Question

Consider a study that compares the Atkins diet to a conventional diet. A study at the University of Pennsylvania selected a sample of 63 subjects from the local population of obese adults. Researchers randomly assigned 33 to the Atkins diet and 30 subjects to a conventional diet. Test whether there is a significant difference in the mean weight loss (measured in pounds) across the two different diet programs.

Using software:

Generate summary statistics (central tendency and variability measures) for the two samples and briefly summarize what they say.

b. Conduct a test of significance for the difference between the mean weight across the different diet programs. Be sure to show the output from the software and interpret the results.

c. Construct a 95% confidence interval for the difference parameter in mean weight lost and make an interpretation.

d. Finally, are there any other factors, besides the type of diet, that could possibly influence weight loss (identify at least 2)? Include a brief explanation of each.

Atkins   Conventional  
27   26  
31   26  
34   29  
31   24  
28   25  
32   22  
33   27  
27   24  
34   25  
25   28  
31   30  
26   27  
28   25  
30   23  
26   20  
26   22  
31   29  
34   28  
27   21  
28   25  
33   22  
26   24  
26   22  
30   25  
26   29  
34   24  
25   26  
32   21  
29   22  
33   21  
27      
29      
25      
      
      

Answer 1

Using excel:

a. Generating summary statistics for the given data:

Data -- > Data Analysis Tool pack --> Descriptive Statistics:

The summary statistics reveal that the mean weight of subjects under Atkins diet is greater than those under conventional diet.Also the former exhibits higher variability as compared to the latter. To test how significant the increase in weight and their variability is, we may go for independent samples t test for means and F test for variability.

b. To test whether difference between the mean weight across the different diet programs is significant, we need to run a independent sample t test which assumes equality of its variances. Hence, first testing the equality of its variances using F test:

To test:

Vs

where denote the variances of the groups Atkins and Conventional diet.

Running a t test accordingly:

To test: Vs  

where denote the mean weight of subjects under Atkins and Conventional diet.

Since, the p-value of the F test 0.209 > 0.05, we fail to reject H₀ at 5% level of significance.We may conclude that there is enough evidence to assume that the variances are equal.

Since, the p-value of the t test 0.000 < 0.05, we may reject H₀ at 5% level of significance.We may conclude that there is enough evidence to conclude that there is a significant difference between the mean weight across the different diet programs.

(c) A 95% confidence interval for the difference parameter in mean weight lost can be constructed using the formula:

where, is the pooled variance

Substituting the values:

  

= 3.036

Using excel function TINV(0.05,61) = 1.9996

Substituting the value, we get,

(3.251,6.313)

Hence,  95% confidence interval for the difference parameter in mean weight lost . It implies that if we draw 100 repeated samples, the actual mean weight lost would lie within (3.251,6.313) 95 out of 100 times.

(d) Two common factors that trigger weight loss would be Physical activity and a broader cause that may include various social (eg. Money) and environmental factors (Disease: Medication and Drugs). An increase in physical activity causes decrease in weight. Also, Money place a major role in nutrition (acting as an instrumental variable) of the individual thereby affecting his diet.Specific Drugs and disease conditions can also trigger weight loss.