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 your statistical software, you will also use the G*Power 3 software to complete this assignment. Answer each question, providing statistical software or G* Power analysis output when necessary to support your answer.
Use the data file provided by your instructor for this assignment. You will be conducting a post-hoc power analysis and an a priori power analysis on an independent samples t-test with extra credit as the grouping variable (no ＝ 1; yes ＝ 2) and Total 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 the supplied data set, conduct an independent samples t-test with extra credit as the grouping variable (no ＝ 1; yes ＝ 2) and Total as the outcome variable.
Paste the output and then report:
The sample size for no (n1) and sample size for yes (n2).
The means for no (M1) and yes (M2) on Total.
The calculated mean difference (M1 – M2).
The standard deviations for no (s1) and yes (s2) on Total.
The Levene test (homogeneity of variance assumption) and interpretation.
t, degrees of freedom, t value, and p value. State whether or not to reject the null hypothesis. Interpret the results.
Calculate Cohen′s d effect size and interpret it. Specifically, if the homogeneity of variance assumption is met, calculate Cohen′s d as described below. 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.
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 ＝ 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.
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).
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.
Written communication: Should be free of errors that detract from the overall message.
APA formatting: References and citations are formatted according to current APA style guidelines. Refer to Evidence and APA for more information on how to cite your sources.
Length: 8–10 double-spaced pages, in addition to the title page and references page.