Question

Text book: Essentials of Biostatistics in Public Health 3rd ed. by Lisa Sullivan

Instructor provided question: An SBB instructor wants to determine if there is a correlation between the students incoming GPA and their overall score on their ASCP exam. Several potential confounders were also considered including years of clinical practice in blood bank and gap between completing the program and taking the exam. Perform the appropriate analysis on the data below and interpret the results. Do SBB ASCP scores correlate with student’s GPAs? Do confounders exist? Justify your response.

SBB ASCP Score	GPA	BB Experience (years)	Gap (months)
698	3.98	3	0.5
540	3.12	8	0.25
572	3.24	2	2
440	3.46	10	3
401	3.71	7	12
380	2.95	13	5
660	3.55	15	0.5
398	2.62	3	4
498	3.16	2	2
557	3.32	20	0.5
613	3.48	2	1
474	3.21	5	3
487	2.89	7	2
522	3.81	2	3
501	3.65	9	2
422	2.86	5	1
475	2.98	8	1
555	3.71	10	1
514	2.98	17	0.5
439	2.62	2	2

Answer 1

We will solve this problem with the help of Excel.

First, we would try to find the correlation between the students incoming GPA and their overall score on their ASCP exam.

Load the data into Excel.

Go to Data>Megastat.

Select the option Correlation/Regression and go to Regression.

Select GPA as the independent variable, x.

Select SBB ASCP Score as the dependent variable, y.

Click OK.

The output will be as follows:

	r²	0.336	n	20
	r	0.579	k	1
	Std. Error	71.815	Dep. Var.	SBB ASCP Score
ANOVA table
Source	SS	df	MS	F	p-value
Regression	46,896.8742	1	46,896.8742	9.09	.0074
Residual	92,833.3258	18	5,157.4070
Total	1,39,730.2000	19
Regression output					confidence interval
variables	coefficients	std. error	t (df=18)	p-value	95% lower	95% upper
Intercept	95.9902
GPA	125.9754	41.7763	3.015	.0074	38.2068	213.7441

The regression equation of the model is:

y = 95.9902 + 125.9754*x

Or

SBB ASCP Score = 95.9902 + 125.9754*GPA

This regression equation suggests that there is a positive correlation between SBB ASCP Score and GPA of the student. For every one-point increment in GPA, SBB ASCP Score will increase by 125.9754.

If the confounders are also considered including years of clinical practice in the blood bank and the gap between completing the program and taking the exam, then we gave to perform a regression analysis again.

Load the data into Excel.

Go to Data>Megastat.

Select the option Correlation/Regression and go to Regression.

Select GPA, BB Experience (years)​​​​​​​, Gap (months)​​​​​​​ as the independent variable, x.

Select SBB ASCP Score​​​​​​​ as the dependent variable, y.

Click OK.

The output will be as follows:

	R²	0.743
	Adjusted R²	0.695	n	20
	R	0.862	k	3
	Std. Error	47.369	Dep. Var.	SBB ASCP Score
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,03,828.7048	3	34,609.5683	15.42	.0001
Residual	35,901.4952	16	2,243.8434
Total	1,39,730.2000	19
Regression output					confidence interval
variables	coefficients	std. error	t (df=16)	p-value	95% lower	95% upper
Intercept	102.7217
GPA	140.8871	27.7325	5.080	.0001	82.0967	199.6774
BB Experience (years)	-0.8510	2.0352	-0.418	.6814	-5.1654	3.4634
Gap (months)	-21.2045	4.2165	-5.029	.0001	-30.1431	-12.2660

The regression equation of the model is:

y = 102.7217 + 140.8871*x₁ -0.8510*x₂ -21.2045*x₃

Or

SBB ASCP Score = 102.7217 + 140.8871*GPA -0.8510*BB Experience (years) -21.2045*Gap (months​​​​​​​)

This regression equation suggests that there is a positive correlation between SBB ASCP Score and GPA of the student. For every one-point increment in GPA, SBB ASCP Score will increase by 140.8871 when BB Experience (years) and Gap (months​​​​​​​) are kept constant. But when the confounders are increased, then the SBB ASCP Score will decrease making a negative correlation between SBB ASCP Score and GPA of the student.