KHA350 Lecture Notes - Lecture 11: Linear Regression, Analysis Of Covariance, Covariate
25 Jun 2018
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Research Methods week 11: Analysis of covariance and step-down analysis
following MANOVA
Shared relationships between two variables: secondary variables that correlate with
the dependent variables in the study
- why do we care about secondary variables correlated with dependent variable
does the presents or absence of IV have a causal effect on the
DV
oSetting up experiment:
Need to control for all factors apart from IV effect on dv
So that any differences are definitely due to treatment
oStatistical control procedure:
Mathematically adjust the scores on the DVD to be what we
think they would be if everyone had the same score on
covariant
oTo ensure this, any secondary variables are controlled for by
elimination
oSometimes we cant use these methodological control procedures
Removing the variance associated with it using ANCOVA
Example: car drivers
- Want to see differences between car types
- duration of car experience will have impact
oneed to do something to the experiment to control for it
oan important factors that will influence our measure
oover and above the influences of car type
- Ways of controlling for experience:
oIgnore it
oOnly select participants with exactly 10 years experience
oDivide into level of experience:
0-5 years experience
and so on
make another IV this is
want to check whether the difference in driving performance
between car types, is consistent across each of the levels of
driving experience
oMeasure and statistically adjust driving score
If everyone had the same degree of driving experience
Comes up with estimation of what scores would be if everyone
had the same score on the covariate
- Applications of ANCOVA:
oElimination of experimental confound
Secondary variables impacting on the DV
Differences between groups on a pre-test measure of the DV
Adjust scores on the post test to what they would be if
everyone had the same score on the pretest
May be differences at pretest
find more resources at oneclass.com
find more resources at oneclass.com
Use the technique to mathematically adjust their scores
on posttest to what they would be if everyone had the
same pretest
oClarification of experimental findings:
Stepdown analyses of MACOVA: determining which of a set
of correlated DVs was responsible for a significant
MANCOVA
A series of correlated variables: work out what are the most
significant variables
Using step down procedures
Useful: if there is a secondary variable impacted on the DV, we
want to remove this from the equation
Gives us a more sensitive test of treatment effects
Gets rid of extraneous noise: unexplained variation
Remember that ANOVA compares the amount of
variance due to treatment vs. the amount of unexplained
variance
Removing the variance that is due to differences on the
covariate will reduce the amount of unexplained
variance
- ANCOVA processes:
oIn an example where:
IV: two different teaching methods
DV: end of year exam mark
CV: pre-treatment aptitude test
ANCOVA procedures closely parallel a two way
ANOVA
Need to know that the two groups are similar in other
respects at baseline
Individual differences
Wont be a fair comparison of the DV
EG. Take people’s second year stats mark and treat it as
a covariate
oWill be pretty strongly correlated with third year
marks
oIe. CV correlated with DV
This gives us:
Main effect of treatment: is there any difference in third
year mark between scores of one teaching method and
the other
oTests whether the means of the groups are
significantly different after controlling for the
effect of the CV on the DV
Ie. If everyone had the average score
after second year
oAlternatively, tests whether the means of the
groups on the DV are significantly different at
the mean of the CV
find more resources at oneclass.com
find more resources at oneclass.com
MAIN EFFECT OF COVARIATE:
oALWAYS LOOK AT THIS FIRST
oWANT IT TO BE SIGNIFICANT: IF NOT,
there is no point in doing a ANCOVA
oIf the CV isn’t correlated with the dv THEN
THERE IS NO POINT
oBecause its not having a significant impact on
the DV to begin with
Interaction between the treatment and the CV
oTests whether the relationship between the CV
and the DV is the same for all the treatment
groups
- Basic principles of ANCOVA:
oSPSS runs regression models:
For the relationship between the CV and the DV
Does this for both of your groups
Experimental group and control group
Uses these regression lines as a way to estimate what
participants score will be at a particular value of your CV
oBe cautious: regression is not always an accurate estimate
oANCOVA assumes:
The relationships between the CV and the DV are equal
The slopes between these two regression lines are equal
Important: if they are equal it doesn’t matter at what value of
the CV; the size of the difference will always be the same
Because the lines will run in parallel
Linear regression lines
If the linear regression has the same slope for each
experimental group, then it is possible to control for differences
between the groups on the CV by determining their respective
DV scores at a single point on the CV
oIf the linear regression line has different slopes for each experimental
group, then it is still possible to control for differences between groups
on the CV by determining their respective DV scores at a single point
on the CV
- Rephrasing of ANCOVA tests:
oIn two group design with 1 DV and 1 CV
oMain effect of the covariate:
Is the slop of the regression line for the DV-CV relationship
significantly different to zero?
Is there a correlation between the scores on the DV and the CV
oMain effect of the IV:
Are the intercepts on the regression lines for each group the
same?
If not, then there is a significant difference between the groups
on the DV when the cv IS 0
oInteraction
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Research methods week 11: analysis of covariance and step-down analysis following manova. Shared relationships between two variables: secondary variables that correlate with the dependent variables in the study. Why do we care about secondary variables correlated with dependent variable does the presents or absence of iv have a causal effect on the. Need to control for all factors apart from iv effect on dv. So that any differences are definitely due to treatment: statistical control procedure: Removing the variance associated with it using ancova. Ways of controlling for experience: ignore it, only select participants with exactly 10 years experience, divide into level of experience: Want to check whether the difference in driving performance between car types, is consistent across each of the levels of driving experience: measure and statistically adjust driving score. If everyone had the same degree of driving experience. Comes up with estimation of what scores would be if everyone had the same score on the covariate.
