Question

Data from the framingham study was extracted to determine prevalence of diabetes based on hemoglobin A1c values (%). The laboratory performed a comparison study of Hb A1c in 41 participant using two different analyzers, the DCA 2000 and the pathology. the purpose of the comparison study is to determine if there is a significant difference in results by two methods using correlation, regression and hypothesis testing. Report:

a. Pearson correlation.

b. Regression (R2, slope and intercept).

c. Hypothesis testing of this matched continuous data using provided data below.

d. line plot

e. provide null hypothesis and research hypothesis.

f. explain if these results indicate the two methods provided within 95% confidence, a statistical difference in results.

	Hemoglobin A1c values DCA 2000	Pathology
1	10.4	10.3
2	13	11.9
3	11.5	11.2
4	7.3	7.8
5	7.5	8.1
6	8.2	8.2
7	8.8	8.6
8	8.6	8.3
9	7.5	7.7
10	8.3	8.6
11	7.9	7.9
12	7.9	7.7
13	7.8	7.8
14	8.9	7.1
15	7.4	7.4
16	7.6	7.8
17	8.3	8.2
18	8.2	7.9
19	9.2	9.3
20	9.3	9.2
21	7.9	8.3
22	12	12.3
23	14	14.7
24	14	13.7
25	9.9	9.9
26	12	11.9
27	8.7	8.8
28	12.3	12.1
29	11.7	11.8
30	10.1	10.6
31	13.4	12.8
32	11.2	10.4
33	9.2	9.3
34	7.7	8.1
35	9.7	9.7
36	10.1	10
37	7.4	8.2
38	8.3	8.6
39	11.5	11.3
40	11.1	12
41	14	14.2

Answer 1

a. Pearson correlation.

r = 0.972

b. Regression (R2, slope and intercept).

R2 = 0.945

Slope = 0.9503

Intercept = 0.4824

c. Hypothesis testing of this matched continuous data using provided data below.

The hypothesis being tested is:

H₀: β₁ = 0

H₁: β₁ ≠ 0

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the relationship is significant.

d. line plot

e. provide null hypothesis and research hypothesis.

The hypothesis being tested is:

H₀: β₁ = 0

H₁: β₁ ≠ 0

f. explain if these results indicate the two methods provided within 95% confidence, a statistical difference in results.

Since there is a relationship between the variables, there is a statistical difference in results.