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SOCY 211
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Carl Keane
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Week 10, Lecture 1 CORRELATION COEFFICIENTS
- Measured ideally at the interval level measure
- Pearson Correlation Coefficient/ Pearson’s r/Correlation Coefficient r
- r is probably the most widely used measure of association in the social sciences
- r is a symmetric measure of association- means that the correlation between the two variables will be
the same value/number regardless of which variable is the independent and which is the dependent
- r is a measure of the extent to which cases are clustered around the regression line
o can be referring to survey respondents, or participants
o if these cases/responses are tightly clustered around the regression line, the r value will be large
in value
o a large correlation coefficient represents a strong relationship
- if responses are widely scattered, the r value will be small; weak association
- tightly clustered data will give you a large r value
- weak relationship on the graph will result in a small r value
- a perfect association would occur if all the dots were on the line
- range for r: -1.0 to +1.0
- .50 + = Strong Relationship
.20 to .50 = Moderate Relationship
< .20 = Weak Relationship
o These are guidelines, it might change when you look it up in other sources
- (1) r is a measure of a linear relationship- measure of how well the regression line fits the data
o If you get an r value of 0 it means the two things are not associated
You have to be careful of situations like these!
1 - (2) r can be affected by a few extreme values of either the independent or dependent variable (outliers)
- Extreme scores may cause a fake relationship to occur when really it is not there- the r value may be
much stronger than what is actually occurring
- Extreme values may also pull the regression line down and you may end up with a weaker r value than
you may expect
- Outliers mess up the data- you have to determine what they represent and decide how you will deal with
them
o They may appear in your data as mistakes ex. Someone in your sample being 150 years when
really, it was meant to be 50 years
o If you increase the sample size you will see that outliers are more common than you thought
o Another option is to exclude the outliers
- The r value, like the mean, is a summary measure so it can be affected by outliers—you need to look
beyond the r value to make sure the relationships are real
- Will also inform us of statistical significance, if it is significant we can generalize to the population
- * = statistically significant at the .05 level
- ** = statistically significant at the .01 level
- *** = statistically significant at the .001 level
Correlations- Example 1
Age group Average number of evening
(in years) activities respondent goes out for
in a month.
Age group Pearson 1 -.405
(in years) Correlation
Sig. (2- . .000
tailed)
N 1519 1519
Average Pearson -.405 1
number of Correlation
evening
activities
respondent
goes out for
in a month.
Sig. (2- .000 .
tailed)
N 1519 1519
** Correlation is significant at the 0.01 level.
- The strength of the relationship between age and number of activities is moderate (-0.405)
- The direction is negative meaning it is inverse- as one variable increases in value, the other decreases in
value
o Meaning, as you get older, the number of evening activities decreases
2 i
r
f
u
o
e
This is what you end up with first
t
e
d
o 70
s
r 60
s
t
i 50
c
a
n 40
n
e 30
e
o
r 20
b
m
n 10
e
. 0
t
o
m -10
a 0 2 4 6 8 10 12 14 16
i
r
f Age group (in years)
u
o Cases weighted by WGHT_PER
e
This lets us more easily see what is happening
t
e
d
o 70
s
r
s 60
t
i 50
c
a
g 40
n
e
e 30
o
r 20
b
m
u 10
e
g
r 0
v
A -10
0 2 4 6 8 10 12 14 16
Age group (in years)
Cases weighted by WGHT_PER
3 Correlations- Example 2
Age group # times you had 5+ drinks past
(in years) month
Age Pearson 1 -.212
group (in Correlation
years)
Sig. (2-tailed) . .000
N 1519 1068
# times Pearson -.212 1
you had Correlation
5+ drinks
past
month
Sig. (2-tailed) .000 .
N 1068 1068
** Correlation is significant at the 0.01 level.
- It is statistically significant, not as strong as the first sample but still of moderate strength for association
- It is a negative association implying that as you get older you binge drink less
40
h
n 30
o
t
a
p 20
k
r
d
5 10
d
h
u
y 0
s
m
t
# -10
0 2 4 6 8 10 12 14 16
Age group (in years)
Cases weighted by WGHT_PER
4 30
t
o
m 20
s
p
s
i
d 10
+
5
a
u 0
o
s
e
t
# -10
0 2 4 6 8 10 12 14
Age group (in years)
Cases weighted by WGHT_PER
Correlations- Example 3
Highest level of education: Annual personal
10 grps income
Highest Pearson 1 -.381
level of Correlation
education:
10 grps
Sig. (2-tailed) . .000
N 1519 1351
Annual Pearson -.381 1
personal Correlation
income
Sig. (2-tailed) .000 .
N 1351 1351
** Correlation is significant at the 0.01 level.
- The association between the two variables is moderate with a negative direction
- This means that as education goes up, income goes down—this should send a red flag! It doesn’t make
sense
o You need to look into why these results came up because it doesn’t make sense

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