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Owner: muellerr1
Created: Apr 17, 2010
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LSA measurements 6-3
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Description: Random samples of 100 women were taken from each of four groups: Group A -- Normal Controls; Group B -- Patients with benign breast disease; Group C -- Patients with primary breast cancer; Group D -- Patients with recurrent metastatic breast cancer. For each person sampled, a serum lipid-bound sialic acid (LSA) measurement was taken in mg/dl. Conduct a complete analysis (including checking assumptions) to determine if there is a difference in the mean LSA measurement among the four different disease classifications. Use a significance level of 0.01.

 <report1>

Report one contains the histogram for LSA measurements. The histograms do appear to be somewhat bell-shaped and symmetric. The data is interval/ratio in nature. Two assumptions have been met for the use of the ANOVA.

<report2>

Report two contains the summary statistics for LSA measurements. The mean LSA measurements for Group D are the highest (23.292), followed by Group B (20.48), Group C (19.976) and lastly Group A (16.249).  Twice the smallest standard deviation (2.684053) equals 5.368106, which  exceeds the largest standard deviation  (3.1308398) and satisfies the assumption of equal population variances. 

The null hypothesis for this study is that there is no difference in the mean LSA measurement across the four breast cancer groups, which will be tested against the alternative of at least one difference. The significance level for the test is 0.01; thus the null hypothesis will be rejected if the p-value of the test is less than 0.01.

<report3>

Report three contains the one way ANOVA for the LSA measurements.

At the 0.01 level (f=96.408394, p=<0.0001) there is evidence of at least one difference in the mean LSA measurement across the four different groups (A-normal, B- patients with benign breast disease, C-patients with primary breast cancer, D- patients with recurrent metastatic breast cancer).

The first interval estimates the mean LSA measurement between normal patients (A) and benign disease (B). Both upper and lower limits are positive, so this allows one to conclude that the mean LSA level for benign breast disease patients is between 2.9246638 and 5.5373363 mg/dl greater than the means for normal patients. The interval estimating the difference in the mean between primary breast cancer (C) and normal is also positive (upper and lower limit), so we can conclude that the mean LSA measurement  for primary breast cancer is between 2.4206638 and 5.0433336 mg/dl greater than the normal patients. The interval estimating the difference in the mean between recurrent metastatic breast cancer (D) and normal breasts is also positive (upper and lower limit), so we can conclude that the mean LSA measurement for recurrent metastatic breast cancer is between 5.73663 and 8.349337 mg/dl greater than the normal breast patients.

The second interval estimates the mean LSA measurement between (B) benign disease and primary breast cancer (C) has a negative lower limit and a positive upper limit, so nodifferences can be detected in the mean LSA measurements for these two groups. The interval estimating the difference in the mean between benign disease and recurrent metastatic breast cancer has both positive upper and lower limits. So we can conclude that the mean LSA measurement for D (metstatic recurrent breast cancer) is between 1.5056638 and 4.118336 mg/dl greater than group B (benign disease).

The third interval estimates the mean LSAmeasurement between (C) primary breast cancer) and (D) metastatice recurrent breast cancer. Again the upper and lower limits are positive, allowing one to conclude that the mean LSA measurement for metastatic disease (D) is between 2.0096638 and 4.6223364 mg/dl greater than group (C) primary breast cancer.

We can conclude that the LSA measurements for the normal breast patients are lower than the patients with both benign and cancerous disease. And those with recurrent metastatic breast cancer have higher LSA levels than both the benign breast disease and primary breast cancer patients.

 

Result 1: Histogram for LSA measurements 6-3   [Info]
Right click to copy

Result 2: Column Statistics for LSA measurements 6-3   [Info]
Summary statistics for LSA:
Group by: Group
Group n Mean Variance Std. Dev. Std. Err. Median Range Min Max Q1 Q3
A 100 16.249 7.20414 2.684053 0.2684053 16.25 10.1 10.8 20.9 14.6 18.45
B 100 20.48 8.690303 2.947932 0.2947932 20.3 13.7 13.3 27 18.35 22.55
C 100 19.976 9.069721 3.0115979 0.30115977 20 14.7 13.1 27.8 18.15 21.9
D 100 23.292 9.802157 3.1308398 0.31308398 23.3 20.6 13.1 33.7 21.9 25.05

Result 3: One Way ANOVA for LSA measurements 6-3   [Info]
Analysis of Variance results:
Responses stored in LSA.
Factors stored in Group.
Factor means
Group n Mean Std. Error
A 100 16.249 0.2684053
B 100 20.48 0.2947932
C 100 19.976 0.30115977
D 100 23.292 0.31308398


ANOVA table
Source df SS MS F-Stat P-value
Treatments 3 2513.824 837.9413 96.408394 <0.0001
Error 396 3441.866 8.691581
Total 399 5955.69


Tukey 99% Simultaneous Confidence Intervals

A subtracted from
Lower Upper
B 2.9246638 5.5373363
C 2.4206638 5.033336
D 5.736664 8.349337


B subtracted from
Lower Upper
C -1.8103362 0.8023363
D 1.5056638 4.118336


C subtracted from
Lower Upper
D 2.0096638 4.6223364

HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=13684">LSA measurements 6-3</A>

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