Week 6 revision

Question 1

What is the key distinction between experimental designs (3) and correlational designs (2)?

Answer 1

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.

Question 2

What is the distinction between design issues and statistical issues, and why the two
should not be confused?

Answer 2

Design issues include randomised/experimental vs unrandomised/correlational designs while statistical is how continuous or grouped data is analysed

Question 3

What is random assignment the only way of inferring

Answer 3

Causation

Question 4

Define covariance

Answer 4

The average cross-product (multiplication) of the deviation scores (subtracted mean)

Question 5

What is covariance main limitations?

Answer 5

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.

Question 6

Define correlation in relation to covariance.

Answer 6

Correlation is the measurement of variables relative covariance to a common standard deviation OVER the average cross-product (multiplication) of their standard scores

Question 7

How does correlation address the limitations of covariance?

Answer 7

It is standardized so you can compare data from different scales.

Question 8

What are the terms used to indicate a bivariate correlation? (3)

Answer 8

Pearsons correlation
bivariate correlation
zero-order correlation

Question 9

Define the coefficient of determination in the context of bivariate correlation, what letter indicates it?

Answer 9

The coefficient of determination is the proportion of variance in one variable that is explained by variance in another. Indicated by r(squared)

Question 10

What is the relationship between the coefficient of determination and error/residual variance?

Answer 10

The error/residual variance is the variance left over from the coefficient of determination. (1-r(squared))

Question 11

What question is being addressed when we test r for significance, and which statistical test is used for this purpose?

Answer 11

is there a significant correlation between the way two factors vary, is used for a statistical test of correlation.

Question 12

What is the difference between r and r(adjusted)?

Answer 12

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.

Question 13

What is the relationship between bivariate correlation and bivariate regression?

Answer 13

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.

Question 14

What are the various components of the bivariate regression equation representing? (4)

Answer 14

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)

Question 15

What is the relationship between b and β (beta)?

Answer 15

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.

Question 16

What is the least squares criterion (in bivariate regression)?

Answer 16

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.

Question 17

What is the standard error of the estimate is (in words) and what it tells us (in
bivariate regression)?

Answer 17

Reflects the amount of variability around the regression line, and tells us how much data should deviate from the regression line.

Question 18

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?

Answer 18

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.

Question 19

What do SSY, SSregression, and SSresidual represent?

Answer 19

SSY = Total variability
SSregression = prediction average / treatment variability
SSresidual = observation prediction / error variability

Question 20

How is the F ratio calculated in regression and what question is it used to test?

Answer 20

MSregression/Msresidual
Does the model account for significant variance in the DV? H0 rsquare=0

Question 21

What does “ANCOVA” stand for?

Answer 21

Analysis of Covariance

Question 22

What is covariance?

Answer 22

The tendency for two scores to vary together/ in a similar way.

Question 23

What are the key similarities between ANCOVA and blocking?

Answer 23

Both reduce the size of the error term by including a factor that explains a proportion of variance in the DV.

Question 24

What are the key differences between ANCOVA and blocking?

Answer 24

ANCOVA statistically adjusts the error term, and can use control variables that are continuous.

Question 25

What kinds of variables can serve as covariates?

Answer 25

Anything that is continuous and has no interaction with the DV.

Question 26

How does ANCOVA reduce error variance?

Answer 26

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.

Question 27

How does the reduction of error variance help increase statistical power for the test of the focal IV ?

Answer 27

The partitioning of variance by the covariate reduces the size of the error term, just like in blocking designs.

Question 28

Why would ANCOVA want to adjust the treatment means.

Answer 28

Because it helps to adjust for differences int he covariation in the focal IV and error term.

Question 29

When ANCOVA adjusts the treatment means what research question is being addressed?

Answer 29

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

Question 30

When ANCOVA adjusts the treatment means how is it done?

Answer 30

1. Calculate the overall covariae sample mean
2. Assume that an unconfounded populaiton would share this mean and adjust the mean scores on the DV to share the covariate mean
3. Test group main effect using adjusted means

Question 31

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)

Answer 31

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.

Question 32

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)?

Answer 32

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.

Question 33

Identify the structural model of ANCOVA.

Answer 33

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

Question 34

What are the assumptions of ANCOVA? (6)

Answer 34

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)

Question 35

What if there is an interaction between the covariate and the focal IV in ANCOVA?

Answer 35

The study is confounded.