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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.
Hypothesis testing
H0: m1=m2=m3=....=mk
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 betweengroup variance is larger than withingroup
variance
similar to checking if total variance is larger than error
variance
withingroup variance is an estimate of error variance
betweengroup variance is error variance + a function of
systematic variance
**BOOK ERROR ABOVE**
harken back to project 1
To test if the difference is significant, one uses an Ftest
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
Calculations
Sums of squares
SStotal = S(xi  GM)2
Note that total variance = SStotal / n1
The total sum of squares = between group SS and withingroup
SS
Within group variance is an estimate of error variance
SSwg = S (x1  xbar1) 2 + S(x2  xbar2) 2 + ... (xkxbark) 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
variance
If there is no systematic variance, between group variance is an
estimate of error variance.
SSbg = n1 (xbar1GM) 2 + n2 (xbar2GM) 2 + nk (xbarkGM) 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
variance.
Use an Ftest to compare the two:
To determine if the F is significant, you look up a critical F in
an Ftable (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
considered significant.
Also, note that the .01 table has higher F values  larger effects are
needed if...
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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
 chance
 Psychology

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