Beta error and Effect Size

[seminoma]

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How does an increase in expected effect size decrease beta error (FA15 page 54)? If you expect a larger effect size aren't you more likely to interpret the data as negative and therefore make a beta-type error?

Like if I expect men to weigh more than women and I set my expected effect to 100lbs I'm more likely to not reject my null hypothesis than if I set my expected effect to 5lbs (i.e. it's more likely than men will be 5+lbs heavier than women compared to 100lbs+).

 

[stepone2015]

Effect size is the actual difference between two groups.

Say every man in your study weighed 200 lbs +/- 10 lbs and every woman weighed 120 lbs +/- 10 lbs.

On average, the effect size is 80 lbs. That huge effect size means making a false negative error (saying both groups weigh the same on average) by measuring those two groups is tiny.

If the men weighed 110 lbs and the women stayed the same at 120, now the effect size is only 10 lbs and the two groups even have overlap within a single standard deviation. The chances of a false negative (saying both groups weigh the same on average) is far more likely.

 

[seminoma]

Effect size is the actual difference between two groups.

Say every man in your study weighed 200 lbs +/- 10 lbs and every woman weighed 120 lbs +/- 10 lbs.

On average, the effect size is 80 lbs. That huge effect size means making a false negative error (saying both groups weigh the same on average) by measuring those two groups is tiny.

If the men weighed 110 lbs and the women stayed the same at 120, now the effect size is only 10 lbs and the two groups even have overlap within a single standard deviation. The chances of a false negative (saying both groups weigh the same on average) is far more likely.

Perfect, thanks!