Question

In the following situation we want to compare the mean responses in several populations.

It is generally accepted that regular exercise provides health benefits to individuals with type 2 diabetes, although the exact exercise regimen (aerobic vs. resistance vs. both) is unclear. The subjects in this study were sedentary 30- to 75-year-old adults with type 2 diabetes and elevated hemoglobin A1c levels above 6.5%. The level of hemoglobin A1c correlates very well with a person's recent overall blood sugar levels. If the blood sugars have generally been running high during the previous few months, the level of hemoglobin A1c will be high. In a randomized controlled study, 44 subjects were assigned to a nonexercise control group, 78 to resistance training only, 75 to aerobic exercise only, and 79 to combined aerobic and resistance training. The weekly duration of exercise was similar for all three exercise groups, and subjects remained on the exercise regimens for nine months. At the end of nine months, the hemoglobin A1c levels of subjects were measured. Identify the populations and the response variable. Then give I, the ni, and N. Finally, give the degrees of freedom of the ANOVA F statistic.

Answer 1

I = 4

N = 276

Degrees of freedom for Numerator = 3

Degrees of freedom for Denominator = 272

Explanation:

Response variable the hemoglobin A1c levels.

There are four independent groups. So I = 4

44 subjects were assigned to a non-exercise control group. So n-control = 44,

78 to resistance training only, therefore n-resistance= 78

75 to aerobic exercise only, therefore n-aerobic = 75

79 to combined aerobic and resistance training, therefore, n-combined= 79

N = Total number of observations = 44 + 78 +75 + 79 = 276

Degrees of freedom for Numerator = # of independent variable - 1

= k - 1 = 4 - 1 = 3

Degrees of freedom for Denominator = N - k = 276 - 4 = 272