Chapter 7

Question 1

relationship between correlation and prediction

Answer 1

• if two scores are correlated, we can do a better job of making a prediction of a person’s score on one variable based on the other variable
• The greater the correlation, the more accurate our prediction will be

Question 2

how does correlation help when it comes to tests?

Answer 2

• Can establish reliability (do people get similar scores if they re-take it?)
• Can establish validity (does it measure what it’s supposed to?)

Question 3

bivariate distribution

Answer 3

distribution that shows the relation between 2 variables

Question 4

positive vs. negative vs. no correlation

Answer 4

• Positive correlation: linear relationship; high scores on one variable are paired with high scores on the other (and vice versa)
• Negative correlation: linear relationship; high scores on one variable are paired with low scores on the other (and vice versa)
• No correlation: both high and low values on the first variable are equally paired with high and low values on the second variable

Question 5

values of r

Answer 5

range from –1 (perfect negative correlation) to 0 (no correlation) to +1 (perfect positive correlation)

Question 6

what correlations are not

Answer 6

• Causation (variable x doesn’t cause variation in variable y)
• Percentages (a .50 correlation does not mean they’re 50% correlated, and it is not twice as strong as a .25 correlation)

Question 7

what do correlations really mean?

Answer 7

• A +1 correlation indicates that 100% of the scores on the second variable will be above the mean (or below the mean on a –1 correlation)
• A 0 correlation indicates that 50% of the scores on the second variable will be above the mean and 50% will be below
• The correlation coefficient is really an index of how similar paired z scores are

Question 8

n

Answer 8

in formulas for correlation coefficient, note that n stands for the number of pairs of scores

Question 9

Spearman’s rank-order correlation coefficient (rs)

Answer 9

• Used when aspects of a measure have been rank-ordered (ie. Employees rank best aspects of the job, employers rank aspects based on what they think employees would rank, and we want to calculate correlation between the rankings)
• Also used when measures are in score form
• Used when n is relatively small

Question 10

why can’t correlation equal causation?

Answer 10

• X may cause y, but…
• Y might be causing X
• A third variable may be influencing X and Y
• A complex set of interrelated variables may be influencing X and Y
• X and Y might influence each other

Question 11

r and transformations

Answer 11

• r is unaffected by any positive linear transformations of raw scores
• Ex. You could add/subtract 100 from all scores or multiply/divide all scores by 100, and the distribution of scores won’t change -> r will remain the same
• The rankings in Spearman’s, however, will change
• r will also remain the same whether it’s computed using raw scores, z-scores, etc. (mean changes and sd may change, but r won’t)
• exponents, square roots, and non-linear transformations will change shape of distribution and therefore, correlation

Question 12

hugging principle

Answer 12

the more closely the scores hug the line of best fit, the higher the value of r

Question 13

characteristics of r

Answer 13

• used for linear relationships only
• R is sensitive to the range of talent (variability) in the distribution of scores (Ie. If we restrict the range of scores, the correlation will likely change)
• R is subject to sampling variation (r may be different if you’d gotten a different sample from the population) -> R will fluctuate more from sample to sample when the samples are smaller
• Pooling samples can change the correlation depending on where the samples lie relative to each other -> If pooled samples hug regression line, correlation increases (and vice versa)
• There is no such thing as “the” correlation coefficient for variables

Question 14

r

Answer 14

• Pearson product-moment coefficient of correlation

- sample statistic -> population parameter equivalent = rho

Question 15

when correlation is 0 regardless of score on 1 variable, what’s the best prediction for the other score?

Answer 15

the mean

Question 16

types of correlations on a scatterplot

Answer 16

• fencing sword: perfect correlation (1.00)
• hot dog: high correlation (0.7-0.8)
• football: moderate correlation (0.5)
• soccer ball: no correlation (0)

Question 17

does a 0 correlation rule out the possibility of causation?

Answer 17

No

Question 18

r as an inferential statistic

Answer 18

• r is a consistent estimator -> as size of random sample increases, the absolute difference between r and parameter (rho) decreases
• r is not an unbiased estimate of rho -> its expected value is slightly less than rho (but the amount is negligible unless n is quite small)

Question 19

effect of measurement error on r

Answer 19

• true relationship between 2 variables will be stronger than the observed relationship because of measurement error
• the greater the measurement error (and lower the reliability), the lower the value of r (lower correlation)

Question 20

correlation, range, and reliability

Answer 20

• lower range of scores = higher reliability
• tests with smaller range better correlate with itself if the same person is taking it repeatedly -> if a test can’t correlate with itself, it won’t correlate with anything else

Question 21

effect of heterogeneity on correlation

Answer 21

• value of r influenced by heterogeneity (dissimilarity) of sample
• more homogenous -> lower value of correlation coefficient (and vice versa)
• restricting range of scores will diminish correlation coefficient
• between groups variance can inflate, decrease, or change the correlation coefficient