5. hypothesis testing errors and power

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8 steps of hypothesis testing

1. determine purpose of test 2. state the hypotheses (and decide one-tailed vs. two-tailed test) 3. set the significance (alpha) level 4. compute the test statistic 5. determine the degrees of freedom of freedom (if necessary) 6. identify the critical value and find the rejection region 7. make a statistical decision 8. make a clinical/substantive conclusion.

null hypothesis

hypothesis being tested

alternative hypothesis

research hypothesis

when we write the null and alternative hypotheses always use the...parameter (remember we are testing a sample statistic to...info about the population)

population, infer

one tailed test

directional. interested in whether the mean of group 1 is significantly larger or smaller than the mean of group 2

two-tailed test

nondirectional. interested in whether the mean of group 1 is significantly different than the mean of group 2. looking for a difference without specifying whether the difference is higher or lower

significance level

level of willingness to make an error in rejecting the null hypothesis.

Type 1 error

the null hypothesis is rejected when it is true. the probability to make this kind of error equals alpha. is a false positive.

type 2 error

the null hypothesis is not rejected when it is false. probability to make this kind of error is beta. is a false negative.


=1-beta. probability of rejecting the null hypothesis when it is false. the probability of making a correct decision to reject the null

factors that affect power

alpha level, effect size, sample size

effect size

simple way to quantify the difference between groups (i.e. magnitude). a measure of the effectiveness of the treatment.

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