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

>