13.2 Hypothesis testing steps
- Define a hypothesis
- Make a test statistic
- compute a p-value (to quantify the prob of having a value which is equal or more extreme than the t-test result)
- decide if to reject H0
Step 1 is what we decide based on our investigation.
Step 2 is to construct a t-statistic, it summarize the relation with H0.
if: H0:μt=μc we have a two sample test as we are searching values on the left and on the right of the t-test results T=μt−μcs√1nt+1nc s=√(nt−1)s2t+(nt−1)s2cnt+nc−2 A large absolute value of the T-statistic is against the H0.
Step 3 is to compute a p-value, the probability of observing a value which is equal or more extreme than the observed value.
P-value is observing a T-stat which is equal or more extreme than the observed statistic
The p-value let’s us interpret the scale of out t-statistic absolute result.
The t-stat value is arbitrarily “LARGE”, the p-value rescale it to (0 to 1), in terms of probability to find an equal or more extreme value.
Step 4 is to identify if to reject H0 or fail to reject H0. The smaller the p-value is the stronger is the evidence AGAINST the NULL hypothesis.
- Type I error reject H0 when H0 is TRUE
- Type I error Rate is the prob of type I error
- Type II error no reject H0 when H0 is FALSE
- POWER of hypothesis is the prob of not making type II error
There is a trade-off between type I & type II error