Summa Week 13

Question 1

What do we refer to as analysis of covariance?

Answer 1

ANCOVA

Question 2

When and why do we use ANCOVA?

Answer 2

to test for differences between group means when we know that an extraneous variable affects the outcome variable

Question 3

What does ANCOVA control?

Answer 3

known extraneous and confounding variables

Question 4

What is an advantage for ANCOVA re: variance?

Answer 4

reduces error variance by explaining some of the unexplained variance (SSerror), the error variance in the model can be reduced

Question 5

What is an advantage for ANCOVA re: control?

Answer 5

greater experimental control of confounds earns the researcher greater insight into the effect of the predictor variable(s)

Question 6

How do we partition variance in ANCOVA?

Answer 6

SStotal = SStreatment + SSerror + covariate

Question 7

What kind of test would have nine participants randomly assigned to 1 of three groups instructed by three teaching methods: A, B, C, and the DV is a measure of math achievement obtained after the experiment is completed?

Answer 7

a simple 1-way between-subjects ANOVA with the IV of teaching method (3 levels) and DV of math achievement test score

Question 8

If in a simple 1-way between-subjects ANOVA with the IV of teaching method (3 levels) and DV of math achievement test score test an experiment measures math aptitude before the experiment begins, what kind of test does it become?

Answer 8

a 1-way between subjects ANCOVA
IV: teaching method (3 levels)
covariance: math aptitude
DV: math achievement test score

Question 9

In a 1-way between subjects ANCOVA
IV: teaching method (3 levels)
covariance: math aptitude
DV: math achievement test score, why is it ANCOVA?

Answer 9

We cannot reasonably attribute the group difference in math achievement to teaching methods, and we cannot ignore the measurement of math aptitude. the differences among the mean scores of math achievement tests are caused by different instruction methods AND participants’ math aptitudes

Question 10

Why does the effect of the covariate need to be removed when using the regression method?

Answer 10

to control the source of variation due to the initial difference from the IV, not the covariate, a confounding variable

Question 11

Why do we use adjusted means for ANCOVA?

Answer 11

it acknowledges the potential impact of the ANCOVA by zeroing in on what is due to the covariate, thereby limiting the data to the potential impact of the IV(s) alone

Question 12

What is the first step for adjusting means in ANCOVA?

Answer 12

do a regression analysis of the DV from the covariate for each group, and then get the slope value

Question 13

What is the second step for adjusting means in ANCOVA?

Answer 13

calculate the adjusted means by using the formula:

= the adjusted mean of the DV for each group equals the mean of the DV for EACH group minus the slope which is multiplied by (the mean iof the covariate for each group minus the mean of the covariate for ALL groups)
= MadjDV = MDV - b*(Mcovpergroup - Mcovtotal)

e.g. adjusted means of achievement scores = means of achievement scores minus slope times (mean of aptitude test per group - mean of aptitude test for all groups)

Question 14

What does the adjusted means process look like given the example of the achievement scores using teaching and covariate of aptitude test?

Answer 14

= MadjDV = MDV - b*(Mcovpergroup - Mcovtotal)

e.g. adjusted means of achievement scores = means of achievement scores minus slope times (mean of aptitude test per group - mean of aptitude test for all groups)

= MadjA = 4.33 = 0.75 * (6.00 - 7.11) = 5.16 (vs. DV of 4.33)
= MadjB = 8.33 - 0.93 * (6.67 - 7.11) = 8.74 (vs. DV of 8.33)
= MadjC = 11.33 - 0.71 *(8.67 - 7.11) = 10.22 (vs. DV of 11.33)

Question 15

What is the assumption of equal slopes?

Answer 15

the ANCOVA assumes a LINEAR relationship between the covariate and the DV and there is no interaction between the covariate and treatments

Question 16

Is there a strong linear relationship between the DV and covariate scores within all levels of the IV?

Answer 16

if so, then it is a significant relationship in a 1-way between-subjects ANCOVA

Question 17

Are the slopes of the liens relating DV and covariate the same for the three levels of IV?

Answer 17

If so, then it would imply a significant IV-by-covariate interaction, which would require looking into the simple effects. If not found significant, then looking at the main effects would be preferable

Question 18

How do you test the assumption of equal slopes in SPSS?

Answer 18

Analyze - General LInear MOdel - Univariate;
select DV and move it to the DV, select IV and move it to the fixed factor box, and covariate to the covariate, with options for IV in factor and move it to the Display means, select Descriptive stats, estimates of effect size, and homogeneity tests, as well as model - custom in the factors and covariate, select IV and covariate and move them into the model box for main effects as build terms, select them again for interaction as well

Question 19

What line is the test of the homogeneity of slopes assumption in an ANCOVA SPSS summary table?

Answer 19

found in the interaction line between the IV and covariate (METHOD * APT for example), with the df, and F value and Signature indicated for the analysis

Question 20

How would you present a homogeneity-of-slopes analysis in APA?

Answer 20

e.g. A preliminary analysis evaluating the homogeneity-of-slopes assumption indicated that the interaction effect of teaching method and math aptitude test score is not significant, F(2,3) = 0.18, p = .846. The covariate (math aptitude test score) was linearly related to the DV (math achievement test score) within all levels of the teaching methods. The homogeneity-of-slopes assumption was met and we could proceed to conduct a one-way ANCOVA.

Question 21

What does a significant homogeneity-of-slopes analysis imply?

Answer 21

differences in the DV are attributable not only to differences among the IV, but also to the initial differences in the covariate

Question 22

In order to control the source of variability in a homogeneity-of-slopes analysis, what stat technique is used?

Answer 22

ANCOVA

Question 23

What lines in the SPSS output are used for the homogeneity-of-slopes analysis in an ANCOVA test?

Answer 23

the Source line for labelling the covariate, the method, and the CORRECTED total (note the regular total uses a df that is too high)

Question 24

What can be done following a significant result in an ANCOVA?

Answer 24

pairwise comparisons to figure out which adjusted means differ with each other (ANCOVA is still an omnibus test)

Question 25

An example of an ANCOVA analysis for APA:

Answer 25

A one-way ANCOVA was conducted. the IV included ___ levels: A, B, and C. the DV was ___ and the covariate was the ____. The results of the ANCOVA indicated that there were significant differences among the three adjusted means, F(2,5) = 54.29, p < .001, suggesting a strong relationship between DV and IV, controlling for covariate. A pairwise comparison of levels of IV indicated that…