Week 4 ANCOVA from the Text Books

Question 1

What is ANCOVA in a nutshell?

Answer 1

ANCOVA is a more powerful version of ANOVA
• ANCOVA brings ANOVA & Correlation together
• ANCOVA is an extension to any type of ANOVA including MANOVA

Question 2

What does ANCOVA do?

Answer 2

• ANCOVA statistically controls for a Covariate(s)
i.e. another variable that is related to the DV
o therefore ANCOVA removes the effect of background error variance
o actually changing scores on the DV
o The DV scores are adjusted to what we would predict they would have been if everyone had scored the same on the covariate

Question 3

What is the F Ratio again?

Answer 3

• The F ratio is the ratio of between-groups variance divided by error variance
o Reducing the error variance (the denominator) produces a larger F ratio
- This larger F ratio has a greater likelihood of achieving significance

Question 4

What is ANCOVA based on?

Answer 4

•ANCOVA is based on the correlation between the covariate(s) & the DV using regression to predict DV scores from the covariate(s)
o The part of the DV score that can be predicted by the covariate(s) is, literally removed from the observed DV score for each participant to produce an adjusted DV score

Question 5

What’s an example of the partitioning of the variance?

Answer 5

In the case of a positive correlation: participants with high scores on a covariate would have their DV scores reduced somewhat whilst those with low scores on the covariate would have their DV scores increased somewhat – to remove the portion of the DV that can be accounted for by the covariate

Question 6

I often hear that ANCOVA needs to be used with discretion. What are the ANOVA assumptions my results must adhere to in order to consider ANCOVA?

Answer 6

•assumes the independence,
normality and homogeneity of the variances
•require homoscedasticity,

Question 7

I often hear that ANCOVA needs to be used with discretion. What are some of the assumptions my results must adhere to in order to consider ANCOVA?

Answer 7

• covariates = interval or ratio (dichotomous can work)
• The correlation between covariates & the DV should be significant
• Multiple covariates need to be chosen sparingly based on a sound theoretical understanding of their relevance. -CV’s should not be too highly correlated with one another
• The CV(s) should be normally distributed (in each group)
• There needs to be a linear relationship between the CV(s) & the DV (in each group)
• The CV(s) should be reliable
• There must be homogeneity of regression.

Question 8

Why should the the correlation between covariates & the DV should be significant?

Answer 8

To ensure reliability of ANCOVA results

Question 9

Why must there be homogeneity of regression?

Answer 9

There must be homogeneity of regression, that is, relationship between the covariate(s) & the DV must be the same across groups.
• This is because adjustments are made to the DV scores according to the overall correlation between the covariate(s) & the DV.
• Such adjustments would be nonsensical if the correlations were actually different across groups

Question 10

When running a true experiment, the CV must not be related to the IV. Why is this?

Answer 10

Otherwise there is a confound – even if covariates are statistically removed using ANCOVA there is no way of knowing what else may be associated with them, hence causal inference is compromised

Question 11

When running a true experiment, why do participants need to be measured on the covariate(s) before being exposed to the experimental manipulations?

Answer 11

To avoid the possibility of the manipulation also affecting the covariate
- Were this to happen, removing the effect of the covariate might also remove part of the effect of the IV

Question 12

What are the rules when running Quasi experiments & Natural Group Designs?

Answer 12

• The covariate(s) must be measured prior to any experimental manipulation in Quasi experiments that use ‘intact’ groups
• For both quasi experiments & non-experimental natural group designs, the covariate(s) may well be related to the IV.

Question 13

It is common for the covariate(s) may well be related to the IV when running Quasi experiments & Natural Group Designs. When does this happen and what can be done about it?

Answer 13

This can occur in quasi experiments when groups differ on the pre-test & also the post-test) & the pre-test is used as the covariate to statistically remove the effects of the pre-existing differences, thereby ‘equating’ the groups.
• Correlations between the covariate(s) & DV are common in natural group designs.
o In these cases ‘interpretation is fraught with difficulty’
o Researchers really need to know what they are doing to use ANCOVA appropriately & need to consult specialised texts beforehand

Question 14

What is the word of caution Hills offers with regard to Populations & Individuals?

Answer 14

*The adjustment of DV scores are only ever predicted adjustments
Thus there is always a degree of error in such predictions
•Whilst ANCOVA is a powerful technique to help establish whether population groups differ overall (i.e., in their means), it tells us very little about what to expect with particular individuals
o This is true for all ANOVA designs, & to all statistical tests; though even more so for ANCOVA (I guess because we are removing the effect of background error variance
i.e., actually changing scores on the DV)

Question 15

According to Andy Field, What are continuous or Covariates?

Answer 15

• Continuous variables predict the outcome / dependent variable
• Continuous or covariates are not part of the main experimental manipulation but have an influence on the DV

Question 16

What can we achieve by measuring the Covariates?

Answer 16

by measuring the CV’s it is possible to control for the influence they have on the DV by including them in the regression model
*If we enter the CV’s into the regression model first, & then enter the dummy variables representing the experimental manipulation, we can see what effect an independent variable has after the effect of the covariate

Question 17

What are the 2 reasons Andy Field gives for including covariates in ANOVA?

Answer 17

• To reduce within-group error variance

* To eliminate Confounds

Question 18

How does ANCOVA reduce within-group error variance?

Answer 18

If we can explain some of the ‘unexplained’ error variance (as found in t-tests & ANOVA’s (SSr) in terms of other variables (CV’s) we then reduce the error variance allowing us to more accurately assess the effect of the independent variable (SSm)

Question 19

How does ANCOVA eliminate Confounds?

Answer 19

In any experiment, there may be unmeasured variables that confound the results.

• If any variables are known to influence the DV being measured, then ANCOVA is ideally suited to remove the bias of these variables.
• Once a possible confounding variable has been identified, it can be measured & entered into the ANCOVA

Question 20

What is a continuous variable?

Answer 20

A CONTINUOUS variable is one that gives us a score for each person and can take on any value on the measurement scale that we are using.

Question 21

What does a CONTINUOUS VARIABLE entail when talking about an ANOVA and/or ANCOVA?

Answer 21

The regression equation for ANOVA can be extended to include one or more continuous variables that predict the outcome (DV).
Continuous variables such as these, that are not a part of the main experimental manipulation but have an influence on the DV, are known as COVARIATES and they can be included used in the ANOVA analysis.
We measure COVARIATES and include them in an ANOVA and call it analysis of covariance (ANCOVA).

Question 22

Field describes the Elimination of confounds:

P.397.

Answer 22

In any experiment, there may be unmeasured variables that confound the results (other than in the exp manip that affect the outcome).
If any variables are known to influence the dependent variable being measured, then ANCOVA is ideally suited to remove the bias of these variables. Once the possible confounding variable is identified, it can be measured and entered into the analysis as a COVARIATE.

Question 23

Two additional assumptions for ANCOVA over ANOVA are:

Answer 23

1. Independence of the COVARIATE and treatment effect.

2. Homogeneity of regression slopes.