- What makes a good sample
- Obvious potential biases e.g. non-response
- Precision as a guide to sample size
- Null and alternative hypothesis
- Two types of error, measured by
and 
- Acceptable error rates should relate to the cost of the error
Todays class; hypothesis testing
Hypothesis tests on means
- All todays tests are standard error counters
- How many standard errors is the null hypothesis mean away from the sample mean
- If the null hypothesis mean is many standard errors (typically greater than 2) away from the sample mean, then the observed data is not in accordance with the null hypothesis, and we believe the data and reject the null
- Types of test
- One sample t-test; testing a single population mean, p.104,105
- Two sample t-test; assuming equal variances, p.139,147,152
- Two sample t-test; NOT assuming equal variances, p.140,147
- Paired t-test; p.161,166
- Assumptions within groups
- Independence
- Constant variance
- Approximately normal
The paired t-test
- The idea; two repeat observations on the same experimental unit
- Twins, feet etc
- Controls for unwanted variability between subjects
- Essentially a one sample t-test on the differences
The p-value
- A measure of the credibility of the null hypothesis
- Small p-values give evidence against the null
- In English; the probability that if you did the experiment again and the null hypothesis was true, that you would observe a value of the test statistic as extreme as the one you saw the first time.
- It picks up the repeatability idea. If something is true (ie the null hypothesis) then you should be able to replicate the observed results. A small p-value says that it would be hard to replicate, hence the small p-value offers evidence against the null