#### Statistical p-value quiz answers

#### They're all false. Here's why:

1. You have disproved the null hypothesis (the hypothesis that there is no statistical difference in recovery times).

[false] You can never disprove the null hypothesis within classical statistics. You only reject it based on statistical arguments (proof is based on a deductive argument).

2. You have obtained more evidence against the null hypothesis than if the p-value were p=0.045.

[false] All p-values below the alpha-criterion are treated identically. Otherwise, the alpha-criterion would lose its meaning: it would no longer set the error rate if you treated p-values below the alpha-criterion differently based on how much smaller they were.

3. You have found the probability of the null hypothesis being true.

[false] You cannot define the probabilities of hypotheses within classical statistics. This can only be done within the Bayesian definition of probability.

4. You have proved your hypothesis (that there is a reliable statistical difference in recovery time).

[false] You can never claim 'proof' within a statistical argument. Proof is reserved for deductive arguments.

5. From the p-value, you can deduce the probability of the experimental hypothesis being true.

[false] You cannot define the probabilities of hypotheses within classical statistics. This can only be done within the Bayesian definition of probability.

6. You are able to lower your alpha-criterion and report this effect as significant at the 0.02 level

[false] This misunderstands the definition of the alpha-criterion. It must be selected before experiments, so that any results based on a given pre-set criterion will have a Type-I error rate equal to that alpha-criterion. Changing the criterion after the experimental results are in simply nullifies this. [also see 2]

7. You know, if you decide to reject the null hypothesis, the probability that you are making the wrong decision.

[false] This suggests you know the probability in a particular case (this particular decision to reject). You cannot define probabilities of for single cases within classical statistics. This can only be done within the Bayesian definition of probability.

8. You have a reliable experimental finding in the sense that if, hypothetically, the experiment were repeated a great number of times, you would obtain a significant result on 98.5% of occasions.

[false] The p-value does not tell you about this kind of reliability. If you were to know the true improvement in time-to-recovery based on your new drug (rather than just the experimentally measured value), then Effect-size calculations can be used to tell you this. Those calculations would be based on a known effect size and pre-set alpha-criterion, and not on the p-value from any one dataset.

9. You have found the probability of the alternative hypothesis being false.

[false] You cannot define the probabilities of hypotheses within classical statistics. This can only be done within the Bayesian definition of probability.

10. You have computed the data analog of the type-I error rate, meaning there is a 1.5% chance you will incorrectly reject the null hypothesis when it is actually true

[false] this conflates alpha criterion and p-value. The alpha criterion tells you your error rate if you maintain that criterion across experiments. It has no statistical meaning within a single experiment, because probabilities are defined as frequencies within classical statistics. You can only talk about the probabilities of single events within the Bayesian definition of probability.