Now that we are familiar with many of the core concepts behind hypothesis testin

Question

Now that we are familiar with many of the core concepts behind hypothesis testing lets take a closer look at the concept of alpha levels. Imagine your a researcher in the following scenario: You conduct a study looking at the effect of sugar pills (placebo) on depressed individuals. Your hypothesis is that much of the improvement observed in these patients, once prescribed medication, arises not from the drug itself but from the belief that these drugs will improve one's mental status. You test a sample of 50 individuals and come up with a result that is near significance (p 0.06) but doesn't quite reach criteria to reject the null. What do you do now? Clearly your sample's depression levels have decreased considerably. But because of our arbitrarily defined critical values, technically your result is "no effect." Is this fair? How do we solve this problem? This post is due by July 2 at 11:59 PM CST.

Explanation / Answer

If at p = 0.06, we are unable to reject the null hypothesis, then this means that our critical value must be 0.05 or less.

With a critical value of 0.05 or less, we can't reject the null hypothesis for p = 0.06, so with a critical value of 0.05 or less only, we are not rejecting the null hypothesis at p = 0.06

No effect using the arbitrarily defined critical value means that we are using a critical value which is less than 0.06

Arbitrarily defined critical values must be less than 0.06 because for these values the p value of 0.06 is more than the critical values which means the p value is insignificant and hence, we can reject the alternate hypothesis and can conclude that there is "no effect"

Yes, this is fair because the p value is insignificant for all critical values less than 0.06.

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