How does standard deviation affect power

Naturally, the larger the effect size, the more likely it is that an experiment would find a significant effect. Figure 2. There is a trade-off between the significance level and power: the more stringent lower the significance level, the lower the power. Figure 3 shows that power is lower for the 0. Naturally, the stronger the evidence needed to reject the null hypothesis, the lower the chance that the null hypothesis will be rejected.

Figure 3. Power is higher with a one-tailed test than with a two-tailed test as long as the hypothesized direction is correct. A one-tailed test at the 0. Further, for any given difference in means, power is greater if the standard deviation is smaller. In the following exercise, we will use the power applet to explore how the effect size influences power. Your task is to find a good way to explain how this works to a friend.

Click here for more information on effect sizes. How likely is it that a rival competitor, the DEUCE training program, will provide convincing evidence? Power analysis will allow us to answer these questions. We begin with a test of ACE graduates. We assume that for the population of non-graduates of a training course, the mean on VAST is with a standard deviation of For the population of ACE graduates the mean is and the standard deviation is Both distributions are assumed to be normal.

How large is the effect size? The formula for d shown below indicates that the effect size for the ACE program is.

How many of your ten simulated samples allowed you to reject the null hypothesis? What is the power for this test from the applet? Click here to see how power can be computed for this scenario.

Why is statistical power greater for the TREY program? If sample size and alpha are not changed, then the power is greater if the effect size is larger. If nothing else differs, the program with the larger effect size has the greater power because more of the sampling distribution for the alternate population exceeds the critical value. In Exercises 1a and 1b, we examined how differences between the means of the null and alternative populations affect power.

In this exercise, we will investigate another variable that impacts the effect size and power; the variability of the population. If the standard deviation for graduates of the TREY program was only 50 instead of , do you think power would be greater or less than for the DEUCE program assume the population means are for graduates of both programs?