Ch. 16

Question 1

correlation coefficient

Answer 1

Measures the strength are direction of the relationship between two numerical variables

Question 2

Parameter and estimate of the correlation coefficient?

Answer 2

rho (p) (Parameter) and r (estimate)

Question 3

What is the covarience?

Answer 3

The coveriance is the measure of the relationship between X and Y

Σ(Xi - X_mean)(Y_i - Y_mean) / n-1

See pg. 521

Question 4

t-test for the null hypothesis of no relationship? (p=0)

Answer 4

t = r/SEr

Question 5

Coefficient of determination (r²)

Answer 5

Describes the proportion of variation in one variable that can be predicted from the other

Question 6

Assumptions of correlation?

Answer 6

Random sample

Bivariate normal distribution (i.e. X is normally distributed with equal variance for all values of Y, and Y is normally distributed with equal variance for all values of X)

Question 7

Bivariate normal distribution

Answer 7

X is normally distributed with equal variance for all values of Y

Y is normally distributed with equal variance for all values of X

(i.e. a bell-shape probably distribution in 2-D space)

Question 8

What does a bvariate normal distribution look like?

Answer 8

Partial list

• Linear relationship
• cloud of scatter plot is circular or elliptical in shape
• Frequency distributions of X and Y (individually) are normal
• Histograms of X and Y should both appear normal

Question 9

Methods to go around assumption of bivariate normality?

Answer 9

Transform the data (suggest log, square root, or arcine)

Use non-parametric methods

Question 10

Spearman’s rank correlation

Answer 10

Measure the strength and direction of the linear association between the ranks of two variables

Question 11

Assumptions of spearman’s rank?

Answer 11

Individuals are randomly chosen from a population

Assumes monotonic relationship (i.e. assumes linear relationship between X and Y)

Question 12

Measurement error

Answer 12

The difference between the true value of a variable for an individual and its measured value

Question 13

Attenuation

Answer 13

Bias in correlation estimate caused by measurement error in X or Y (or both)

The more attenuation, the lower the estimated magnitude of p (closer to 0 on average).

Question 14

How does the correlation coefficient depend on range?

Answer 14

The correlation will be expected to be weaker when a narrow range of X values is represented

Question 15

Degrees of freedom for t-test?

Answer 15

n-2 (as you need to use two summaries of the data, X bar and Y bar, when calculating r)