Week 6 revision Flashcards
What is the key distinction between experimental designs (3) and correlational designs (2)?
Experimental determines causation between manipulated IV’s and conditions that are randomly assigned, correlation is correlation between measured IV’s with the DV being an outcome.
What is the distinction between design issues and statistical issues, and why the two
should not be confused?
Design issues include randomised/experimental vs unrandomised/correlational designs while statistical is how continuous or grouped data is analysed
What is random assignment the only way of inferring
Causation
Define covariance
The average cross-product (multiplication) of the deviation scores (subtracted mean)
What is covariance main limitations?
It doesn’t give us any scale information to intercept strength of association/relationship, so we can’t compare covariances based on different scales because they aren’t standardized.
Define correlation in relation to covariance.
Correlation is the measurement of variables relative covariance to a common standard deviation OVER the average cross-product (multiplication) of their standard scores
How does correlation address the limitations of covariance?
It is standardized so you can compare data from different scales.
What are the terms used to indicate a bivariate correlation? (3)
Pearsons correlation
bivariate correlation
zero-order correlation
Define the coefficient of determination in the context of bivariate correlation, what letter indicates it?
The coefficient of determination is the proportion of variance in one variable that is explained by variance in another. Indicated by r(squared)
What is the relationship between the coefficient of determination and error/residual variance?
The error/residual variance is the variance left over from the coefficient of determination. (1-r(squared))
What question is being addressed when we test r for significance, and which statistical test is used for this purpose?
is there a significant correlation between the way two factors vary, is used for a statistical test of correlation.
What is the difference between r and r(adjusted)?
r is the correlation between two variables in terms of standard deviation in a sample, while r(adjusted) is the same thing for the population. r/r(adjusted) becomes more conservative as the group gets bigger.
What is the relationship between bivariate correlation and bivariate regression?
Bivariate correlation assesses the association between two variables in terms of strength and direction, while bivariate regression goes a step further by modeling the relationship between the variables and allowing for prediction of one variable based on the other.
What are the various components of the bivariate regression equation representing? (4)
Yhat = predicted value of Y (DV)
b = slop of regression line ( changes in DV/Y with a 1 unit change in IV/X)
X = Value of predictor (IV/X)
a = intercept (Value of Y when X=0)
What is the relationship between b and β (beta)?
b (standardized regression coefficient) and β (Beta coefficient) both represents the change in the outcome variable (dependent variable) per one-unit change according to the SD in the predictor variable (independent variable), while holding all other predictors constant.
What is the least squares criterion (in bivariate regression)?
The least squares criterion seeks to find the line that minimizes the distance between the observed data points and the corresponding points on the regression line according to the predicted Y.
What is the standard error of the estimate is (in words) and what it tells us (in
bivariate regression)?
Reflects the amount of variability around the regression line, and tells us how much data should deviate from the regression line.
What question is being addressed when we test the regression slope (i.e., b or β) for significance, and which test is used for this purpose?
Whether the slope of the regression line is significantly different from zero, indicating whether the predictor variable(s) have a non-zero effect on the outcome variable, we use a t-test to do this.
What do SSY, SSregression, and SSresidual represent?
SSY = Total variability
SSregression = prediction average / treatment variability
SSresidual = observation prediction / error variability
How is the F ratio calculated in regression and what question is it used to test?
MSregression/Msresidual
Does the model account for significant variance in the DV? H0 rsquare=0
What does “ANCOVA” stand for?
Analysis of Covariance
What is covariance?
The tendency for two scores to vary together/ in a similar way.
What are the key similarities between ANCOVA and blocking?
Both reduce the size of the error term by including a factor that explains a proportion of variance in the DV.
What are the key differences between ANCOVA and blocking?
ANCOVA statistically adjusts the error term, and can use control variables that are continuous.
What kinds of variables can serve as covariates?
Anything that is continuous and has no interaction with the DV.
How does ANCOVA reduce error variance?
Uses a variable that will account for some systematic variance unexplained by the focal IV, which will reduce the amount of unexplained variance in the overall design.
How does the reduction of error variance help increase statistical power for the test of the focal IV ?
The partitioning of variance by the covariate reduces the size of the error term, just like in blocking designs.
Why would ANCOVA want to adjust the treatment means.
Because it helps to adjust for differences int he covariation in the focal IV and error term.
When ANCOVA adjusts the treatment means what research question is being addressed?
Would the focal IV have an effect on the DV if all participants were equivalent in the covariate?
When ANCOVA adjusts the treatment means how is it done?
- Calculate the overall covariae sample mean
- Assume that an unconfounded populaiton would share this mean and adjust the mean scores on the DV to share the covariate mean
- Test group main effect using adjusted means
In the F table for an ANCOVA what does a significant effect of the covariate mean, and what are the likely implications for the test of the focal IV (i.e., the IV we care about)
It suggests that the covariate is influencing the dependent variable independently of the main independent variable, could change the significance of the IV or be considered a confound.
In the F table for an ANCOVA what does a non-significant effect of the covariate means, and what are the likely implications for the test of the focal IV (i.e., the IV we care about)?
it suggests that the covariate does not significantly contribute to explaining the variability in the dependent variable (DV) or the existence of systematic error, will loose power and the error will not be reduced.
Identify the structural model of ANCOVA.
Xij = u.. + aj + βZji + eij
The DV of participant I in jth group = the grand mean + 1st IV for group j + 2nd IV (Score on variable Z multiplied by beta) + error
What are the assumptions of ANCOVA? (6)
Homogenous variables
Normal distribution
Independence of error
Relationship between covariate/DV is linear
Also linear within each group
DV and covariate is equal across all groups with no interaction (homogeneity of regression slopes)
What if there is an interaction between the covariate and the focal IV in ANCOVA?
The study is confounded.
