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
The Bootstrap Approximation of the Sampling Distribution
2.1.1
Sampling with and without replacement
2.1.2
Limitations to bootstrapping
2.1.3
Any sample statistic can be bootstrapped
2.2
Bootstrapping in SPSS
2.2.1
Instructions
2.3
Exact Approaches to the Sampling Distribution
2.3.1
Exact approaches for categorical data
2.3.2
Computer-intensive
2.4
Exact Approaches in SPSS
2.4.1
Instructions
2.5
Theoretical Approximations of the Sampling Distribution
2.5.1
Reasons for a bell-shaped probability distribution
2.5.2
Conditions for the use of theoretical probability distributions
2.5.3
Checking conditions
2.5.4
More complicated sample statistics: differences
2.5.5
Independent samples
2.5.6
Dependent samples
2.6
SPSS and Theoretical Approximation of the Sampling Distribution
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
Imaginary population values
3.5.2
Confidence interval
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
Null Hypothesis Significance Testing
4.1.1
Null hypothesis
4.1.2
Alternative hypotesis
4.1.3
Alpha
4.1.4
Power
4.1.5
1 - Alpha
4.1.6
Beta
4.1.7
Test statistic
4.1.8
P-value
4.1.9
True effect size
4.1.10
Observed effect size
4.1.11
Observed power
4.1.12
Meta analysis
4.2
A Binary Decision
4.3
Statistical Tests
4.3.1
The null hypothesis
4.3.2
Significance level (
\(\alpha\)
), significance, rejection region, and Type I error
4.3.3
p
Value
4.4
Research hypothesis, alternative hypothesis, and nil hypothesis
4.5
One-Sided and Two-Sided Tests
4.5.1
Boundary value as hypothesized population value
4.5.2
One-sided – two-sided distinction is not always relevant
4.5.3
From one-sided to two-sided
p
values and back again
4.6
Testing a Null Hypothesis with a Theoretical Probability Distribution
4.7
Testing a Null Hypothesis with an Exact Approach or Bootstrapping
4.7.1
Relation between null-hypothesis tests and confidence intervals
4.7.2
Testing a null hypothesis with bootstrapping
4.8
Test Recipe and Rules for Reporting
4.8.1
Reporting to fellow scientists
4.8.2
Reporting to the general reader
4.9
Specifying Null Hypotheses in SPSS
4.9.1
Specify null for binomial test
4.10
Capitalization on Chance
4.10.1
Example of capitalization on chance
4.10.2
Correcting for capitalization on chance
4.10.3
Specifying hypotheses afterwards
4.11
Take-Home Points
5
Which Sample Size Do I Need? Power!
Summary
5.1
Sample Size and Test Requirements
5.2
Effect Size
5.2.1
Practical relevance
5.2.2
Unstandardized effect size
5.2.3
Standardized effect size: Cohen’s
d
for one or two means
5.2.4
Obtaining Cohen’s
d
with SPSS
5.2.5
Association as effect size
5.2.6
Standardized effect size and sample size
5.3
Hypothetical World Versus Imaginary True World
5.3.1
Imagining a population with a small effect
5.3.2
The world of the researcher
5.3.3
The alternative world of a small effect
5.3.4
Type II error
5.3.5
Power of the test
5.3.6
Post hoc power
5.4
Sample Size, Effect Size, and Power
5.4.1
So how do we determine sample size?
5.5
Research Hypothesis as Null Hypothesis
5.6
Take-Home Points
6
Critical Discussion of Null Hypothesis Significance Testing
Summary
6.1
Criticisms of Null Hypothesis Significance Testing
6.1.1
Statistical significance is not a measure of effect size
6.1.2
Knocking down straw men (over and over again)
6.2
Alternatives for Null Hypothesis Significance Testing
6.2.1
Estimation instead of hypothesis testing
6.2.2
Meta-analysis
6.2.3
Replication
6.2.4
Bayesian inference
6.3
What If I Do Not Have a Random Sample?
6.3.1
Theoretical population
6.3.2
Data generating process
6.4
Take-Home Points
7
Moderation with Analysis of Variance (ANOVA)
Summary
7.1
Different Means for Three or More Groups
7.1.1
Mean differences as effects
7.1.2
Between-groups variance and within-groups variance
7.1.3
F
test on the model
7.1.4
Assumptions for the
F
test in analysis of variance
7.1.5
Which groups have different average scores?
7.2
One-Way Analysis of Variance in SPSS
7.2.1
Instructions
7.3
Different Means for Two Factors
7.3.1
Two-way analysis of variance
7.3.2
Balanced design
7.3.3
Main effects in two-way analysis of variance
7.4
Moderation: Group-Level Differences that Depend on Context
7.4.1
Types of moderation
7.4.2
Testing main and interaction effects
7.4.3
Assumptions for two-way analysis of variance
7.5
Reporting Two-Way Analysis of Variance
7.6
Two-Way Analysis of Variance in SPSS
7.6.1
Instructions
7.7
Take-Home Points
8
Regression Analysis And A Categorical Moderator
Summary
8.1
The Regression Equation
8.1.1
A numerical predictor
8.1.2
Dichotomous predictors
8.1.3
A categorical independent variable and dummy variables
8.1.4
Sampling distributions and assumptions
8.2
Regression Analysis in SPSS
8.2.1
Instructions
8.3
Different Lines for Different Groups
8.3.1
A dichotomous moderator and numerical predictor
8.3.2
Interaction variable
8.3.3
Conditional effects, not main effects
8.3.4
Interpretation and statistical inference
8.3.5
A categorical moderator
8.3.6
Common support
8.3.7
Visualizing moderation and covariates
8.4
A Dichotomous or Categorical Moderator in SPSS
8.4.1
Instructions
8.5
Take-Home Points
9
Regression Analysis With A Numerical Moderator
Summary
9.1
A Numerical Moderator
9.1.1
Interaction variable
9.1.2
Conditional effect
9.1.3
Mean-centering
9.1.4
Symmetry of predictor and moderator
9.1.5
Visualization of the interaction effect
9.1.6
Statistical inference on conditional effects
9.1.7
Common support
9.1.8
Assumptions
9.1.9
Higher-order interaction effects
9.2
Reporting Regression Results
9.3
A Numerical Moderator in SPSS
9.3.1
Instructions
9.4
Take-Home Points
10
Regression Analysis And Confounders
Summary
10.1
Controlling for Effects of Other Predictors
10.1.1
Partial effect
10.1.2
Confounding variables
10.2
Indirect Correlation
10.2.1
Indirect correlation and size of confounding
10.2.2
Confounders are not included in the regression model
10.2.3
Randomization for avoiding confounders
10.3
Two Types of Confounders
10.3.1
Suppression
10.3.2
Reinforcement and spuriousness
10.4
Comparing Regression Models in SPSS
10.4.1
Instructions
10.5
Take-Home Points
11
Mediation with Regression Analysis
Summary
11.1
Mediation as Causal Process
11.1.1
Criteria for a causal relation
11.1.2
Mediation as indirect effect
11.1.3
Causal process
11.2
Path Model with Regression Analysis
11.2.1
Requirements
11.2.2
Size of indirect effects
11.2.3
Direction of indirect effects
11.2.4
Parallel and serial mediation
11.2.5
Partial and full mediation
11.2.6
Significance of indirect effects
11.3
Controlling for Covariates
11.4
Reporting Mediation Results
11.5
Mediation with SPSS and PROCESS
11.5.1
Instructions
11.6
Criticisms of Mediation
11.6.1
Causal order assumed
11.6.2
Time order
11.6.3
Causality or underlying construct?
11.6.4
Every effect in a path model can be confounded
11.6.5
Recommendations
11.7
Combining Mediation and Moderation
11.8
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
Statitstical Inference
2.4
Exact Approaches in SPSS
2.4.1
Instructions
Figure 2.6: Performing an exact test in SPSS.
Figure 2.7: Interpreting exact test results in SPSS.