Hello All,
I'm using SPSS, and I have a question concerning the estimated
standard errors that are reported with the emmeans in an unbalanced
design (ANOVA) when using
SSTYPE(3). First, I want to make sure I'm fully understanding how
they're computed, and then I want to see if I can then make a leap to
calculating (reporting) the estimated standard deviation based on this
information.
So, I'll use as an example a 2 x 2 factorial design in which males and
females were asked to indicate their enjoyment of a film clip that was
either nonviolent or violent. So, the first factor is gender (male,
female), and the second factor is film violence (violent, not
violent). Subjects were assigned, and the n's for each of the four
cells are (please note that this is just an example - not real data):
Male;Nonviolent = 3
Male;Violent = 5
Female;Nonviolent = 5
Female;Violent = 3
When I look at the emmeans table for gender, for example, here are the
estimated marginal means and standard errors:
Male
Mean: 5.433
SE: .357
Female
Mean: 3.500
SE: .357
Now, based on reading info on the SPSS site, I see that the estimated
standard error for the MODEL is equal to SQRT(MS Error), which in this
example is:
SE Model = SQRT(.956) = .9775
I also learn that the estimated standard errors reported with the
emmeans (for a one-way ANOVA) are equal to:
Estimated SE = SE Model / SQRT (n for the cell)
Now, when it's a factorial anova with unequal cell sizes, it *seems*
that the n for the cell for main effects or lower order interactions
is equal to 2 X harmonic n for the cell.
For example, let's say that I wanted to figure out the estimated SE
for males (across levels of film violence). Given 3 males in the
nonviolent condition and 5 males in the violent condition, this would
be:
2 x (( 2 x (3 x 5)) / (3 + 5)) =
2 x 3.75 = 7.5
With this, the Estimated SE for Males (across levels of film violence)
is:
Estimated SE for Males = .9775 / SQRT(7.5) = .3569
This is exactly the figure provided to me via SPSS.
So, my first question is --- is this reasoning right here? I want to
make double sure because I can't find information about the specific
calculations that SPSS is using, and so I'm feeling my way through
this by generating multiple examples and seeing if it holds (which it
seems to so far).
And, my second question is this. It is possible to then use the same
logic to generate the estimated standard deviation for the cell?
For example (using the same male example):
Would it be: ?
Estimated SD = SE * SQRT(harmonic n)
Estimated SD = .3567 * SQRT(3.75) = .6907
Or would it be: ?
Estimated SD = SE * SQRT(2 x harmonic n)
Estimated SD = .3567 * SQRT(2 x 3.75) = .9769
The reason I'm asking this estimated standard deviation question is
because I find that many of the journals in my field want to see SD
rather than SE with the means. Also, I just want to know if my
thinking is okay on this one.
So, thanks for your help!
Kind regards,
Mary Beth Oliver
Penn State
College of Communications
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