Chapter 14-Correlations and Regressions

Question 1

What are correlations?

Answer 1

• Correlation is a statistical method used to measure and describe the relationship between two variables (X and Y) as they exist naturally.
• There is no attempt to manipulate one of the variables
• A relationship exists when changes in X tend to be accompanied by consistent and predictable changes in Y

Question 2

Pearson correlation

Answer 2

• The most common form of correlation is a straight line (linear relationship), which is most frequently measured by the Pearson correlation coefficient, r
• The strength/consistency of the relationship is measured by the numerical value of the correlation (1.00=perfect positive relationship, -1.00=perfect negative relationship, 0.00=no relationship at all)
• Pearson also requires that the scores be from an interval or ratio scale of measurement

Question 3

How to calculate Pearson’s r?

Answer 3

covariability (tendency for x+y to vary together) / variability of X and Y scores

Question 4

What are some potential data problems that can distort Pearson’s r?

Answer 4

• Outliers (individuals w X or Y values that are substantially different than the other individuals in a sample)
• Restriction of range: relationship between X and Y is obscured when the data are limitied to a restricted range of values

Question 5

Alternatives to the Pearson Correlation-Spearman correlation

Answer 5

• Used when examining the relationship between two ordinal variables/ used when the form of the relationships between two variables are curvilinear or exponential
• Requires: the observations for each variable are rank ordered (each variable is ranked separately) and after the correlation is computed by using the Pearson formula but with the ranked data

variables must be converted to ranks before the correlation is completed

Question 6

Alternatives to the Pearson Correlation: the point-biserial correlation

Answer 6

• A specific use case of a Pearson correlation when one variable is dichotomous and the other is on an interval or ratio scale (closely related to the independent measures t-test)
• Code the dichotomous as 1 or 0

Question 7

The phi-coefficent alternative to the pearson correlation

Answer 7

• a specific use case of a pearson correlation when both variablesare dichotomous
• recode the dichotomous variable values as 0 or 1

Question 8

Hypotheses for non-directional pearson correlation

Answer 8

• H0: There is no association between X and Y (p=0)
• H1: X is associated with Y (p=/ 0)

Question 9

Directional

Answer 9

• H0: Greater X is not associated with greater Y (p<= 0)
• H1: Greater X is associated with greater Y (p>0)

DF for r is n-2

Question 10

How to calculated effect size measure for pearson’s r?

Answer 10

Square the r value

Small: .01-.08 med: .09-.24 large: .25+