3. Bivariate Correlation and Regression

Question 1

What variables can Pearson’s correlation coefficient be used with?

Answer 1

• Binary/categorical variables

- Continuous variables

Question 2

Strength of correlations (Pearson’s r):

Weak =
Moderate =
Strong =

Answer 2

Weak = +/- .1

Moderate = +/- .3

Strong= +/- .5

Question 3

What does r squared tell us?

Answer 3

Amount of shared variance

AKA: The coefficient of determination

Question 4

What does the F ratio tell you (SPSS output)?

Answer 4

The ratio of how much the prediction of DV has improved by fitting the model, compared to how much error still remains

Question 5

What is a correlation?

Answer 5

It is a way of measuring the extent to which two variables are linearly related

• It measures the pattern of responses across variables

Question 6

What assumptions is the validity of Person correlation based on?

Answer 6

• data is at continuous (scale/interval/ratio) level
• data values are independent of each other; i.e. only one pair of readings per participant is used
• a linear relationship is assumed when calculating Pearson’s coefficient of correlation
• observations are random samples from normal or symmetric distributions

Question 7

Non-parametric correlation

Spearman’s p (rho, rs)

Answer 7

• Variables are not normally distributed and the measures are on ordinal scale ( e.g. grades)
• Works by first ranking the data n(numbers converted into ranks), and then running Pearson’s r on the ranked data

Question 8

Kendall’s τ (tau)

Answer 8

• For small datasets, many tied ranks

- Better estimate of correlation in population than Spearman’s ρ

Question 9

Biserial correlation

Answer 9

When one variable is dichotomous, but there is an underlying continuum (e.g. pass/fail on an exam)

• A point-biserial and biserial correlation is used to correlate a dichotomy with an interval scaled variable. The difference is that the point-biserial correlation is used when the dichotomous variable is a true or discrete dichotomy and the biserial correlation is used with an artificial dichotomy

Question 10

Point-biserial correlation

Answer 10

When one variable is dichotomous, and it is a true dichotomy (e.g. gender(?), pregnancy)

• A point-biserial and biserial correlation is used to correlate a dichotomy with an interval scaled variable. The difference is that the point-biserial correlation is used when the dichotomous variable is a true or discrete dichotomy and the biserial correlation is used with an artificial dichotomy

Question 11

Partial correlation

Answer 11

In partial correlation the effect of the third variable on BOTH variables is controlled

• focuses on unique contributions-compares the unique variation of one variable to the unique variation of the other

Question 12

Semipartial correlation

Answer 12

the effect of the third variable is controlled ONLY FOR ONE of the variables

• compares the unique variation of one variable with the unfiltered variation of the other
• focuses on the predictive value of
  all variables combined
• shows the increment in the correlation of one variable above and beyond another

Question 13

What is a regression?

Answer 13

A way of predicting things that you have not measured

• Predicting an outcome variable from one predictor variable.

OR

• Predicting a dependent variable from one independent variable

Question 14

What is the SSm

Answer 14

SSM is the difference between SST and SSR and represents the amount of improvement in predictions when using the Best model over the most basic model (the mean).

Question 15

Differences between group means can be characterized as a regression (linear) model if:

Answer 15

The experimental groups are represented by a binary variable (i.e. coded 0 and 1).

in this case the predictor variables are categorical and can be expressed in a regression linear model if substituted with dummy variables