Question

Melanoma treatment. An experiment evaluated the use of genetically engineered white blood cells in the treatment of patients with melanoma.^y 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	1.4	1.0	1.3	1.0	1.3	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 download the file MORGAN2006.* from the companion website. Most statistical programs require you to enter that data into two columns: one column 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 BrightStat. com.^z Use of BrightStat.com is free. However, you must register as a user in order to access its ANOVA features.

(a)   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?

(b)   Conduct Levene’s test for unequal variance. Show all hypothesis testing steps. What do you conclude?

I have my data from SPSS, but I am having some difficulty interpreting the results.  

Answer 1

Answer:

Either create a file with these data or download the file MORGAN2006.* from the companion website. Most statistical programs require you to enter that data into two columns: one column 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 BrightStat. com.^z Use of BrightStat.com is free. However, you must register as a user in order to access its ANOVA features.

Spss used

spss syntax:

ONEWAY doubling BY cohort
/STATISTICS DESCRIPTIVES HOMOGENEITY
/MISSING ANALYSIS.

(a)   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?

Descriptives
doubling
	N	Mean	Std. Deviation	Std. Error	95% Confidence Interval for Mean		Minimum	Maximum
					Lower Bound	Upper Bound
Cohort 1	3	10.200	1.6093	.9292	6.202	14.198	8.7	11.9
Cohort 2	11	1.173	.4606	.1389	.863	1.482	.6	2.0
Cohort 3	4	1.625	1.1236	.5618	-.163	3.413	.9	3.3
Total	18	2.778	3.5148	.8284	1.030	4.526	.6	11.9

Large sd= 1.6093

Smaller sd = 0.4606

Ratio of variances = 1.6093^2/0.4606^2 = 12.2075 which is greater than 2.

This tells us that group variances are significantly different. There is evidence of heteroscedasticity.

(b)   Conduct Levene’s test for unequal variance. Show all hypothesis testing steps. What do you conclude?

H_1: the variances are not equal for at least one pair

SPSS output

Test of Homogeneity of Variances
		Levene Statistic	df1	df2	Sig.
doubling	Based on Mean	4.259	2	15	.034
	Based on Median	1.527	2	15	.249
	Based on Median and with adjusted df	1.527	2	7.176	.280
	Based on trimmed mean	3.830	2	15	.045

Calculated test statistic ( based on median) 1.527, P=0.249 which is > 0.05 level of significance. Ho is not rejected.

We conclude that the variances are equal.