Measures of correlation

1. Republic of the Philippines
MINDANAO STATE UNIVERSITY
COLLEGE OF EDUCATION
Fatima, General Santos City
Module 5: Education Statistics
Lesson 5: Measures of Variability and
Correlation: Measures of Correlation
Presented to:
Dr. Ava Clare Marie O. Robles
Class Schedule: MTh / 1:00-2:30
Presented by:
Abbygale Jade P. Delos Reyes

2. To compute the
Pearson’s Product
Moment
Correlation
accurately.

3. Pearson’s Product-
Moment Correlation
• This measure of relation is used
when factors to be correlated are
both metric data. By metric data
are meant measurements, which
can be subjected to the four
fundamental operations.
Conception, Benjamin.et.al. (2016). LET Reviewer: MET Review Center, Manila.

4. 1. Compute the sum of each set of scores
(SX, SY).
2. Square each score and sum the square
(SX2, SY2).
3. Count the number of paired
observations (N).
4. Multiply each X score by its
corresponding Y score.
5. Sum the score products X and Y (SXY).
6. Calculate the correlation.
Conception, Benjamin.et.al. (2016). LET Reviewer: MET Review Center, Manila.

5. r =
𝑁 ∑𝑋𝑌 − ∑𝑋 ∑𝑌
𝑁 ∑𝑋2−(∑𝑋)2 𝑁 ∑𝑌2− (∑𝑌)2
Where,
N = number of paired observations
SXY = sum of the cross products of
X and Y
SX = sum of the scores under
Variable X
SY = sum of the scores under
Variable Y
(SX)2 = sum of X scores squared
(SY)2 = sum of Y scores squared
SX2 = sum of squared X scores
SY2 = sum of squared Y scores
Conception, Benjamin.et.al. (2016). LET Reviewer: MET Review Center, Manila.

6. Example: Scores of 10 students in
1st (X) and 2nd (Y) Test
X Y 𝑿 𝟐 𝒀 𝟐 XY
86 87 7396 7569 7482
88 87 7744 7569 7656
90 92 8100 8464 8280
95 97 9025 9409 9215
93 92 8649 8464 8556
89 88 7921 7744 7832
94 95 8836 9025 8930
96 97 9216 9409 9312
81 82 6561 6724 6642
87 86 7569 7396 7482
∑𝑋 = 899 ∑Y = 903 ∑𝑋2= 81017 ∑𝑌2= 81773 ∑XY= 81387

7. r =
𝑁 ∑𝑋𝑌 − ∑𝑋 ∑𝑌
𝑁 ∑𝑋2−(∑𝑋)2 𝑁 ∑𝑌2− (∑𝑌)2
Given Formula:
r =
[10 81387 − 899 903 ]
10 81017 − 8992 [10 81773 − 9032 ]
r =
2073
√(1969)(2321)
This indicates a very high degree of
relationship exists between the test
scores in 1st and 2nd test.