School

Queen's University
Department

Social Sci, Edu and Soc Work - Sociology

Course Code

SOCY 211

Professor

Carl Keane

Week 10, Lecture 1 CORRELATION COEFFICIENTS

- Measured ideally at the interval level measure

- Pearson Correlation Coefficient/ Pearsonâ€™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

ïƒ 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 outliersâ€”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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