Question

A psychologist is planning a study to test whether people are more likely to call events "natural" that are otherwise frequently attributed to "supernatural forces" if they have seen a particular film critical of "superstitions." Discuss the three things the psychologist should consider in order to maximize power for the planned study. Be specific, i.e., describe the statistical principles and explain how each works to increase power

Answer 1

Increase the power of a hypothesis test

You can use any of the following methods to increase the power of a hypothesis test.

• Use a larger sample.

  Using a larger sample provides more information about the population and, thus, increase power. Using a larger sample is often the most practical way to increase power.

• Improve your process.

  For a hypothesis test of means (1-sample Z, 1-sample t, 2-sample t, and paired t), improving your process decreases the standard deviation. When the standard deviation is smaller, the power increases and smaller differences can be detected.

• Use a higher significance level (also called alpha or α).

  Using a higher significance level increases the probability that you reject the null hypothesis. However, be cautious, because you do not want to reject a null hypothesis that is actually true. (Rejecting a null hypothesis that is true is called type I error.)

• Choose a larger value for Differences.

  It is easier to detect larger differences in population means.

• Use a directional hypothesis (also called one-tailed hypothesis).

  A directional hypothesis has more power to detect the difference that you specify in the direction that you specify. (The direction is either less than or greater than.) However, be cautious, because a directional hypothesis cannot detect a difference that is in the opposite direction.

Increase the power of an ANOVA

You can use any of the following methods to increase the power of a one-way ANOVA.

• Use a larger sample.

  Using a larger sample provides more information about the population and, thus, increase power. Using a larger sample is often the most practical way to increase power.

• Choose a larger value for Values of the maximum difference between means.

  It is easier to detect larger differences in population means.

• Improve your process.

  Improving your process decreases the standard deviation and, thus, increases power.

• Use a higher significance level (also called alpha or α).

  Using a higher significance level increases the probability that you reject the null hypothesis. However, be cautious, because you do not want to reject a null hypothesis that is actually true. (Rejecting a null hypothesis that is true is called type I error.)