```avganova(1)                 General Commands Manual                avganova(1)

NAME
avganova - compare images using nested analysis of variance

SYNOPSIS
avganova

DESCRIPTION
Avganova will do statistical comparisons, using nested analysis of
variance, on the output of the program Imavgstat(10.

This output consists of mean, standard deviation, and standard error of
the mean for all of the summing areas in a series of different data
sets.  The summing areas were derived from a set of summing regions
specified by an IMOD model; each summing region was divided into one or
more summing areas.

To set up a comparison, you designate one collection of data sets as
Group 1, and another collection of data sets as Group 2.  (The ANOVA
requires that each group contain more than one data set.)  You then
specify a collection of summing regions.  The ANOVA will be run sepa-
rately on each summing area within those regions.  More generally, you
can do a multiple comparison of differences among more than 2 Groups.

Each of the data sets included in a comparison may be rescaled indepen-
dently; i.e. a particular linear scaling may be applied to all of the
areas in a data set, a different scaling may be applied to all areas in
another set, etc.  It is also possible to apply the same scaling, or
the same form of scaling, to all data sets without entering values for
each set separately.  Scaling may be specified in four ways:  1) One
may directly specify a factor to multiply by and a factor to add.  4)
One may specify that the values for a set are all to be divided by the
value for a specified area of that set.  3) One may specify that a
given set should have its values shifted (without any multiplication)
so that the mean of a particular collection of summing regions matches
the corresponding mean for some other data set.  4) One may do a least-
squares linear regression between the data points of the set being
scaled and the corresponding data points of some other set, and use the
coefficients of the regression to determine the scaling factors.  The
data points used for regression are the means from the summing areas
within a particular collection of summing regions.

Entries to the program are now described in order as they are first
encountered.  After doing one comparison, one may loop back to a vari-
ety of different points in order to change different parameters.

Name of statistics file output by Imavgstat

Number of groups of sets

List of numbers of the sets to include in Group 1.  Sets are
numbered from 1.  You can enter ranges separated by commas,
e.g. 1-3,7-9

List of numbers of the sets to include in Group 2.

List of numbers of the sets to include in Group 3, if any, etc.

List of numbers of the regions to compare.  Ranges are OK

0 to compare the means of the summing areas, or 1 to compare the
integrals, which are the means times the number of pixels.

List of numbers of sets to rescale - ranges may be entered, or just
Return for no rescaling, or enter / to select either all sets or
the sets selected last time, as indicated by the prompt.

IF you select rescaling, first enter 0 to specify scaling separately
for each set, or 1 to apply the similar scaling to all sets.

IF you select rescaling, next make the following entries for each
set that you specified for rescaling:

0 to specify scaling factors directly, 999 to divide values by the
value in one area, or the number of another data set, if you
wish to regress this set against the other set, or the negative
of the number of another set, if you wish to shift this set to
have the same mean as that set.

IF you entered 0, next enter the factor to multiply by, and the

IF you entered 999, next enter the region number, and the number
of the area within that region, to divide by.

BUT, IF you entered a set number, next enter a list of the numbers
of the regions to use for comparing the two data sets.

For each comparison, the program first prints a t-statistic (with sig-
nificance level) for a simple comparison of the mean of the means in
Groups 1 and 2.  This statistic is not as valid as the one from the
ANOVA which follows.  However, it is a one-tailed statistic and might
be more suitable for evaluating whether the two groups differ in a
direction that was expected a priori.  The top line of the ANOVA table
shows the significance of difference between the two groups.  The sec-
ond line shows the significance of differences among the different data
sets within each group (subgroup differences).  If the conditions for
the Satterthwaite approximation are satisfied, then the results from
that approximation are printed next and should be used for comparison
between groups, instead of the first line of the table.

After the comparisons, enter one of the following: 1 to loop back to
the specification of rescaling of sets 2 to loop back to entering the
list of regions to compare 3 to loop back to entering the list of data
sets in the groups 4 to loop all the way back and read a new data file
5 to exit

HISTORY
Written by David Mastronarde, 4/23/90

BUGS
Email bug reports to mast at colorado dot edu.

IMOD                                4.9.10                         avganova(1)
```