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SOCY211 Week 10, Lecture 1

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SOCY 211
Carl Keane

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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