Covariance & Correlation

Question 1

What is covariance?

Answer 1

Reflects the degree to which two variables vary together

Question 2

How does covariance relate to correlation?

Answer 2

They both measure the linear relationship between two variables; covariance is taken from original scale scores so is affected by measurement scale; correlation is not, it’s a standardised measure

Question 3

How do you interpret a covariance coefficient?

Answer 3

It’s the average product of the deviation scores of two variables

Question 4

How do you interpret a correlation coefficient?

Answer 4

Pearson’s r; it tells us whether a relationship is likely to have occurred by chance (0-1 indicates magnitude of relationship; sign (+/-) indicates direction); divide covariance by SxSy (standard deviations of x & y)

Question 5

Why do we need to test r for significance?

Answer 5

To determine whether the linear relationship between two variables in a sample is large enough to infer a linear relationship in the population, or if the correlation is due to sampling error

Question 6

What’s the best predictor of the criterion (variable on Y axis)?

Answer 6

The mean of the criterion

Question 7

Describe the line of best fit

Answer 7

It captures the relationship between the variables on a scatterplot

Question 8

What does the numerator of covariance involve?

Answer 8

Finding extent to which scores differ from the mean of a variable (both X & Y); multiplying the two deviation scores (XY) for each participant; adding up deviation scores across all participants (SPxy)

Question 9

What does the denominator of covariance involve?

Answer 9

Dividing SPxy by N-1 so that the covariance is independent of the number of scores

Question 10

How do we calculate Pearson’s r?

Answer 10

Divide covariability of X & Y (COVxy) by the separate variabilities of X & Y (SxSy)

Question 11

If we use the standard score formula (ZxZy/N-1) what don’t we need to do?

Answer 11

Calculate the covariance (but still must calculate standard scores for X & Y)

Question 12

State the statistical & conceptual hypotheses for testing the significance of r

Answer 12

Null: rho (correlation in population) = 0; there is no linear relationship between X & Y in the population; Alternative: rho /= 0; there is a linear relationship between X & Y in the population

Question 13

What formula do we use to test the significance of r?

Answer 13

t = r x square root of N - 2 divided by the square root of 1 - r squared

Question 14

What is the degrees of freedom?;

Which table do we look up?

Answer 14

N - 2;

t table

Question 15

The larger the N, the smaller the what?

Answer 15

Absolute value of r needed for significance

Question 16

What are the assumptions of Pearson’s correlation coefficient r?

Answer 16

A bivariate (linear) normal distribution based on interval or ratio scales

Question 17

What does r squared mean?;

What does k squared mean?

Answer 17

Coefficient of determination; proportion of variance in one variable that is explained by the variance on another;
Coefficient of non-determination (aka error or residual variance); amount of variance that can’t be predicted by the other variable

Question 18

What do the point-biserial & Spearman’s rank (Spearman’s rho) correlations test?

Answer 18

Point-biserial examines the relationship between a dichotomous variable & a continuous variable; Spearman’s rho assesses degree of agreement between ranks, monotonic relationships, linear relationships, skewed data & data with extreme outliers; it tests significance but with less power if N<10

Question 19

Describe the process of conducting a point-biserial correlation;
What other test could we use to get the same result?

Answer 19

Assign/dummy code values to the levels of the IV (e.g. 0 & 1); calculate SPxy, SSx & SSy; use Pearson’s r to calculate r pb; test for significance (t formula); compare with crit t (df = N-2); interpret result;
Independent groups t-test

Question 20

In a point-biserial correlation, what depends on the scoring of the dichotomous variable?;
What does not?;
How is the direction of the difference observed?

Answer 20

The sign;
Absolute value of r pb;
By looking at the means

Question 21

Describe the process of conducting a Spearman’s rho correlation

Answer 21

If needed, assign the X & Y scores to ranks; calculate SPxy, SSx & SSy; use Pearson’s r formula to calculate r(s); interpret result

Question 22

If the two variables are not normally distributed, can we determine a correlation coefficient

Answer 22

Yes

Question 23

If r = .50, what is the amount of variance that the two variables share?

Answer 23

.25

Question 24

If we use descriptive statistics to test relationships or differences in samples, what do we use inferential statistics for?

Answer 24

To determine if there is sufficient evidence to conclude that a relationship or difference is likely to genuinely exist in the population

Question 25

What allows you or doesn’t allow you to make causal inferences?

Answer 25

Research design, not the statistical test