Question

In: Statistics and Probability

The following data was collected in a clinical trial evaluating a new compound designed to improve...

  1. The following data was collected in a clinical trial evaluating a new compound designed to improve wound healing in trauma patients. The new compound was compared against a placebo. After treatment for 5 days with the new compound or placebo, the extent of wound healing was measured and the data are shown below. (10 points)

Percent Wound Healing

Treatment

0-25%

26-50%

51-75%

76-100%

New Compound (n=125)

15

37

32

41

Placebo (n=125)

36

45

34

10

Is there a difference in the extent of wound healing by treatment? (Hint: Are treatment and the percent wound healing independent?) Run the appropriate test at a 5% level of significance.

  1. Use the data in Problem #1 and pool the data across the treatments into one sample of size n=250. Use the pooled data to test whether the distribution of the percent wound healing is approximately normal. Specifically, use the following distribution: 30%, 40%, 20% and 10% and a=0.05 to run the appropriate test. (10 points)

Percent Wound Healing

Treatment

0-25%

26-50%

51-75%

76-100%

Total

Number of Patients

51

82

66

51

250

Solutions

Expert Solution

Chi-square test of independence

The Chi-square test of independence is performed to test the association between the extent of wound healing and the type of treatment

Hypothesis:

H0​: The two variables are independent

Ha: The two variables are dependent

Chi-Square statistic:

The observed values are,

Percent Wound Healing
Treatment 0-25% 26-50% 51-75% 76-100% Total
New Compound (n=125) 15 37 32 41 125
Placebo (n=125) 36 45 34 10 125
Total 51 82 66 51 250

The expected values are obtained using the following formula,

Percent Wound Healing
Treatment 0-25% 26-50% 51-75% 76-100% Total
New Compound (n=125) 125*51/250=25.5 125*82/250=41 125*66/250=33 125*51/250=25.5 125
Placebo (n=125) 125*51/250=25.5 125*82/250=41 125*66/250=33 125*51/250=25.5 125
Total 51 82 66 51 250

The Chi-Square value is obtained using the formula

Observed, Oi Expected, Ei
15 25.5 4.32
37 41 0.39
32 33 0.03
41 25.5 9.42
36 25.5 4.32
45 41 0.39
34 33 0.03
10 25.5 9.42
Sum 28.33

Critical value:

The critical value for the chi-square statistic is obtained from the chi-square distribution table for,

degree of freedom = (r-1)(c-1) = (2-1)(4-1) = 3

Where r is the number of rows and c is the number of columns in the table.

For significance level = 0.05 and degree of freedom = 3, the critical value is,

Conclusion:

Since the chi-square value is greater than the critical value, It can be concluded that the null hypothesis is rejected at a 5% significance level.

Hence the extent of wound healing and the type of treatment are dependent.

Chi-Square Goodness of fit test

The Chi-Square Goodness of fit test is used here to test whether the samples are from normal distribution within a given proportion.

Hypothesis:

Null hypothesis: There is no significant difference between the observed frequency and the expected frequency.

Chi-Square statistic:

The observed values are,

Treatment Observed
0-25% 51
26-50% 82
51-75% 66
76-100% 51
Total 250

The expected values are obtained by multiplying the total population by the given proportion,

Treatment Expected
0-25% 250*0.30=75
26-50% 250*0.40=100
51-75% 250*0.20=50
76-100% 250*0.10=25

The Chi-Square statistic is obtained using the formula,

Treatment Observed Expected
0-25% 51 75 7.68
26-50% 82 100 3.24
51-75% 66 50 5.12
76-100% 51 25 27.04
Total 43.08

Critical value:

The critical value for the chi-square statistic is obtained from the chi-square distribution table for,

degree of freedom = 4-1 = 3 and significance level = 0.05

Conclusion:

Since the chi-square statistic is greater than the critical value at a 5% significance level. it can be concluded that the null hypothesis is rejected. Hence we can conclude that the distribution of percent wound healing doesn't follow a normal distribution.


Related Solutions

The following data was collected in a clinical trial evaluating a new compound designed to improve...
The following data was collected in a clinical trial evaluating a new compound designed to improve wound healing in trauma patients. The new compound is compared against a placebo. After treatment for 5 days with the new compound or placebo the extent of wound healing is measured and the data are shown below. Percent Wound Healing Treatment 0-25% 26-50% 51-75% 76-100% New Compound (n=125) 15 37 32 41 Placebo (n=125) 36 45 34 10 Is there a difference in the...
data are collected in a clinical trial evaluating a new compound designed to improve wound healing...
data are collected in a clinical trial evaluating a new compound designed to improve wound healing in trauma patients. The new compound is compared against a placebo. After treatment for 5 days with the new compound or placebo, The extent of wound healing is measured and the data are shown in Table 7-6. Is there a difference in the extent of wound healing by Treatment? (Hint: are treatment and the percent wound healing independent? ) run the appropriate test at...
1. The following data was collected in a clinical trial evaluating a new compound designed to...
1. The following data was collected in a clinical trial evaluating a new compound designed to improve wound healing in trauma patients. The new compound was compared against a placebo. After treatment for 5 days with the new compound or placebo, the extent of wound healing was measured and the data are shown below Percent Wound Healing Treatment 0-25% 26-50% 51-75% 76-100% New Compound (n=125) 15 37 32 41 Placebo (n=125) 36 45 34 10 Is there a difference in...
A clinical trial evaluates a new compound designed to improve wound healing in trauma patients. The...
A clinical trial evaluates a new compound designed to improve wound healing in trauma patients. The new compound is compared against a placebo. After treatment for 5 days with the new compound or placebo, the extent of wound healing is measured. See chart below: Wound Healing by Treatment Percent of Wound Healing Treatment 0-25 26-50 51-75 76-100 New Compound (n=125) 15 37 32 41 Placebo (n=125) 36 45 34 10 Is there a difference in the extent of wound healing...
A clinical trial evaluates a new compound designed to improve wound healing in trauma patients. The...
A clinical trial evaluates a new compound designed to improve wound healing in trauma patients. The new compound is compared against a placebo. After treatment for 5 days with the new compound or placebo, the extent of wound healing is measured and the data are shown in table 7-51. Is there a difference in the extent of wound healing by treatment? Run the appropriate test at a 5% level of significance. (Hint : Are treatment and the percent of wound...
7. The following data were collected in a clinical trial to compare a new drug to...
7. The following data were collected in a clinical trial to compare a new drug to a placebo for its effectiveness in lowering total serum cholesterol. New Drug (n=75) Placebo (n=75) Total Sample (n=150) Mean (SD) Total Serum Cholesterol 182.0 (24.5) 206.3 (21.8) 194.15 (23.2) % Patients with Total Cholesterol < 200 78.0% 65.0% 71.5% a) Generate the 95% confidence interval for the difference in mean total cholesterol levels between treatments b) Generate a 95% confidence interval for the difference...
1. The data in Table 7–6 were collected in a clinical trial to evaluate a new...
1. The data in Table 7–6 were collected in a clinical trial to evaluate a new compound designed to improve wound healing in trauma patients. The new compound was compared against a placebo. After treatment for 5 days with the new compound or placebo, the extent of wound healing was measured. Is there a difference in the extent of wound healing between the treatments? (Hint: Are treatment and the percent wound healing independent?) Run the appropriate test at a 5%...
A clinical trial was conducted using a new method designed to increase the probability of conceiving...
A clinical trial was conducted using a new method designed to increase the probability of conceiving a girl. As of this​ writing, 962 babies were born to parents using the new​ method, and 863 of them were girls. Use a 0.01 significance level to test the claim that the new method is effective in increasing the likelihood that a baby will be a girl. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final...
6. A clinical trial was conducted using a new method designed to increase the probability of...
6. A clinical trial was conducted using a new method designed to increase the probability of conceiving a girl. As of this​ writing, 961 babies were born to parents using the new​ method, and 898 of them were girls. Use a 0.01 significance level to test the claim that the new method is effective in increasing the likelihood that a baby will be a girl. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and...
A clinical trial was conducted using a new method designed to increase the probability of conceiving...
A clinical trial was conducted using a new method designed to increase the probability of conceiving a girl. As of this​ writing, 935 babies were born to parents using the new​ method, and 895 of them were girls. Use a 0.05 significance level to test the claim that the new method is effective in increasing the likelihood that a baby will be a girl. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT