Correlation, regression, & ANCOVA Flashcards
What is covariance mathematically speaking?
Average cross product of deviation scores.
What are the degrees of freedom in a correlation t test?
N-2
What is the statistic, conceptually?
The ratio of systematic variance to error variance
What is rho? What is an estimate of rho called?
Population correlation coefficient. R-adjusted.
How can you achieve scale-independent coefficients?
Express in terms of standard deviation.
What is the standard error of the estimate?
The standard deviation of criterion scores around the regression line
As correlations become larger what happens to the standard error of the estimate? What does this reflect?
The SEE reduces. Greater accuracy of prediction.
What can the standard error of the estimate inform us about typical error in prediction?
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.
What is the effect of small samples on (1) R squared and (1) standard error of the estimate?
R squared is inflated above its population value. SEE is underestimated (hides true variability in population).
What is the null hypothesis when testing a correlation or regression coefficient?
The true value is 0, I.e. no relationship
How do two methods of using a second IV to reduce error work?
- At the level of design (I.e. randomised stratification)
2. Adjusting the model statistically (I.e. including a covariate)
What does it mean if, in ANCOVA, you have an interaction between the focal IV and the covariate?
You have violated an assumption of ANCOVA, it should not be used.
Which ‘type’ of error does ANCOVA affect? What is a consequence of this?
It reduces type 2 error by reducing the error used in tests of the focal IV. It increases the power to detect an effect.
In terms of calculation, how does ANCOVA adjust the error term?
It uses Y - Yhat, instead of Y - Ybar, to calculate error.
Why does ANCOVA have more power than Blocking?
It uses a continuous variable with more variation that can be reduced.
By adjusting the treatment means, ANCOVA allows you to ask the question …
Would the focal IV have an effect on the DV if all participants were equivalent on the covariate?
What are two assumptions you must make in using ANCOVA to adjust treatment means?
- The overall covariate sample mean is the population mean for the covariate.
- In an unconfounded population, all groups of the focal IV would have the covariate mean.
What are 3 crucial assumptions re: ANCOVA?
- Covariate relationship with DV is linear
- Covariate relationship with DV is linear within each IV group
- Homogeneity of regression slopes within each IV group (no interaction)
If adjusted and observed group means are very different, what could this indicate?
There could be either a confound or a meaningful aspect of the focal IV that has been controlled for without good reason.
