13.10 Melanoma treatment. An experiment evaluated the use of genetically enginee
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Question
13.10 Melanoma treatment. An experiment evaluated the use of genetically engineered white blood cells in the treatment of patients with melanoma. Patients were divided into three cohorts. Patient cohort 1 received genetically engineered lymphocytes that were cultured ex vivo for 19 days. Cohort 2 received cells that were cultured for between 6 and 9 days. Cohort 3 received cells that were generated by a second rapid expansion performing after 8 to 9 days. Cell doubling times were as follows.
Cohort 1 8.7 11.9 10.0
Cohort 2 11.4 1.0 1.3 1.0 2.0 0.6 0.8 0.7 0.9 1.9
Cohort 3 0.9 3.3 1.2 1.1
Either create a file with these data or downloading the file MORGAN 2006. From the companion website. Most statistical programs require you to enter that data into two columns: for the explanatory variable (COHORT) and the other for the response variable (DOUBLING). Your final data table should have 2 columns and 18 rows.
If you do not have access to a statistical program, consider using Bright Stat. Com. Use of BrightStat.com is free. However, you must register as a user in order to access its ANOVA features.
Calculate the means, standard deviations, and sample sizes of each group. Use the “double the standard deviation” benchmark to assess whether group variances are significantly different. Is there evidence of heteroscedasticity?
Conduct Levene’s test for unequal variance. Show all hypothesis testing steps. What do you conclude?
Explanation / Answer
Result:
Calculate the means, standard deviations, and sample sizes of each group. Use the “double the standard deviation” benchmark to assess whether group variances are significantly different. Is there evidence of heteroscedasticity?
Conduct Levene’s test for unequal variance. Show all hypothesis testing steps. What do you conclude?
Test for Equal Variances: Cohort1, Cohort2, Cohort3
Method
Null hypothesis
All variances are equal
Alternative hypothesis
At least one variance is different
Significance level
= 0.05
95% Bonferroni Confidence Intervals for Standard Deviations
Sample
N
StDev
CI
Cohort1
3
1.60935
(0.021151, 606.185)
Cohort2
10
3.28133
(0.656929, 21.549)
Cohort3
4
1.12361
(0.150628, 20.875)
Individual confidence level = 98.3333%
Tests
Method
Test
Statistic
P-Value
Multiple comparisons
—
0.715
Levene
0.11
0.894
Calculated Levene test value = 0.11, P=0.894 which is > 0.05 level of significance.
Ho is not rejected.
There is no evidence to conclude that group variances are significantly different.
Null hypothesis
All variances are equal
Alternative hypothesis
At least one variance is different
Significance level
= 0.05
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