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1. A null hypothesis

2. An alternative hypothesis

3. A test statistic which is calculated from sample data which should have different behavior when the null is false than when it is true (or the test is not helpful).

4. A rejection rule (from which a significance level could be obtained) or a significance level (from which a rejection rule is obtained)

A rejection rule says under what circumstances (what values of the test statistic) the null would be rejected. The significance level is the probability of rejecting the null when it's true (or the highest such probability if the null is not simple). Either will tell you the other.

1. A null hypothesis

2. An alternative hypothesis

3. A test statistic which is calculated from sample data which should have different behavior when the null is false than when it is true (or the test is not helpful).

4. A rejection rule (from which a significance level could be obtained) or a significance level (from which a rejection rule is obtained)

   A rejection rule says under what circumstances (what values of the test statistic) the null would be rejected. The significance level is the probability of rejecting the null when it's true (or the highest such probability if the null is not simple). Either will tell you the other.

a. power curves for several tests, including a couple of power comparisons of different tests

b. binomial test

c. effect of changing significance level on power

For the most common tests, many of these things are well understood; as an example, a chi-squared test of multinomial goodness of fit is known not to be unbiased in general but is asymptotically efficient. Most goodness of fit tests have bias issues (e.g. try the Anderson-Darling test with uniform null against a "hill shaped" symmetric beta alternative)

a. power curves for several tests, including a couple of power comparisons of different tests

b. binomial test

c. effect of changing significance level on power

For the most common tests, many of these things are well understood; as an example, a chi-squared test of multinomial goodness of fit is known not to be unbiased in general but is asymptotically efficient. Most goodness of fit tests have bias issues (e.g. try the Anderson-Darling test with uniform null against a "hill shaped" symmetric beta alternative)

For the most common tests, many of these things are well understood; as an example, a chi-squared test of multinomial goodness of fit is known not to be unbiased in general but is asymptotically efficient.

For the most common tests, many of these things are well understood; as an example, a chi-squared test of multinomial goodness of fit is known not to be unbiased in general but is asymptotically efficient. Most goodness of fit tests have bias issues (e.g. try the Anderson-Darling test with uniform null against a "hill shaped" symmetric beta alternative)