Chong Ho (Alex) Yu
Illustrate the purpose, the concept, and the
application of ANOVA between-subject design
 will NOT walk through the procedure of handcalculation; you will use a statistical software
package to do your exercises.
 By the end of the lesson you will understand the
meaning of the following concepts:

•
•
•
•
•
•
One-way ANOVA vs. Two-way ANOVA
Grouping factor and level
Between-subject and within-subject
Parametric assumptions
Variance and F-ratio
Confidence intervals and diamond plots
 Analysis
of variance: a statistical
procedure to compare the mean
difference
• Null hypothesis: all means are not significantly
different from each other
• Alternate: Some means are not equal
 There
must be three or more groups. If
there are two groups only, you can use a
2-independent-sample t-test.
 The independent variable is called the
grouping factor. The group is called the
level. In this example, there is one factor
and three levels (Group 1-3).
.
There are two grouping factors.
Unlike one-way ANOVA, in this design it is
allowed to have fewer than three levels (groups)
in each factor.
 In this example, there are two factors: A and B. In
each factor, there are two levels: 1 and 2. Thus, it
is called a 2X2 ANOVA between-subject design.
 In this lesson we focus on one-way ANOVA only,
but you need to know why on some occasions
there are only two groups in ANOVA.


 Between-subject: The
subjects in each
level (group) are not the same people
(independent).
 Within-subject: The
subjects in each level
are the same people (correlated). They
are measured at different points of time.
 In this lesson we will focus on the
between-subject ANOVA only
 If
we want to compare the means, why is
it called Analysis of Variance, not
Analysis of Mean?

In the unreal world, the
people in the same group
have the same response to
the treatment:
• All people in Group 1 got 10.
• All people in Group 2 got 11.
• All people in Group 3 got 12.

But in the real world, usually
there is variability in each
group (dispersion). We
must take the variance into
account while comparing
the means.
 Independence: The
responses to the
treatment by the subjects in different
groups are independent from each other.
 Normality: The sample data have a
normal distribution.
 the variances of data in different groups
are not significantly different from each
other.
 Three
different teaching formats (levels)
are used in three different classes







F = signal /noise(error)
Between-group variance is the signal; we want to see whether
there is a significant difference (variability) between the
groups.
Within-group variance is the noise or the error; it hinders us
from seeing the between-group difference when the withingroup variances overlap.
F = mean square between / mean square within
MSB = Sum of square between / DF between
MSW = Sum of square within/ DF within
Effect size = eta square = SS effect (between) / SS total
Mean square between and mean square error  F
ratio  Probability (p value)
 The p value is smaller than .05 and therefore we
reject the null hypothesis.
 Somewhere there is a difference.
 But, where is the difference? Which group can
significantly outperform which?
 Many textbooks go into multiple comparison
procedures or post hoc contrast at this point, but let’s
try something else.


• Grand sample mean: represented by a horizontal
dot line
• Group means: the horizontal line inside each
diamond is the group means
• Confidence intervals: The diamond is the CI for
each group
 Download
the dataset one_way.jmp from the
Ch15 folder.
 Run a one-way ANOVA with this hypothesis:
There is no significant difference between
difference academic levels in test
performance.
 Use level as the IV and score as the DV
 Use Test of unequal variances to check whether
the group variances are equal.
 If OK, create a diamond plot.
 Is there any performance gap?