects
6.4.3
Assumptions for two-way analysis of variance
6.5
Reporting Two-Way Analysis of Variance
6.6
Two-Way Analysis of Variance in SPSS
6.6.1
Instructions
6.7
Take-Home Points
7
Regression Analysis And A Categorical Moderator
Summary
7.1
The Regression Equation
7.1.1
A numerical predictor
7.1.2
Dichotomous predictors
7.1.3
A categorical independent variable and dummy variables
7.1.4
Sampling distributions and assumptions
7.2
Regression Analysis in SPSS
7.2.1
Instructions
7.3
Different Lines for Different Groups
7.3.1
A dichotomous moderator and numerical predictor
7.3.2
Interaction variable
7.3.3
Conditional effects, not main effects
7.3.4
Interpretation and statistical inference
7.3.5
A categorical moderator
7.3.6
Common support
7.3.7
Visualizing moderation and covariates
7.4
A Dichotomous or Categorical Moderator in SPSS
7.4.1
Instructions
7.5
Take-Home Points
8
Regression Analysis With A Numerical Moderator
Summary
8.1
A Numerical Moderator
8.1.1
Interaction variable
8.1.2
Conditional effect
8.1.3
Mean-centering
8.1.4
Symmetry of predictor and moderator
8.1.5
Visualization of the interaction effect
8.1.6
Statistical inference on conditional effects
8.1.7
Common support
8.1.8
Assumptions
8.1.9
Higher-order interaction effects
8.2
Reporting Regression Results
8.3
A Numerical Moderator in SPSS
8.3.1
Instructions
8.4
Take-Home Points
9
Regression Analysis And Confounders
Summary
9.1
Controlling for Effects of Other Predictors
9.1.1
Partial effect
9.1.2
Confounding variables
9.2
Indirect Correlation
9.2.1
Indirect correlation and size of confounding
9.2.2
Confounders are not included in the regression model
9.2.3
Randomization for avoiding confounders
9.3
Two Types of Confounders
9.3.1
Suppression
9.3.2
Reinforcement and spuriousness
9.4
Comparing Regression Models in SPSS
9.4.1
Instructions
9.5
Take-Home Points
10
Mediation with Regression Analysis
Summary
10.1
Mediation as Causal Process
10.1.1
Criteria for a causal relation
10.1.2
Mediation as indirect effect
10.1.3
Causal process
10.2
Path Model with Regression Analysis
10.2.1
Requirements
10.2.2
Size of indirect effects
10.2.3
Direction of indirect effects
10.2.4
Parallel and serial mediation
10.2.5
Partial and full mediation
10.2.6
Significance of indirect effects
10.3
Controlling for Covariates
10.4
Reporting Mediation Results
10.5
Mediation with SPSS and PROCESS
10.5.1
Instructions
10.6
Criticisms of Mediation
10.6.1
Causal order assumed
10.6.2
Time order
10.6.3
Causality or underlying construct?
10.6.4
Every effect in a path model can be confounded
10.6.5
Recommendations
10.7
Combining Mediation and Moderation
10.8
Take-Home Points
Appendix
Flow chart statistical test selection
All SPSS Tutorial Videos List
Formulating Statistical Hypotheses
Proportions: shares
Testing proportions in SPSS
Mean and median: level
Testing one mean or median in SPSS
Variance: (dis)agreement
Testing two variances in SPSS
Answers
Association: relations between characteristics
Score level differences
Comparing means in SPSS
Answers
Combinations of scores
Testing associations in SPSS
Answers
References
11
Chapter 4 leftovers
11.1
Testing a Null Hypothesis with a Theoretical Probability Distribution
11.2
Specifying Null Hypotheses in SPSS
11.2.1
Specify null for binomial test
11.3
Take-Home Points
12
Which Sample Size Do I Need? Power!
Summary
12.1
Effect Size
12.1.1
Practical relevance
12.1.2
Unstandardized effect size
12.2
Hypothetical World Versus Imaginary True World
12.2.1
Imagining a population with a small effect
12.2.2
The world of the researcher
12.2.3
The alternative world of a small effect
12.2.4
Type II error
12.2.5
Power of the test
12.2.6
Post hoc power
12.3
Sample Size, Effect Size, and Power
12.3.1
So how do we determine sample size?
12.4
Research Hypothesis as Null Hypothesis
12.5
Take-Home Points
Statitstical Inference
9.4
Comparing Regression Models in SPSS
9.4.1
Instructions
Figure 9.9: Identifying confounders with regression in SPSS.