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Week 5 â€“ More Proportions
Chapter 21 goes into detail about some of the nuances of hypothesis testing. Of particular importance are the following points:
- P-values are conditional probabilities. They tell us the probability of getting a result at least as unusual as the observed statistics, given that the null hypothesis is true.
- Generally speaking, we operate with a 95% confidence level, which would equate to an alpha of .05. There are occasions, though, where we want to be even more certain (i.e. 99% confidence interval, corresponding to an alpha of .01), or less certain. This alpha level is often called the significance level.
- Confidence intervals and hypothesis tests (two-tailed) are very similar. Actually, if you want to perform a two-tailed hypothesis test, another approach is to create a confidence interval, and determine whether the observed statistic is within (donâ€™t reject) or outside of (reject) that interval.
- There is built in error to hypothesis testing. Two types of errors in particular are noted: Type 1 â€“ when the null is true, but we reject it; and Type 2 â€“ when the null is false, but we fail to reject it. There is tension between Type 1 and Type 2 errors, and the only way to reduce both types of errors is to collect more data.
- Power tells us the probability that a test correctly rejects a false null, and the effect size is the distance between the null hypothesis value and the truth.