Bivariate Correlation, Regression and ANCOVA Flashcards
What are the features of experimental research?
- Determines causation through manipulation of IVs
- Random assignment
What are the features of correlational research?
- Measures level of association of IVs with the DV
- Cannot determine causation
What is covariance?
A scale dependant measure of the relationship between IVs and DVs
What is correlation?
Standardised covariance; it expresses the relationship between two variables in terms of their standard deviations
What are different names given to correlation?
r, Pearson correlation, bivariate correlation, zero-order correlation
What is the difference between covariance and correlation?
Covariance is scale-dependant and cannot be directly compared to other covariances. Correlation is standardised and can be
What is the coefficient of determination?
The proportion of the in one variable that is explained by the variance in another (r2)
What is error/residual variance?
The proportion of variance that is not accounted for by the other variable (1 - r2)
What is r as a population estimate?
radj is the population correlation coefficient
What is the difference between r and radj
radj is smaller and more conservative than r, but the difference decreases as sample size increases
What is bivariate correlation?
Estimating a score on one variable on the basis of scores on the other variable
Regress DV on IVs
What is the standardised regression slope?
β: standard deviation change in Y expected from a one standard deviation change in X
What is the difference between b and β?
β is standardised and can be compared to other standardised regression slopes
What is the standard error of the estimate?
Sx.y: the amount of variability around the slope
Actual scores compared to Yhat
What does the standard error of the estimate tell us?
The units between which 68% of individuals will score from the regression line (Yhat)
What is included in the structural model of regression?
A score is equal to the effect of:
The slope
The intercept
Error
How is variance partitioned in regression?
SSy = SSregression + SSresidual
What is SSy?
The sum of differences of a score from the mean
What is SSregression?
The sum of differences of the expected score on the regression line (Yhat) from the mean
What is SSresidual?
The sum of differences of the score from the expected score on the regression line (Yhat)
What is dfy?
N-1
What is dfregression?
P (no. of predictors)
What is dfresidual?
N - p - 1
What is F in regression?
MSregression/MSresidual
What is ANCOVA?
Analysis of covariance: a strategy to maximise power when variables are continuous
What does ANCOVA do?
Increases power by shrinking the error term and purifying the treatment effect
What forms of ANOVA can be performed with a covariate?
All forms
What is the structural model of ANCOVA for a one-way ANOVA?
A score is the effect of:
The grand mean
The first predictor
The covariate * the slope
Error
How is ANCOVA different to blocking designs?
- The error term is adjusted statistically as opposed to in the design
- Treatment means are adjusted: treatment effect is also purified
Why is the treatment mean adjusted in ANCOVA?
To account for differences on the covariate across the groups of the IV
How are treatment means adjusted in ANCOVA?
- Calculate overall covariate sample mean
- Adjust the groups ‘expected’ mean to what it would be if the group’s covariate mean was the overall covariate mean by using the regression line
What are some assumptions of ANCOVA?
- All previous ANOVA assumptions
- The relationship between the covariate and DV is linear
- There is no interaction between the DV and the covariate
