Question

1. which of the following best describes a p - value?

a. the probability of observing the data, or something more extreme, if the null hypothesis were true.
b. a measure that directly calculates the effect size of the study.
c. the probability that the null hypothesis is true.
d. the likelihood that the alternative hypothesis is false.

Explanation:

The p - value is defined in the context of hypothesis testing. When the null hypothesis ($H_0$) is assumed to be true, the p - value calculates the probability of obtaining the observed data or data more extreme.

• Option b: The p - value is not a direct measure of effect size. Effect size measures like Cohen's d or Pearson's r are used for that purpose.
• Option c: The p - value is not the probability that the null hypothesis is true. Hypothesis testing assumes the null hypothesis is true for the sake of calculating the p - value, but it doesn't give the probability of the null hypothesis being true in an absolute sense.
• Option d: The p - value is not related to the likelihood of the alternative hypothesis being false. It is centered around the null hypothesis assumption.

Answer:

a. The probability of observing the data, or something more extreme, if the null hypothesis were true.