### Power Analysis

This is a three-part assignment in which you will demonstrate your ability to:

- Analyze components of a
*t*test required for power analysis. - Compute and interpret a post hoc power analysis.
- Compute and interpret an
*a priori*power analysis.

In addition to IBM SPSS, you will also use the G*Power software to complete this assignment. Answer each question, providing IBM SPSS or G*Power analysis output when necessary to support your answer. Save your work in a Word file. The deadline for submitting your work is 11:59 p.m. Central time on Sunday of week 2.

The data file for this assignment, BP Study Dataset, is given in the resources. You will be conducting a post hoc power analysis and an a priori power analysis on an independent samples *t* test of gender as the grouping variable (male = 1; female = 2) and HR1 (heart rate) as the outcome variable. There are three sections of this assignment. After reporting the *t* test results, you will then conduct a post hoc power analysis followed by an a priori power analysis.

#### Section 1: Reporting the *t* Test Results

Using BP Study Dataset, conduct an independent samples *t* test in SPSS with gender as the grouping variable (male = 1; female = 2) and HR1 (heart rate) as the outcome variable.

Paste the SPSS output and then report:

- The sample size for males (
*n*1) and sample size for females (*n*2). - The means for males (
*M*1) and females (*M*2) on HR1. - The calculated mean difference (
*M*1 –*M*2). - The standard deviations for males (
*s*1) and females (*s*2) on HR1. - The Levene test (homogeneity of variance assumption) and interpretation.
*t,*degrees of freedom,*t*value, and probability value. State whether or not to reject the null hypothesis. Interpret the results.

Calculate Cohen’s *d* effect size from the SPSS output and interpret it. Specifically, if the homogeneity of variance assumption is met, divide the mean difference ( *M*1 – *M*2) by either *s*1 or *s*2. Violation of the homogeneity of variance assumption requires calculation of *S*pooled. Homogeneity assumed:

Cohen’s *d* = ( *M*1 – *M*2) ÷ *s*1 or Cohen’s *d* = ( *M*1 – *M*2) ÷ *s*2

To be comprehensive, report Cohen’s *d* based on a calculation with *s*1 and a calculation with *s*2. Round the effect size to two decimal places. Interpret Cohen’s *d *with Table 5.2 of your Warner text.

#### Section 2: Post Hoc Power Analysis

Open G*Power. Select the following options:

- Test family =
*t*tests. - Statistical test = Means: Difference between two independent groups (two groups).
- Type of power analysis = Post hoc: Compute achieved power.
- Tails(s) = Two.
- Effect size
*d*= Cohen’s*d*obtained from Section 1 above (using either*s*1 or*s*2). - α err prob = standard alpha level.
- Sample size group 1 =
*n*1 from Section 1 above. - Sample size group 2 =
*n*2 from Section 1 above. - Click
**Calculate**.

Provide a screenshot of your G*Power output. Report the observed power of this post hoc power analysis. Interpret the level of power in terms of rejecting a null hypothesis. Do you have sufficient power to reject a false null hypothesis? Interpret power in terms of committing a Type II error.

#### Section 3: A Priori Power Analysis

In G*Power, now select:

- Type of power analysis = A priori: Compute required sample size.
- Input effect size
*d*from Section 1. - Specify α err prob.
- Specify Power (1 – β) = .80.
- Set the Allocation ratio to 1 (that is, equal sample sizes).
- Click
**Calculate**.

Provide a screenshot of your G*Power output. Interpret the meaning of a .80 power value. Specifically, report the estimated *n*1, *n*2, and total *N *to achieve obtain a power of .80. How many total subjects ( *N*) would be needed to obtain a power of .80? Would you have expected a required *N *of this size? Why or why not?

Next, in G*Power, change the Cohen’s *d* effect size value obtained in Section 1 and set it to .50 (conventional “medium” effect size). Click **Calculate**. How many total subjects ( *N)* are needed to obtain a power of .80? Compare and contrast these two estimated *N*s.

In conclusion, reflect on the importance of conducting an a priori power analysis in psychological research plans.