Introduction and Reader’s Guide
Intended Audience and Setting
Interactive Content
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
Introduction
2.2.2
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 sizes
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
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
Hypothesis
4.1.1
Null hypothesis
4.1.2
Alternative hypothesis
4.1.3
Testing hypothesis
4.2
Null Hypothesis Significance Testing
4.2.1
Alpha
4.2.2
1 - Alpha
4.2.3
Power
4.2.4
Beta
4.2.5
Test statistic
4.2.6
P-value
4.2.7
True effect size
4.2.8
Observed effect size
4.2.9
Post hoc power
4.2.10
Meta analysis
4.2.11
Sample size
4.2.12
One-Sided and Two-Sided Tests
4.3
Reporting test results
4.3.1
Reporting to fellow scientists
4.3.2
Reporting to the general reader
4.4
Statistical test selection
4.5
Confidence Intervals to test hypotheses
4.5.1
Estimation in addidion to NHST
4.5.2
Bootstrapped confidence intervals
4.6
Bayesian hypothesis testing
4.7
Critical Discussion
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
What If I Do Not Have a Random Sample?
4.7.5
Specifying hypotheses afterwards
4.7.6
Replication
4.8
Take home points
5
Moderation with Analysis of Variance (ANOVA)
Summary
5.1
Different Means for Three or More Groups
5.1.1
Mean differences as effects
5.1.2
Between-groups variance and within-groups variance
5.1.3
F
test on the model
5.1.4
Assumptions for the
F
test in analysis of variance
5.1.5
Which groups have different average scores?
5.2
One-Way Analysis of Variance in SPSS
5.2.1
Instructions
5.3
Different Means for Two Factors
5.3.1
Two-way analysis of variance
5.3.2
Balanced design
5.3.3
Main effects in two-way analysis of variance
5.4
Moderation: Group-Level Differences that Depend on Context
5.4.1
Types of moderation
5.4.2
Testing main and interaction effects
5.4.3
Assumptions for two-way analysis of variance
5.5
Reporting Two-Way Analysis of Variance
5.6
Two-Way Analysis of Variance in SPSS
5.6.1
Instructions
5.7
Take-Home Points
6
Regression Analysis And A Categorical Moderator
Summary
6.1
The Regression Equation
6.1.1
A numerical predictor
6.1.2
Dichotomous predictors
6.1.3
A categorical independent variable and dummy variables
6.1.4
Sampling distributions and assumptions
6.2
Regression Analysis in SPSS
6.2.1
Instructions
6.3
Different Lines for Different Groups
6.3.1
A dichotomous moderator and numerical predictor
6.3.2
Interaction variable
6.3.3
Conditional effects, not main effects
6.3.4
Interpretation and statistical inference
6.3.5
A categorical moderator
6.3.6
Common support
6.3.7
Visualizing moderation and covariates
6.4
A Dichotomous or Categorical Moderator in SPSS
6.4.1
Instructions
6.5
Take-Home Points
7
Regression Analysis With A Numerical Moderator
Summary
7.1
A Numerical Moderator
7.1.1
Interaction variable
7.1.2
Conditional effect
7.1.3
Mean-centering
7.1.4
Symmetry of predictor and moderator
7.1.5
Visualization of the interaction effect
7.1.6
Statistical inference on conditional effects
7.1.7
Common support
7.1.8
Assumptions
7.1.9
Higher-order interaction effects
7.2
Reporting Regression Results
7.3
A Numerical Moderator in SPSS
7.3.1
Instructions
7.4
Take-Home Points
8
Regression Analysis And Confounders
Summary
8.1
Controlling for Effects of Other Predictors
8.1.1
Partial effect
8.1.2
Confounding variables
8.2
Indirect Correlation
8.2.1
Indirect correlation and size of confounding
8.2.2
Confounders are not included in the regression model
8.2.3
Randomization for avoiding confounders
8.3
Two Types of Confounders
8.3.1
Suppression
8.3.2
Reinforcement and spuriousness
8.4
Comparing Regression Models in SPSS
8.4.1
Instructions
8.5
Take-Home Points
9
Mediation with Regression Analysis
Summary
9.1
Mediation as Causal Process
9.1.1
Criteria for a causal relation
9.1.2
Mediation as indirect effect
9.1.3
Causal process
9.2
Path Model with Regression Analysis
9.2.1
Requirements
9.2.2
Size of indirect effects
9.2.3
Direction of indirect effects
9.2.4
Parallel and serial mediation
9.2.5
Partial and full mediation
9.2.6
Significance of indirect effects
9.3
Controlling for Covariates
9.4
Reporting Mediation Results
9.5
Mediation with SPSS and PROCESS
9.5.1
Instructions
9.6
Criticisms of Mediation
9.6.1
Causal order assumed
9.6.2
Time order
9.6.3
Causality or underlying construct?
9.6.4
Every effect in a path model can be confounded
9.6.5
Recommendations
9.7
Combining Mediation and Moderation
9.8
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
9.9
Cohen’s
d
calculatons
9.9.1
Obtaining Cohen’s
d
with SPSS
Colophon
Disclaimer
2016 Acknowledgements
2023 Technical changes
2024 Rewrite
Contribute
License
References
Statitstical Inference
8.4
Comparing Regression Models in SPSS
8.4.1
Instructions
Figure 8.9: Identifying confounders with regression in SPSS.