Researchers have recently hypothesized that patients with myotonic dystrophy (a neuromuscular disease) also have hyperparathyroidism, a syndrome caused by an overactive parathyroid gland. To test this hypothesis, they measured the body’s response to a calcium challenge in patients with myotonic dystrophy, patients with other types of dystrophy (nonmyotonic dystrophy), and normal subjects. One of the biochemical variables they measured was the amount of cAMP excreted by the kidneys. Elevated renal cAMP excretion would be consistent with hyperparathyroidism. The data is contained in the screenshot, where two variables are listed: cAMP – Amount of cAMP excreted by the kidneys, measured in nmol/dL. patient – A factor defining the clinical status of the patient, with three levels: 1, Normal Patient in control group, with no disease. 2, Myotonic Patient with myotonic dystrophy. 3, Nonmyotonic Patient with nonmyotonic dystrophy. (a) Perform an analysis of variance calculation to test the null hypothesis that the mean cAMP levels are the same in all three groups of people. Comment on your results. (b) Perform both (i) a pairwise comparison with a Bonferonni correction and (ii) a Tukey honest significant differences analysis to determine where the significant differences lie. (c) Explain whether you conclude that there is evidence that cAMP excretion is elevated in myotonic dystrophic subjects.

Researchers have recently hypothesized that patients with myotonic dystrophy (a neuromuscular disease) also have hyperparathyroidism, a syndrome caused by an overactive parathyroid gland. To test this hypothesis, they measured the body’s response to a calcium challenge in patients with myotonic dystrophy, patients with other types of dystrophy (nonmyotonic dystrophy), and normal subjects. One of the biochemical variables they measured was the amount of cAMP excreted by the kidneys. Elevated renal cAMP excretion would be consistent with hyperparathyroidism.

The data is contained in the screenshot, where two variables are listed:

cAMP – Amount of cAMP excreted by the kidneys, measured in nmol/dL.
patient – A factor defining the clinical status of the patient, with three levels:
- 1, Normal Patient in control group, with no disease.
- 2, Myotonic Patient with myotonic dystrophy.
- 3, Nonmyotonic Patient with nonmyotonic dystrophy.

(a) Perform an analysis of variance calculation to test the null hypothesis that the mean cAMP levels are the same in all three groups of people. Comment on your results.

(b) Perform both (i) a pairwise comparison with a Bonferonni correction and (ii) a Tukey honest significant differences analysis to determine where the significant differences lie.

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54
CAMP
1.30
1.30
1.34
1.44
1.44
1.50
1.50
1.68
2.00
2.51
2.98
3.31
3.37
3.70
4.65
.48
.60
.69
.69
.78
.78
.91
.98
1.01
1.07
1.07
1.27
1.27
patient
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
3
3
3
var
var
var
var
var

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60
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CAMP
.61
.61
.77
.77
.77
.85
.96
1.01
1.01
1.11
1.11
1.28
.43
.68
.69
.75
.75
.75
.82
.95
1.11
1.23
1.30
1.30
1.34
1.44
1.44
1.50
1.50
1.68
2.00
2.51
patient
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
var
var
var
var
var

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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