I just stumbled across this thread, and am answering for the benefit of
those searching the archives (hopefully the OP has long since finished
this analysis).

Within a tissue type, there are k=4 groups with n=12 observations per
group.

To test the difference between a PRE-SPECIFIED pair of groups, you would
use the t statistic
t = (ave1-ave2)/(S*SQRT(2/12))
where S is the pooled estimate of standard deviation (since a basic
assumption for ANOVA is that the variance is the same within each group)
S = SQRT(MSE) = SQRT((devsq1+devsq2+devsq3+devsq4)/44)
based on 44=k*(n-1) degrees of freedom. The critical value for this
test would be 2.02=TINV(0.05,44).

The shortcoming of the preceding discussion is that the type I error
rate is 5% for each test, so with multiple comparisons, the probability
of an error in at least one comparison is much larger than 5%. In
particular, to identify unspecified significant differences, you are
essentially evaluating all pairwise comparisons, which in this case is
6=COMBIN(4,2) comparisons.

The Bonferroni approach approximates the overall error rate by assuming
that each comparison is independent, so that the null hypothesis
probabilities of non-significance multiply. Hence you would use the
previously discussed t statistics with a critical value of
2.75=TINV(1-(1-0.05)^(1/6),44).

The shortcoming of the Bonferroni approach is that you cannot get six
independent mean differences among only four independent means. Hence
the Bonferroni approach is conservative (the true overall error rate
will be less than 0.05).

Tukey showed that the actual critical value should be 2.67=3.78/sqrt(2)
where 3.78 is interpolated from a table of percentage points for the
studentized range
http://web.umr.edu/~psyworld/virtual...icaltable.html
(k=4, df=44).

If you want to avoid using a table,
http://lib.stat.cmu.edu/apstat/190
gives Fortran code for calculating the p-value
(1-prtrng(3.78,44,4,ifault)) or the critical value
(qtrng(1-0.05,44,4,fault)) for the studentized range.

Since Tukey's HSD multiple comparison procedure uses studentized range
tables, it is more common to work with t*SQRT(2) instead of the usual t
statistic (so you can use the tabled values directly).
http://web.umr.edu/~psyworld/tukeyssteps.htm

If the groups do not all have the same number of observations, then it
is often recommended to use the harmonic mean of the two group sizes
http://davidmlane.com/hyperstat/B95118.html
The greater the differences in sample sizes, the more that this is only
an approximate solution.

Jerry

Per Madsen wrote:

I originally posted this in microsoft.public.mac.office.excel but was
advised to post it here aswell:

I'm afraid I need a little help on this!

I've done a series of measurements on tissues from the Green Shorecrab.

The test specimens were divided into four groups (A-D), with 12
individuals in each. The crabs in each group were destroyed and 8
different tissue sample's were taken from each individual. An average
were calculated for each group. I then performed an ANOVA test to see if
there were differences between the groups in regards to metal content in
the tissues. The test showed that there indeed were differences between
the groups (p < 0.05). The task now, is to determind which groups shows
a significant difference from one another (is it A and B, A and C,
or...ect), for every type of tissue. This can be done with a Bonferroni
test or a Tukey's test. Unfortunately these tools are not included in
the Data Analysis Toolpack. So, my question is: how can I perform a
Bonferroni or Tukey's test in Excel?

E.g.

Tissue: Gills

A B C D


12 13 12 12
. . . .
. . . .
.
.
.
.
.
.
.
.
.
13 12 14 15
--------------------------------------------------

Average:
12 13 14 15

P.S. Sorry 'bout my broken english

Thx in advance!!!

Per Madsen, Denmark

www.madsen.blogdrive.com