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Inferential statistics is concerned with making inferences from relationships found in a sample to relationships found in the population. Inferential statistics can help us decide whether the differences between groups we see in our data are strong enough to support our hypothesis that group differences exist in general, across the entire population.
We'll start with the fundamentals of significance testing, such as the distributions of the sampling and test statistics, p-values, significance levels, power, and type I and type II errors. Then we'll look at a variety of statistical tests and techniques that can assist us in making inferences for different types of data and research designs. We will consider how each statistical test works, what data and design it is appropriate for, and how results should be interpreted. You'll also learn how to run these tests with freely available software.
Syllabus :
1. (A) Before we get started...
- Welcome to Inferential Statistics!
(B) Comparing two groups
- Null hypothesis testing
- P-values
- Confidence intervals and two-sided tests
- Power
- Two independent proportions
- Two independent means
- Two dependent proportions
- Two dependent means
- Controlling for other variables
2. Categorical association
- Categorical association and independence
- The Chi-squared test
- Interpreting the Chi-squared test
- Chi-squared as goodness-of-fit
- The Chi-squared test - sidenotes
- Fisher's exact test
3. Simple regression
- The regression line
- The regression equation
- The regression model
- Predictive power
- Pitfalls in regression
- Testing the model
- Checking assumptions
- CI and PI for predicted values
- Exponential regression
4. Multiple regression
- Regression model
- R and R-squared
- Overall test
- Individual tests
- Checking assumptions
- Categorical predictors
- Categorical response variable
- Interpreting results
5. Analysis of variance
- One-way ANOVA
- One-way ANOVA - Assumptions and F-test
- One-way ANOVA - Post-hoc t-tests
- Factorial ANOVA
- Factorial ANOVA - Assumptions and tests
- ANOVA and regression
6. Non-parametric tests
- Non-parametric tests - Why and when
- The sign test
- One sample - Wilcoxon signed rank test
- Two samples - Wilcoxon/Mann-Whitney test
- Several samples - Kruskal-Wallis test
- Spearman correlation
- The runs test
7. Exam time!
