This document discusses correlation analysis and how it is used to measure the linear relationship between two variables. It provides the formulas for calculating the population and sample correlation coefficients (ρ and r) and describes what each represents. An example is given of a study examining the relationship between grades in Calculus and Fortran Computer Language for 10 students. It asks whether the observed relationship is statistically significant and how the dependent variable could be predicted from the independent variable.

1. Biostatistics

2.  Correlation analysis is used to measure the
degree of linear relationship or association
between two variables.
 A scatter plot or scatter diagram is used to
show the between two variables

6.  The population correlation coefficient ρ
(rho) measures the strength of the
association between the variables
 The sample correlation coefficient r is an
estimate of ρ and is used to measure the
strength of the linear relationship in the
sample observations

7. where:
r = Sample correlation coefficient
n = Sample size
x = Value of the independent variable
y = Value of the dependent variable

8. Coefficients Verbal Interpretation
0.90-1.00
0.60-0.89
0.40-0.59
0.10-039
0.00-0.09
Very high correlatiom
High correlation
Moderate correlation
Low correlation
Very low correlation
Verbal Interpretation

10.  A study was made to determine the relationship
existing between the grade in Calculus and the
grade in Fortran Computer Language. A random
sample of 10 computer students in a certain
university were taken and the following are the
results:
 Is the obtained relationship significant at 0.05
level?
Student
No.
1 2 3 4 5 6 7 8 9 10
Calculus
(x)
75 83 80 77 89 78 92 86 93 84
Fortran (y) 78 87 78 76 92 81 89 89 91 94

11.  Predict the value of a dependent variable
based on the value of at least one
independent variable
 Explain the impact of changes in an
independent variable on the dependent
variable

13.  A researcher wants to know if there is a
relationship between hours spent in studying
a particular subject at home and the
achievement of the student in the subject. If a
significant relationship established, what
prediction equation could be used to estimate
achievement in the subject knowing the
number of hours spent in studying the
subject at home? Let α= 0.05

14. Student No. Hours Spent (X) Achievement Grade
1
2
3
4
5
6
7
8
9
10
2.5
2.75
1.5
1.0
3.0
2.5
1.25
3.5
1.5
2.0
89
88
82
77
90
91
80
93
81
86
What would be the predicted achievement grade of a student who spent
3.25 hours studying the subject?