What test(s) would you use for two measurements of the same subject?
- Normal data: Paired t-test
- Non-normal data: Wilcoxon signed rank test
What does the paired t-test do?
High level: Calculates the difference of means.
More detailed: Calculates the difference within each pair. Tests if the mean of those difference is statistically different from zero.
Example: Measure SBP before and after an intervention
What does the Wilcoxon signed rank test do?
High level: Checks whether the median of the differences between paired observations is zero.
Detailed:
* Calculate diff between each pair of observations.
* Take absolute of the diffs
* Rank the abs diff from smallest to largest
* Add the ranks for positive diffs, and negative. The test stat is the smaller of the two.
* N is the number of non-zero differences in the sample. That determines the row in the table.
Example: Measuring BP in the same 8 people before and after starting a drug.
Assumptions and limitations of the Wilcoxon signed rank test
Assumptions:
1. Distribution-free (no assumption of normality)
2. Less affected by outliers
3. Helpful in datasets with small sample sizes
Limitation:
Less powerful because it ignores some information about the data
What test(s) would you use for a binary or categorical outcome AND a binary independent variable (2 groups)?
- Chi-squared test of association
- Fisher’s exact test
What does the chi-squared test of association do?
High-level: The chi-squared test for association evaluates whether the distribution across categories differs more than expected by chance. It is a global test.
Detailed: Difference in proportions btw observed and expected; χ² statistic & p-value. Only global
1) Make a 2x2, 2xk or rxc table.
2) Calculate the observed counts for each cell by multipling the column total by the row total and dividing by the overall total.
3) Use every observed count to calculate the test statistic (formula below)
4) Calculate degrees of freedom d = (r-1)(c-1)
5) Look up the p-value in the table
Example: Comparing education level categories by vaccine status to determine if there is a relationship between education level and vaccine uptake. Any relationship?
Assumptions and limitations of the chi-squared test of association
Expected counts ≥5 in ≥80% of cells, and no expected count is <1 (this is used to see if it is appropriate given that the test is based on the normal approximation of the chi-squared distribution)
Independent counts
What does the Fisher’s exact test do?
Fisher’s exact test checks whether two categorical variables are associated by calculating the exact probability of the observed table, assuming the row and column totals are fixed, and under the assumption of no association.
When to pick the Fisher’s exact test over the chi-squared test of association
Use Fisher’s when the sample size is smaller and doesn’t meet expected count requirements of chi-squared
What does the chi-squared test for linear trend do?
The chi-squared test for linear trend tests for a linear trend in proportions across ordered groups (dose response).
It gives χ² (1 df) and p-value. Does not estimate an effect size. It is used with an ordered categorical exposure and a binary outcome. Use for >2 ordered groups
Example:
Asking if the proportion of people with lung cancer goes up with higher levels of smoking? Is there a dose response relationship?
In this scenario, which test would you use?
Explanatory variable is >2 ordered groups
Output variable is binary
And you want to see if there is a monotonic relationship
Chi-squared test for linear tread
IF you want to test for a dose response relationship (but not the effect size).
What does the one-sample t-test test? & assumptions
Test whether the mean of one sample (continuous variable) is different from a specific / hypothesized value. It compares one group to a fixed number.
TLDR: One sample, one mean, one reference value.
Use a one-sample t-test when:
* You have one continuous variable
* You want to compare its sample mean to a known or hypothesised population value
* The data are approximately normal (or sample size is reasonably large)
* Observations are independent
Example: Is the average caffeine content in my same different from 65 mg?
What is the difference between the types of t-tests?
One-sample t-test → sample mean vs fixed value
Two-sample t-test → mean vs mean (two groups)
Paired t-test → before vs after (same people)
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