Week 8: Inferential Statistics

What is the purpose of inferential statistics?

To infer or suggest something about the larger population based on data collected from a sample.

What does the null hypothesis (H₀) state?

That any difference in the data is due to random chance, not a real difference in the population.

What does the alternative hypothesis (Hₐ) state?

That any difference in the data reflects a real difference in the population.

What is the typical threshold for statistical significance?

p < 0.05

What does a p-value < 0.05 mean?

There is less than a 5% chance that the result is due to random variation—so it's statistically significant.

What happens if p > 0.05?

We fail to reject the null hypothesis; the difference may be due to chance.

What is a Type I error?

Incorrectly rejecting the null hypothesis when it is actually true (false positive).

What is a Type II error?

Failing to reject the null hypothesis when the alternative is true (false negative).

What is statistical power?

The probability of detecting a difference if one truly exists; ideally ≥ 0.80.

How can you increase power?

By increasing sample size or effect size.

What is the alpha level typically set at?

0.05

What are parametric tests based on?

Normally distributed data.

What are non-parametric tests used for?

Data that is not normally distributed or ordinal data.

Which test compares 2 independent groups (parametric)?

Independent samples t-test.

Which test compares 2 independent groups (non-parametric)?

Mann-Whitney U test.

Which test compares 2 time points within the same group (parametric)?

Paired samples t-test.

Which test compares 2 time points within the same group (non-parametric)?

Wilcoxon signed-rank test.

Which test compares 3+ group means (parametric)?

One-way ANOVA.

Which test compares 3+ groups (non-parametric)?

Kruskal-Wallis test.

Which test compares repeated measures in the same group (parametric)?

Repeated measures ANOVA.

Which test compares repeated measures in the same group (non-parametric)?

Friedman test.

Which test is used for categorical comparisons in large samples?

Chi-square test

Which test is preferred for small or unbalanced samples?

Fisher's exact test

Why is a post-hoc analysis used?

To determine which specific groups differ after finding a significant result in ANOVA.

What does a 95% confidence interval mean?

We are 95% confident that the true population value lies within that range

What does a wide confidence interval indicate?

Less precision in the estimate