Statistic work
mehett
correlation.pdf
Agenda
• Introduction to Correlation • Review Scatterplots and their connection to correlations
• The correlation coefficient
Why Correlation?
• Allows us to examine the strength and direction of a relationship
• Allows us to examine the relationship between an interval level dependent variable and an interval level independent variable
Categorical/Ordinal
Dependent Variable
Interval Dependent
Variable
Categorical/ Ordinal
Independent Variable Chi Square Difference of Means
Interval Independent
Variable Not Covered! Correlation OR
Regression (bivariate)
Review Scatterplot D
e p
e n
d e
n t
va ri
a b
le o
n t
h e
Y A
xi s
Independent variable on the X Axis
Each point represents one data point, both its X and Y values. This point corresponds to Y =8 and X =6
The Importance of Scatterplots to Correlation
The Importance of Scatterplots to Correlation
• Identifying if the relationship is linear • Correlation coefficient only appropriate for linear relationships!
The Importance of Scatterplots to Correlation
The Importance of Scatterplots to Correlation
The Importance of Scatterplots to Correlation
• Researchers should always look at a scatterplot of their variables before calculating a correlation coefficient to: • Get an idea about the strength and direction of the relationship
• Make sure the relationship is linear • If the relationship is not linear calculating a correlation coefficient is not
appropriate and the researcher should not proceed
• Make sure there are no problematic outliers • If problematic outliers are identified the researcher might want to think about
removing them
The Correlation Coefficient (r)
• A coefficient that tells us about the strength and direction of a relationship
• Always ranges from -1 to 1
• Direction: • Positive numbers indicate a positive relationship
• Negative numbers indicate a negative relationship
• Strength:
-1 Perfect Neg. Correlation
1 Perfect Pos. Correlation
-.6 Strong Neg. Correlation
.6 Strong Pos. Correlation
-.3 Moderate Neg. Correlation
.3 Moderate Pos. Correlation
-.1 Weak Neg. Correlation
.1 Weak Pos. Correlation
No Correlation 0
The Correlation Coefficient (r)
The Computational Formula for r
Testing the Significance of r
Correlation – Specific Steps
Correlation – Specific Steps cont.
• Find the critical r in the table • Calculate the degrees of freedom
• N - 2
• α = .05
• Compare calculated r to critical r • If our calculated r is > critical r we reject the null hypothesis
• If our calculated r is < critical r we fail to reject the null hypothesis
Correlation – Example
X Political Knowledge
Y Attention Span
2 3
1 2
5 3
4 2
2 4
1 3
Correlation – Example cont.
Correlation – Example Cont.
X Y XY
2 3
1 2
5 3
4 2
2 4
1 3
15 17
4
4
1
1
25
16
51
9
9
4
4
16
1
51
6
2
15
8
8
3
42
N = 6
Correlation Example X TV Hours
Y Weight
1.5 79
5.0 105
3.5 96
2.5 83
4.0 99
1.0 78
.5 68
Correlation – Example cont.
Correlation – Example Cont. X Y XY
1.5 79
5.0 105
3.5 96
2.5 83
4.0 99
1.0 78
.5 68
18 608
2.25
16
25
1
12.25
6.25
63
6241
9216
11025
6889
9801
6084
53880
118.5
525
336
207.5
396
78
1695
N = 7
.25 4624 34
Correlation – Exercise
• Find the correlation coefficient and determine whether or not it is significant for the following set of data.
X Y
1 5
2 6
3 4
4 2
Next Class
• Partial Correlation
• 3rd Homework Due
