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Unformatted text preview: sence of any difference due to IV levels.
All levels checked simultaneously
Two outcomes: IV had no effect, or some level of the IV had an
effect on the DV.
Ha: not (H0: m1=m2=m3=....=mk)
When you reject the null hypothesis, H0, you do not know which of
the means were different from which others
Post hoc tests required
Conceptually - how it works
Check if between-group variance is larger than within-group
similar to checking if total variance is larger than error
within-group variance is an estimate of error variance
between-group variance is error variance + a function of
**BOOK ERROR ABOVE**
harken back to project 1
To test if the difference is significant, one uses an F-test
F = between group / within group
Note the effect of error variance. 3
REMINDER: We’re dealing with inferential statistics here rather than
the descriptive stats used in Project 1
Sums of squares
SStotal = S(xi - GM)2
Note that total variance = SStotal / n-1
The total sum of squares = between group SS and within-group
Within group variance is an estimate of error variance
SSwg = S (x1 - x-bar1) 2 + S(x2 - x-bar2) 2 + ... (xk-x-bark) 2
To get an index of average error variance, divide this quantity
by the dfwg = n - k
This is an estimate of the error variance - variance not
accounted for by the IV
Between group variance - what does it estimate?
There will be some between group variance simply due to error
If there is no systematic variance, between group variance is an
estimate of error variance.
SSbg = n1 (x-bar1-GM) 2 + n2 (x-bar2-GM) 2 + nk (x-bark-GM) 2
dfbg = k - 1
MSbg = SSbg / k -1
So the goal is to determine whether the between group variance,
MSbg, is very similar to MSwg, thus making it = to the estimate of
the error variance OR whether it is greater than MSwg, thus
meaning that the group variable, the IV, is causing additional
Use an F-test to compare the two:
To determine if the F is significant, you look up a critical F in
an F-table (Appendix A3). Must know the degrees of freedom
and choose an alpha level.
So, the steps are:
1. Find SSwg, divide by n - k to get MSwg
2. Find SSbg, divide by k - 1 to get MSbg
3. Calculate F = MSbg / MSwg
4. Look up Fcritical
5. Compare calculated F to F critical
Anticipated sizes of F values
Note, if you have two groups, F is = t^2
t’s are analogous to ‘std. deviations’
so 2 s.ds above the mean is unusual, i.e. t=2 is a bit unusual.
Hence an F of 4 would be considered large
See 1st column of A3, p. 275 4
Look at table A3 to get an idea of the sizes of F values that are
Also, note that the .01 table has higher F values - larger effects are
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This note was uploaded on 06/30/2012 for the course PSY 211 taught by Professor Chance during the Spring '11 term at University of Phoenix.
- Spring '11