chapter 21 correlation. correlation a measure of the strength of a linear relationship although...
TRANSCRIPT
Chapter 21
Correlation
CorrelationA measure of the strength of a linear
relationshipAlthough there are at least 6 methods
for measuring correlation, we are going to learn 2:– Pearson product-moment correlation
coefficient (Pearson’s r) and– Spearman’s rho (rs)
Pearson’s r
Pearson’s r
Interpreting Pearson’s rr’s vary from -1 to +1
+1 = perfect positive linear relationship
0 = no linear relationship
-1 = perfect negative linear relationship
Magnitude of the RelationshipAbsolute value of r:
0 < r < .25 Low correlation
.25 < r < .50 Moderate correlation
.50 < r High correlation
Spearman’s Rank-Order Correlation“Pearson-on-the-Ranks”Rank each score with respect to the
other scores of that variableCalculate the difference (D) between
the ranks of each bivariate observation, or pair of scores
Square the difference (D2)
Spearman’s Rank-Order CorrelationCalculate rs using:
Review - Steps to Completing Regression (by hand)
1. Construct a data table (1 observation per row)
2. Compute each XiYi, and ΣXiYi
3. Compute n, ΣXi, ΣYi
4. Compute means (MX, MY)
5. Compute ΣXi2, ΣYi
2, ((ΣXi)2, (ΣYi)2)
6. Compute the SS(X), SS(Y), and SPXY
7. Compute m (slope) and b (Y-intercept)8. Find a point on the line: use a value of X on either end of the range,
and compute the corresponding Y
9. Plot the point (MX, MY) and the point just found10. Connect the points, label the line with the equation
Review - Steps to Computing a Pearson r1. Construct a data table (1 observation per row)
2. Compute each XiYi, and ΣXiYi
3. Compute n, ΣXi, ΣYi
4. Compute means ( MX , MY)
5. Compute ΣXi2, ΣYi
2, (ΣXi)2, (ΣYi)2
6. Compute the SS(X), SS(Y), SPXY
7. Compute
Review - Steps to Completing Spearman’s rho (rs) 1. Rank each score with respect to the other scores of
that variable (highest score gets highest rank of 1)
2. Calculate the difference (Di) between the ranks of each bivariate observation, or pair of scores
3. Square the difference (Di2)
4. Calculate
0
2
4
6
8
10
12
0 2 4 6 8 10 12
0
2
4
6
8
10
12
0 2 4 6 8 10 12
Interpreting Scatterplots
0
2
4
6
8
10
12
0 2 4 6 8 10 120
2
4
6
8
10
12
0 2 4 6 8 10 12
Correlation?
0
1
2
3
4
5
6
7
8
0 2 4 6 8 10
Not much
y = 0.0105x + 4.306
R2 = 0.0002
0
1
2
3
4
5
6
7
8
0 2 4 6 8 10
y = -0.9338x + 6.8982
R2 = 0.7855
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
0 1 2 3 4 5
Series1
Linear (Series1)
Other problems
y = 1.1333x + 3.78
R2 = 0.6872
4.8
5
5.2
5.4
5.6
5.8
6
1 1.2 1.4 1.6 1.8 2
Series1
Linear (Series1)
y = 1.0946x - 0.2998
R2 = 0.6359
3
3.2
3.4
3.6
3.8
4
4.2
3 3.2 3.4 3.6 3.8 4
Series1
Linear (Series1)
y = -0.9338x + 6.8982
R2 = 0.7855
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
0 1 2 3 4 5
Series1
Linear (Series1)
0 5 10 15 200
2
4
6
8
10
12
f(x) = − 0.30480754041388 x + 8.41233215733769R² = 0.445490311679994