Using the following example, we will explore the various functions of the power applet:

Suppose that an educational testing company created a training program named “ACE” to help students improve their scores on a standardized exam. The company spokesman boasts that ACE graduates score higher on a standardized test than the population of individuals who do not participate in their training course.

The WISE Power Applet (which is shown below as a static picture) will be used to simulate drawing a sample of graduates from the ACE program. At the top (**Area A**), the blue curve represents the population distribution for non-graduates (**Null Population**) while the red curve represents graduates from the ACE program (**Alternative Population**). For this exercise we assume both populations are normal distributions.

In the textboxes to the right (**Area D**), we can set values for the two population means (** μ_{0}** and

**) and the population standard deviation (**

*μ*_{1}*) by entering values into the textboxes. We can also set the number of cases to be sampled (*

**σ****n**) and our alpha error rate (

**). After changing any of these values, be sure to press**

*α***Enter**.

Pressing the **Sample** button (**Area C**) simulates drawing a sample of size **n** from the **Alternative Population**. The sample of **n** cases is shown as small yellow boxes in **Area A** and the sample mean is shown with a red arrow. The sample mean is also shown below relative to the two theoretical sampling distributions (**Area B**).

The **dashed red line** shows where we have set our alpha criterion. In this case we set **α** = .05, corresponding to the upper 5% of the blue null sampling distribution. If our sample mean is to the right of the dashed line, we can reject the null hypothesis with *p* < .05, one-tailed (and correctly conclude that the sample did not come from the null population). If a sample mean falls to the left of the dashed line, we fail to reject the null hypothesis. This would be a Type II or β error (i.e., failing to reject a false null hypothesis) because the sample was actually drawn from the alternate distribution.

The decision box (**Area F**) shows the sample mean and the *z*-value of the sample mean on the null distribution as well as the one-tailed *p*-value and the decision: Reject or do not reject the null hypothesis (H_{0}). The *z*-score computed on the null sampling distribution allows us to determine the probability of observing a sample mean this large or larger if the null hypothesis is true. In the example shown here, the sample mean is 109.0 and the *z*-value on the null sampling distribution of the mean (blue) is 2.33. The probability of finding a *z*-score greater than 2.33 if we are sampling from the null distribution is *p* = 0.01. Because this probability is less than alpha (i.e., .05), our statistical decision is to reject H_{0}.

**Area D** shows many statistical values including power and effect size, and **Area E** represents sample size (**n**) and power as ‘thermometers.’ In the actual applet on the next page you will be able to change any of these values.

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