Correlation, regression, & ANCOVA

Question 1

What is covariance mathematically speaking?

Answer 1

Average cross product of deviation scores.

Question 2

What are the degrees of freedom in a correlation t test?

Answer 2

N-2

Question 3

What is the statistic, conceptually?

Answer 3

The ratio of systematic variance to error variance

Question 4

What is rho? What is an estimate of rho called?

Answer 4

Population correlation coefficient. R-adjusted.

Question 5

How can you achieve scale-independent coefficients?

Answer 5

Express in terms of standard deviation.

Question 6

What is the standard error of the estimate?

Answer 6

The standard deviation of criterion scores around the regression line

Question 7

As correlations become larger what happens to the standard error of the estimate? What does this reflect?

Answer 7

The SEE reduces. Greater accuracy of prediction.

Question 8

What can the standard error of the estimate inform us about typical error in prediction?

Answer 8

Assuming residuals are normally distributed around the regression line, 1 SE is equal to 1SD, e.g. 34% of Y scores are within 0 to 1SE from the prediction line.

Question 9

What is the effect of small samples on (1) R squared and (1) standard error of the estimate?

Answer 9

R squared is inflated above its population value. SEE is underestimated (hides true variability in population).

Question 10

What is the null hypothesis when testing a correlation or regression coefficient?

Answer 10

The true value is 0, I.e. no relationship

Question 11

How do two methods of using a second IV to reduce error work?

Answer 11

1. At the level of design (I.e. randomised stratification)

2. Adjusting the model statistically (I.e. including a covariate)

Question 12

What does it mean if, in ANCOVA, you have an interaction between the focal IV and the covariate?

Answer 12

You have violated an assumption of ANCOVA, it should not be used.

Question 13

Which ‘type’ of error does ANCOVA affect? What is a consequence of this?

Answer 13

It reduces type 2 error by reducing the error used in tests of the focal IV. It increases the power to detect an effect.

Question 14

In terms of calculation, how does ANCOVA adjust the error term?

Answer 14

It uses Y - Yhat, instead of Y - Ybar, to calculate error.

Question 15

Why does ANCOVA have more power than Blocking?

Answer 15

It uses a continuous variable with more variation that can be reduced.

Question 16

By adjusting the treatment means, ANCOVA allows you to ask the question …

Answer 16

Would the focal IV have an effect on the DV if all participants were equivalent on the covariate?

Question 17

What are two assumptions you must make in using ANCOVA to adjust treatment means?

Answer 17

1. The overall covariate sample mean is the population mean for the covariate.
2. In an unconfounded population, all groups of the focal IV would have the covariate mean.

Question 18

What are 3 crucial assumptions re: ANCOVA?

Answer 18

1. Covariate relationship with DV is linear
2. Covariate relationship with DV is linear within each IV group
3. Homogeneity of regression slopes within each IV group (no interaction)

Question 19

If adjusted and observed group means are very different, what could this indicate?

Answer 19

There could be either a confound or a meaningful aspect of the focal IV that has been controlled for without good reason.