Transcript Document 7737958

Analysis of Covariance
ANCOVA
Chapter 11
ANOVA Terminology
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The purpose of this experiment was to compare
the effects of the dose of ginseng 人蔘 (placebo,
low, high) on the number of bench press
repetitions, while controlling for the energy level
of the strength coach.
The independent variable dose of ginseng is
called a FACTOR.
The FACTOR has 3 LEVELS (placebo, low, high)
The dependent variable in this experiment is the
number of repetitions performed.
Strength coach energy level is a covariate.
Assumptions of ANOVA
Dependent variable is interval or ratio.
 The distributions within groups are
normally distributed.
 The variances between groups are equal.
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The effects of ginseng on repetitions
The effects of ginseng on repetitions
The purpose of this experiment was to compare the effects of the dose of
ginseng 人蔘 (placebo, low, high) on the number of bench press repetitions,
while controlling for the energy level of the strength coach. 15 subjects were
randomly assigned to one of the following conditions (placebo, low dose, high
dose). Strength coach energy (enthusiasm) was coded as 0 = boring thru 7 =
very high enthusiasm.
StrCoach_Energy as Covariate
Check homogeneity of variance if
you have a between subjects factor.
Choose the Sidak post hoc
test.
Plot number of repetitions by ginseng dose
See page 405 of Field for an additional
test to check for homogeneity of
variance.
The groups DO NOT have equal variance,
Levine’s test F(2,27) = 4.618, p = .019
Check homogeneity of variance if
you have a between subjects factor.
The null hypothesis is that the
groups have equal variance. In this
case you retain the null. You don’t
want this to be significant, if it is
significant you are violating an
assumption of ANVOA: homogeneity
of variance.
ANCOVA Results
The Str_Coach energy level was a sig. covariate F(1,26) =
4.959, p = .035.
After controlling for the effects of strength coach energy, there
the dose of ginseng significantly effected the number of
repetitions performed F(2,26) = 4.142, p = .027, power = .68.
Look at posthoc tests to find which groups are different.
Post Hoc
Results
Placebo is different
from High Dose.
Low Dose is NOT
different from High
Dose
Effect Size
The dose of ginseng explained a bigger proportion of the variance not attributed
to other variables than strength coach energy. (see p 415-516).
Assumptions of ANCOVA
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The covariate should be independent from the
experimental factor.
 Run a single factor ANOVA with the covariate as the
dependent variable and the experimental variable as
a fixed factor.
Homogeneity of regression slopes
 Do a scatter plot of each experimental condition with
the covariate on X axis and the dependent variable on
the Y axis.
 Run the ANCOVA with a custom model see p 413 –
415.
Is Covariate Independent of Experimental Factor?
Is there a difference in the covariate (Strength Coach) by experimental factor (Dose)
Is Covariate Independent of Experimental Factor?
No problem. The covariate is
independent from the experimental factor
(Dose), F(2,27) = 1.98, p = .16
Homogeneity of Regression Slopes?
Click the Model Button
1. Highlight Dose, StrCoach
then click Main Effects.
2. Highlight Dose, StrCoach
then click Interaction.
Homogeneity of Regression Slopes?
Look at the interaction term Dose * StrCoach. You
don’t want this to be significant.
In this example the effect is significant, therefore we
are violating the assumption that the regression slopes
are equal.
Homework
Analyze the Task 1 and Task 2 data sets from the book, see
page 419.
Do a Sidak post hoc test instead of the planned contrast
suggested in the book.
Compute the effect size using:
Use the Sample Methods and Results section as a guide to
write a methods and results section for your homework.
Sidak Post Hoc Lacks Power!
According to ANOVA
F(2,11) = 4.32, p = .041
At least 1 pair should be
different, but Sidak
lacks power. You can
either report this p =
0.052, or run a planned
contrast, see the next
page for a planned
contrast example.
Planned Contrast 1-3, 1-2 for HangoverCure
Data Set
Click Contrasts, Choose Simple, Chose First, Click Change, then
Continue. This will run a simple planned contrast of:
1 – 3 and 1 – 2, it does not do 2 – 3.
Planned Contrast 1-3, 1-2 Results for
HangoverCure Data Set
The planned contrast
finds the difference
between 1-2 at p =
0.018.
Where Sidak reported
this difference as
p = 0.052.
This shows that a
planned contrast is
more powerful than a
post hoc test.