G*Power is a statistical software used in research to calculate statistical power. The software was used to conduct a-priori analyses and post-hoc analysis for problems provided in the assignment.
Problem 1
An a-priori analysis was conducted in g*power with a medium effect size i.e. |ρ| = 0.5, an alpha of .05, a power of 0.80, and a two-tailed test. The results showed the total sample size to prevent type II error was 26, as shown in table 1. A type error occurs in the rejection or non-rejection of a null hypothesis. A type II error, also referred to as a false positive, occurs when the researcher fails to reject the null hypothesis, which is false. On the other hand, a type I error, also referred to as a false positive, rejects a true null hypothesis. Increasing the sample size reduces the chance of a type II error as it increases the power of the test and increases the chances that the sample size represents the entire population.
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Table 1
G*Power Output for an a-priori Analysis
t tests - Correlation: Point biserial model
Analysis: A priori: Compute required sample size
Input: Tail(s) = Two
Effect size |ρ| = 0.5
α err prob = 0.05
Power (1-β err prob) = 0.8
Output: Noncentrality parameter δ = 2.9439203
Critical t = 2.0638986
Df = 24
Total sample size = 26
Actual power = 0.8063175
Problem 2
A post hoc analysis was performed with a sample size of 100, a medium effect size i.e. |ρ| = 0.5, an alpha of .01, and a two-tailed test. The power of the study was found to be 0.9990280. Power is the probability of making a correct decision e.g., rejecting the null hypothesis when it is false and avoiding a Type II error. The power value shows a 99.90% chance of making a correct decision and detecting a false null hypothesis. When comparing the difference between publicly traded enterprises and privately held firms, there will be a 99.90% of detecting a false null hypothesis by using the given sample size.
Table 2
G*Power Output for Post hoc analysis
t tests - Correlation: Point biserial model
Analysis: Post hoc: Compute achieved power
Input: Tail(s) = Two
Effect size |ρ| = 0.5
α err prob = 0.01
Total sample size = 100
Output: Noncentrality parameter δ = 5.7735027
Critical t = 2.6269311
Df = 98
Power (1-β err prob) = 0.9990280
Problem 3
An a-prior analysis was conducted using a large effect size i.e. |ρ| = 0.8, an alpha of .05, a power of .95, a two-tailed test, and three groups. The total number of participants needed in the sample is 30. The number of groups was three; hence the number of participants needed in each group was 10. The 10 participants would be chosen from hospital administrators, university administrators, and manufacturing administrators. Having an equal number of participants in each group is essential to have fair results and avoid bias.
Table 3
G*Power results for an a-priori analysis
F tests - ANOVA: Fixed effects, omnibus, one-way
Analysis: A priori: Compute required sample size
Input: Effect size f = 0.8
α err prob = 0.05
Power (1-β err prob) = 0.95
Number of groups = 3
Output: Noncentrality parameter λ = 19.2000000
Critical F = 3.3541308
Numerator df = 2
Denominator df = 27
Total sample size = 30
Actual power = 0.9676791
