Unit 4

Correlation and proxy measure

Proxy measure

• Likert scale is a form of self-report data. But what if sometimes you have no direct access to the sample or to the variable?

• Use proxy

Problem

• The average GPA of APU students is higher than their counterparts at Citrus College.

• Some researcher hypothesizes that it is due to the difference in social-economic status (SES). Most APU students are from upper or upper middles classes. Their parents have more resources and therefore APU students outperform CC students.

Problem

• Whether the performance gap could be attributed to SES is a big question that awaits further investigation, but some people dispute the assertion that the SES of APU students is higher than that of CC students.

• But you have no access to the SES information of their parents. What can you do?

Problem

• You need some indirect measurement.

• One of the possible proxy measures of SES is the vehicle model.

Assignment

• Form a small group of 2-4 people.• Go to the non-faculty/non-staff parking lots of

APU (East and West campuses) and CC.Mark down the automobile models, evaluate their quality (condition), and the degree of luxury (use a 5-point scale, 1 is the lowest whereas 5 is the highest).

• Save the data in Excel and upload the file to Sakai.

AssignmentSchool Make Model Quality LuxuryAPU VW Jetta 4 3APU Acura RSX-5 4 4APU Suzuki SXL-7 3 3APU Acura TSX 5 4APU Honda Accord 2 3APU Toyota Corolla 3 3APU VW Jetta 4 3APU Pontiac G6 3 4APU Hyundai Sonata 5 4APU Ford Escape 4 3CU Toyota RAV4 1 2CU MB E 3 4CU Nissan Versa 4 3CU Chevy Cobalt 4 3CU BMW 650I 5 5CU Honda Accord 2 3CU Toyota Tacoma 4 3CU Nissan Sentra 5 4CU Toyota Tacoma 4 3

Different types of correlation coefficient

• After obtaining the data of two variables, you need to find their relationship.

• Pearson’s r is applicable to measure the association between two continuous-scaled variables.

• Spearman is suitable to rank-order/ordinal data; not affected by sample size.

Different types of correlation coefficient

• But when you have one binary variable (e.g. “yes/no”, “male/female”) and one continuous-scaled variable, the point biserial correlation (PBC) or biserial correlation (BC) coefficient should be used instead.

• In the point biserial correlation coefficient the binary variable should be "naturally" dichotomous, such as gender.

• If the binary variable is artificially dichotomized, this variable may be viewed as having an underlying continuity. For example, an instructor may use a cut score to classify the examinees into “pass” and “fail”. In this case, the biserial correlation is the more appropriate approach.

Misconception: small is insignificant• It is important to point out that sometimes even a very low

correlation may have clinical significance. For example, Thomas Holmes and Richard Rahe investigated over 5,000 medical patients to see whether stress might cause sickness. Patients were asked to tally a check list of 43 life events. It was found that there was a positive correlation of 0.118 between these two variables. Based on this finding, the Holmes-Rahe Stress Scale was developed and validated. 0.118? What a big deal! But in clinical psychology or medical research, we must pay attention to even such a small correlation. http://www.harvestenterprises-sra.com/The%20Holmes-Rahe%20Scale.htm