Frequentist probability asserts that the “probability” of something is the frequency at which it’s observed. Frequentist statistics extends the concept to statistics.

So replace every instance of the words *chance* and *probability* with the word *frequency* (adjusting the sentence as necessary to make logical sense) and you’re golden. ^{1}This advice assumes you know you’re characterizing your data, not your hypothesis.

Alternatively, because this adjustment tends to lead to stilted sentences, replace *x% chance* or *0.x probability* with *x% of*

*Examples (replacing *chance/probability* with *frequency*):*

- Misleading: The
**probability**that this 95% confidence interval contains the test statistic is 95%. - Accurate: The
**frequency**with which 95% confidence intervals (in a number of repeated trials) contain the test statistic is 95% - Misleading: The p-value for this test was 0.03, so the
**probability**of obtaining the data observed, assuming there was no difference between treatments, was 0.03. - Accurate: The p-value for this test was 0.03, so the
**frequency**with which one might obtain the data observed (in a number of repeated trials), assuming there was no difference between treatments, was 3%.

*Examples (replacing *x% chance* or *0.x probability* with *x% of*):*

- Misleading: There is a
**95% chance**that this 95% confidence interval contains the test statistic. - Accurate:
**95% of**95% confidence intervals contain the test statistic. - Misleading: There was a
**3% chance**(p = 0.03) of seeing these observations, assuming there was no difference between treatments. - Accurate:
**3% of**repeated trials (p = 0.03) would see similar observations, assuming there was no difference between treatments.

^{1}Frequentist statistics only helps you draw conclusions on your data, not your hypothesis. It makes more sense to talk about the *frequency* of observing some data than the *frequency* of observing some hypothesis. If you fit your statements into the template

We'd expect [frequency] of repeated trials to have [data], assuming [hypothesis],your new statement is probably accurate. Swapping

*data*and

*hypotheses*leads to incorrect/misleading statements.

*Examples (statements that make it sound like you're testing your hypothesis (misleading) vs. ones that sound like you're testing data (correct)):*

- Misleading (characterizing the hypothesis): There was a 3% chance (p = 0.03) that there was no difference between treatments (because we observed these data).
- Rephrased (still misleading; data and hypothesis are swapped): We'd expect 3% of repeated trials (p = 0.03) to have no difference between treatments, assuming the data were as observed.
- Rephrased (accurate): We'd expect 3% of repeated trials (p = 0.03) to have these data, assuming there was no difference between treatments.

- Accurate (characterizing the data): 3% of repeated trials would observe these data, assuming there was no difference between treatments.
- Rephrased (still accurate): We'd expect 3% of repeated trials to have these data, assuming there was no difference between treatments.

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