13.2 Hypothesis testing steps

  1. Define a hypothesis
  2. Make a test statistic
  3. compute a p-value (to quantify the prob of having a value which is equal or more extreme than the t-test result)
  4. 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=μtμcs1nt+1nc s=(nt1)s2t+(nt1)s2cnt+nc2 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