This document discusses the Pearson r correlation coefficient and how to calculate, interpret, and evaluate the significance of relationships between variables. The Pearson r ranges from -1 to 1, with values closer to these extremes indicating a stronger linear relationship and values near 0 a weaker relationship. A correlation of -0.67 represents the strongest relationship among the options given. The correlation coefficient is calculated using the formula presented. An example calculates the correlation between number of hospitals and maternal mortality rate in various cities. Interpretation of the correlation involves evaluating the magnitude, sign, strength of relationship, and coefficient of determination. Statistical significance can be determined by comparing the correlation to critical values from tables.

1. MEASURING RELATIONSHIPS
Pearson r Product Moment Coefficient of Correlation
Mike Arieh P. Medina, PhD

2. Outline
• What is coefficient of correlation
• How to calculate a correlation
• Assumptions about correlation calculations
• Interpretation of the correlation
• Evaluating the significance of the relationship

3. The correlation coefficient
• Indicated by r
• Ranges from -1.00 to +1.00
– The value indicates the strength of the
relationship
– The closer to 0, the weaker the relationship
– The closer to +/- 1.00 the stronger the relationship
• The sign indicates whether the relationship is
positive or negative

4. Question
• Which of the following coefficient of
correlation indicates the strongest
relationship?
• A. + 0.45
• B. – 0.33
• C. + 0.58
• D. – 0.67

5. The Equation

6. Problem: Is no. of hospitals related to MMR?
City No. of Hospitals Maternal Mortality Rate
A 5 5
B 10 2
C 4 8
D 8 3
E 2 8
F 7 5
G 9 5
H 6 7
I 1 10
J 12 3

7. Hypothesis
• H0: There is no significant relationship
between no. of hospitals and MMR.
• H1: There is a significant relationship between
no. of hospitals and MMR.

8. 0
2
4
6
8
10
12
0 2 4 6 8 10 12 14
MMR
Hospitals
Scatterplot of MMR vs. Hospitals

9. Types of Correlation
Positive Correlation Negative Correlation
No Correlation
Perfect Correlation

10. Types of Correlation
Strong Correlation Weak Correlation

11. Sample Problem
x y xy x2 y2
5 5 25 25 25
10 2 20 100 4
4 8 32 16 64
8 3 24 64 9
2 8 16 4 64
7 5 35 49 25
9 5 45 81 25
6 7 42 36 49
1 10 10 1 100
12 3 36 144 9
Σx = 64 Σy = 56 Σxy = 285 Σx2 = 520 Σy2 = 374

12. Computation
y

13. Computation

14. Computation

15. Correlation Assumptions
• Before you can compute for Pearson r make
sure that the following assumptions are
satisfied:
– The relationship is linear
– The variables are measured on an interval or ratio
scale
– The distribution of the variable is normal
– The distribution is continuous

16. Interpretation
Magnitude of r
Range of r Descriptive label for r
+/- 0.80 – 0.90 Very Strong
+/- 0.60 – 0.79 Strong
+/- 0.40 – 0.59 Moderate
+/- 0.20 – 0.39 Weak
+/- 0.00 – 0.19 Very Weak

17. Interpretation
• r2 = Coefficient of Determination
• Percent variance that is shared between variable x and
variable y
• 1- r2 = Coefficient of Alienation
• Percent variance that is not shared between variable x
and variable y
• Now, compute for the r2 of the previous example and
interpret.

18. Interpretation
Coefficient Value Interpretation
r 0.899
Very Strong negative relationship
between no. of hospitals and
MMR (the more hospitals in a city
the lesser its MMR)
r2 0.808
80.8% of the variation in MMR is
influenced by the variation in the
no. of hospitals
1-r2 0.192
19.2% of the variation in MMR is
influenced by factors other than
no. of hospitals

19. How do we know if it’s a significant
relationship? (Ex. at 0.05)
df = N-2
DOWNLOAD table of critical values of the Pearson Product-Moment correlation

20. Exercise
• Now, compute for the coefficient of
correlation using the population and weight of
waste hypothetical data.
• Population (thousands): 8, 6, 7, 4.5, 5
• Solid Waste (thousand tons): 2, 1.8, 1.5, 1.1, 1.25
• Create a scatterplot
• Interpret the results
• ANS: r = 0.858