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Hypothesis Testing: Bio statistics

Please read the attachment carefully before attempting the problem.

Minitab is the preferred program for analysis.

Excel is not acceptable.

CD4 % LYMPHOCYTES WBC (X1000/ul) HB (g/dl) PLATELETS (x1000/ul) MCV (f/l)
A B C D E

1. Analyze the test data (for the assays given above A, B, C, C, D, E) at the 1, 5, 9 month time points.

2. Determine if the results for each assay at the respective time points do not differ at the 95% significance level.

For Example given assay A (CD4%) there are 160 values for each time point (i.e. 160 for 3 mos, 160 for 5 mos, 160 for 9 mos).

We want to determine if the data sets for this assay at the 3 time points are "the same" (i.e. do not differ from each other) with a 95% significance.

Do this analysis for the remaining assays (B, C, D, and E) and summarize the results. (i.e. do the data sets for the respective assays at the time points differ significantly or can the time points be combined such that each assay has?
3 X 160 values for each assay.

Attachments

Solution Preview

CD4 % LYMPHOCYTES WBC (X1000/ul) HB (g/dl) PLATELETS (x1000/ul) MCV (f/l)
A B C D E

1. Analyze the test data (for the assays given above A, B, C, C, D, E) at the 1, 5, 9 month time points.

The basic descriptive Statistics are given below

Descriptive Statistics:

VISIT
Variable MONTHS Mean StDev Q1 Median Q3
CD4 % LYMPHOCYTES 3 29.231 7.695 24.070 28.555 33.978
5 29.097 7.474 23.825 29.061 33.848
9 29.360 6.033 25.890 30.111 34.073

WBC (X1000/ul) 3 9.821 2.270 8.325 9.800 11.000
5 9.465 2.590 7.500 9.200 10.800
9 9.486 2.947 7.400 8.700 11.075

HB (g/dl) 3 10.503 0.884 9.925 10.600 11.175
5 10.630 0.938 10.025 10.600 11.200
9 10.546 1.048 9.900 10.500 11.200

PLATELETS (x1000/ul) 3 387.61 122.93 310.00 372.50 453.25
5 411.7 127.2 335.5 397.0 477.5
9 411.8 138.3 316.0 404.5 490.8

MCV (f/l) 3 78.401 4.886 76.000 78.650 81.575
5 74.353 5.785 70.800 75.100 78.000
9 70.513 4.838 66.925 71.000 74.075

A visual comparison of these figures can be done in a box plot

The box plot suggests the presence of few outliers is the data sets. These outliers will have an undue influence in the estimates of parameters.

2. Determine if the results for each assay at the respective time points do not differ at the 95% significance level.

• CD4 % LYMPHOCYTES

H0: There is no significant difference in the mean CD4 % LYMPHOCYTES at the three time points.

H1: There is significant difference in the mean CD4 % LYMPHOCYTES at the three time points.

The test statistic used is F-test (one way ANOVA).

Decision rule: Reject the null hypothesis if the p value is ...

Solution Summary

This solution gives the step by step method for ANOVA using MINITAB. The significance levels for clinical test data are provided. The results for each assay at the respective time points do not differ at the 95% significance levels.

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