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My question is: when we talk about the null hypothesis here, are we referring to the sampling distribution constructed:

Before any data is collected (a priori), or

After data has been collected (a posteriori)?

In a one-sample t-test, for example, it is a combination.

A priori, you decide your null hypothesis, say $\mu=0$.

A posteriori, you calculate the sample variance, the sample mean, and the sample size.

All four components go into calculating the test statistic and p-value.

These terms a priori and a posteriori allude to and sound like, but are not the same as, the ideas of prior and posterior distributions in Bayesian statistics.

My question is: when we talk about the null hypothesis here, are we referring to the sampling distribution constructed:

Before any data is collected (a priori), or

After data has been collected (a posteriori)?

In a one-sample t-test, for example, it is a combination.

A priori, you decide your null hypothesis, say $\mu=0$ (in general, $\mu = \mu_0$ for some constant $\mu_0$).

A posteriori, you calculate the sample variance, the sample mean, and the sample size.

All four components go into calculating the sampling distribution, test statistic, and p-value.

$$ \dfrac{\bar X - \mu_0}{s/\sqrt{n}} \sim t_{n - 1} $$

These terms a priori and a posteriori allude to and sound like, but are not the same as, the ideas of prior and posterior distributions in Bayesian statistics.

My question is: when we talk about the null hypothesis here, are we referring to the sampling distribution constructed:

Before any data is collected (a priori), or

After data has been collected (a posteriori)?

In a one-sample t-test, for example, it is a combination.

A priori, you decide your null hypothesis, say $\mu=0$.

A posteriori, you calculate the sample variance, the sample mean, and the sample size.

All four components go into calculating the test statistic and p-value.

These terms allude to, but are not the same as, prior and posterior distributions in Bayesian statistics.

My question is: when we talk about the null hypothesis here, are we referring to the sampling distribution constructed:

Before any data is collected (a priori), or

After data has been collected (a posteriori)?

In a one-sample t-test, for example, it is a combination.

A priori, you decide your null hypothesis, say $\mu=0$.

A posteriori, you calculate the sample variance, the sample mean, and the sample size.

All four components go into calculating the test statistic and p-value.

These terms a priori and a posteriori allude to and sound like, but are not the same as, the ideas of prior and posterior distributions in Bayesian statistics.

In a one-sample t-test, for example, it is a combination.

A priori, you decide your null hypothesis, say $\mu=0$.

A posteriori, you calculate the sample variance, the sample mean, and the sample size.

All four components go into calculating the test statistic and p-value.

My question is: when we talk about the null hypothesis here, are we referring to the sampling distribution constructed:

Before any data is collected (a priori), or

After data has been collected (a posteriori)?

In a one-sample t-test, for example, it is a combination.

A priori, you decide your null hypothesis, say $\mu=0$.

A posteriori, you calculate the sample variance, the sample mean, and the sample size.

All four components go into calculating the test statistic and p-value.

These terms allude to, but are not the same as, prior and posterior distributions in Bayesian statistics.