# Statistics Homework for MathematicsExpert

### 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 ( n1) and sample size for females ( n2).
• The means for males ( M1) and females ( M2) on HR1.
• The calculated mean difference ( M1 – M2).
• The standard deviations for males ( s1) and females ( s2) 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 ( M1 – M2) by either s1 or s2. Violation of the homogeneity of variance assumption requires calculation of Spooled. Homogeneity assumed:

Cohen’s d = ( M1 – M2) ÷ s1 or Cohen’s d = ( M1 – M2) ÷ s2

To be comprehensive, report Cohen’s d based on a calculation with s1 and a calculation with s2. 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 s1 or s2).
• α err prob = standard alpha level.
• Sample size group 1 = n1 from Section 1 above.
• Sample size group 2 = n2 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 n1, n2, 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 Ns.

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

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