Calculating power, statistics assignment help

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Mathematics

Description

Using the Week 1 Dataset (SPSS document) you used for the Week 1 Assignment, complete the following:

  1. Calculate the minimum sample size you will need (using manual calculations) to conduct a t test to determine if the difference in age in people with and without hypertension is significant. Use the standard deviation for age calculated in week 1. Assume a 2-tailed test with alpha = .05 and Power = 80% and that the difference you expect to observe between the 2 groups is 5 years.
  2. Using two different effect sizes in addition to the one used in part 1, perform three power analyses of the sample size computed in step 1 using G*Power. (Assume a 2-tailed independent sample t test with alpha set at .05)
  3. Perform a power analysis using G*Power using the actual sample size presented in the dataset for week 1 (180) and an effect size of .30. What does this mean in terms of the study and the probability of experiencing a type 2 error?

Resources

Daniel, WW & Cross, CL. (2013). Biostatistics: A Foundation for Analysis in the Health Sciences. Hoboken, NJ: Wiley.

  • Chapter 6, “Estimation” ( pp. 161 –213)
  • Chapter 7, “Hypothesis Testing” ( pp. 214 –303)

http://www.gpower.hhu.de/

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Explanation & Answer

attached is my complete solution

Question 1:
The t-test is used to compare two group means. The formula for sample size for a two-tailed test
comparing two independent means is:

n 

2 2  Z1   Z1 /2 

2

 amount of difference 

2

For alpha = .05 and Power = 80%, the critical z-values are obtained from the table

Z1   0.84
Z1 /2  1.96
According to the descriptive statistics, we have that the standa...


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