Lecture 10

Question 1

Correlation coefficient

Answer 1

a measure of the strength of association or relationship between 2 variables.

Question 2

Covariance:

Answer 2

a measure of the average relationship between 2 variables. It is the average cross-product deviation (i.e., the cross-product divided by one less than the number of observations).

Question 3

Coefficient of determination:

Answer 3

the proportion of variance in 1 variable explained by a 2nd variable. It is Pearson’s correlation coefficient squared.

Question 4

Cross product deviations:

Answer 4

a measure of the ‘total’ relationship between 2 variables. It is the deviation of 1 variable from its mean multiplied by the other variable’s deviation from its mean.

Question 5

Curvilinear relationship:

Answer 5

in general, curvilinearity is a upside-down U shape distribution.

Question 6

Dichotomous variable:

Answer 6

nominal variable that consists of only 2 levels/groups

Question 7

Truncated range:

Answer 7

Refer to situations in which the sample is somehow limited. also called a restricted range.

Question 8

Pearson’s r:

Answer 8

standardized covariance

Question 9

What are the two fundamental characteristics of correlation coefficients? Be able to define each.

Answer 9

Direction (pos/neg) and magnitude (strength… how close to +1 or -1)

Question 10

When the correlation coefficient is zero, what is the relationship between the X and Y variable?

Answer 10

no relationship

Question 11

What is a perfect positive correlation? What is a perfect negative correlation?

Answer 11

+1 and -1

Question 12

When would you compute the following correlation coefficients: Pearson product-moment correlation, point-biserial correlation, biserial correlation, phi coefficient, Spearman’s rho? Note: remember the type of correlation depends on the scale of measurement of the X & Y variables (e.g. dichotomous, nominal, ordinal, continuous).

Answer 12

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Question 13

Be able to list and define/describe all of the issues discussed in class that may weaken (or attenuate) the correlation coefficient.

Answer 13

1. Outliers: extreme scores
2. Truncated range: restricted range/variance
3. Curvilinear relationship: nonlinear relationship that Pearson’s r cannot model

Question 14

outliers:

Answer 14

extreme scores

Question 15

truncated range

Answer 15

restarted range/variance

Question 16

curvilinear relationship

Answer 16

nonlinear relationship that person’s r cannot model.

Question 17

Be able to interpret a 95% confidence interval around a sample correlation coefficient.

Answer 17

CI95= The mean +/- (1.96)(standard error of the mean)

Question 18

If given a 95% confidence interval around a sample correlation coefficient, be able to test the null hypothesis that no relationship exists between the two variables (X & Y).

Answer 18

if the confidence interval includes 0 we can say that the population is not significantly different from zero, at a given level of confidence. The confidence intervals of correlation coefficient are computed based on the sample mean r and sample standard deviation.