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Lecture

SOCY211 Week 10, Lecture 1

10 Pages
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Department
Social Sci, Edu and Soc Work - Sociology
Course Code
SOCY 211
Professor
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
ocan be referring to survey respondents, or participants
oif these cases/responses are tightly clustered around the regression line, the r value will be large
in value
oa 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
oThese 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
oIf 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
oThey may appear in your data as mistakes ex. Someone in your sample being 150 years when
really, it was meant to be 50 years
oIf you increase the sample size you will see that outliers are more common than you thought
oAnother 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
(in years)
Average number of evening
activities respondent goes out for
in a month.
Age group
(in years)
Pearson
Correlation
1 -.405
Sig. (2-
tailed)
. .000
N 1519 1519
Average
number of
evening
activities
respondent
goes out for
in a month.
Pearson
Correlation
-.405 1
Sig. (2-
tailed)
.000 .
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
oMeaning, as you get older, the number of evening activities decreases
2
This is what you end up with first
Cases w eighted by WGHT_PER
Age group (in years)
1614121086420
Average number of evening activities respondent goes out for in a month.
70
60
50
40
30
20
10
0
-10
This lets us more easily see what is happening
Cases w eighted by WGHT_PER
Age group (in years)
1614121086420
Average number of evening activities respondent goes out for in a month.
70
60
50
40
30
20
10
0
-10
3

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Description
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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