49G 50G STAT Version 5 Multiple linear regression & Restricted model & Anova 1way

[Gil]

New version 5
including Analysis of variance ANOVA -1 Way
by the linear regression, with model automatically prepared for the user and appropriate conclusion about the equality of the groups means.

Suppose that, as shown below, you have 4 treatments and n=17 observations, with n1 (for 1st treatment) = 3, n2=4, n3=4 and n4=6.

To check the equalities of the 4 means
(mean1=1.7, mean2=2.8, mean3=4.125 and mean4=4.95), we can procede here very simply, just by one touch of key, running the special C.MODEL program (in the directory DATA ANOVA.1WAY), that automatically prepares and calculates/concludes everything.

For treatment 1, the results were
1.6
2.3
1.2

Go to Directory DATA ANOV.1WAY
Save these 3 stack values into the X1 (or other name) Matrix (dimension [3×1]) as follows:
{3 1} —>ARRY 'X1' STO

For treatment 2, the results were
2.5
3
2.8
2.9

Remain in Directory DATA ANOV.1WAY
Save these 4 stack values into the X2 (or other name) Matrix (dimension [4×1]) as follows:
{4 1} —>ARRY 'X2' STO

For treatment 3, the results were
3.5
4.2
4.3
4.5

Remain in Directory DATA ANOV.1WAY
Save these 4 stack values into the X3 (or other name) Matrix (dimension [4×1]) as follows:
{4 1} —>ARRY 'X3' STO

For treatment 4, the results were
4.1
3.9
4.6
5.2
5.9
6

Remain in Directory DATA ANOV.1WAY
Save these 6 stack values into the X4 (or other name) Matrix (dimension [6×1]) as follows:
{6 1} —>ARRY 'X4' STO

Remain in Directory DATA ANOV.1WAY
Now put the following list
(containing the appropriate 4 names that you created)
{X1 X2 X3 X4} in stack level 1

and, always in that directory, just press C.MODEL

Four results a, b, c & d will be automatically generated:
a) for the n (here 4) groups of treatments, creation of new n-1 (here 3) independent variables always called TR.1 TR.2... TR.n-1 (no TR.n!), here then TR.1 TR.2 & TR.3 (no TR.4!), and creation also of the dependent variable always called Y.TR that contains all the results of the n (here 4) treatments groups;
b) a "hidden" list for the linear model that will be used automatically, here
{1 TR.1 TR.2 TR.3 Y.TR} (with always the constant 1 as first element and then the variables TR.1 TR.2 TR.3 Y.TR specially adapted for the ANOVA-1Way Analysis with the linear regression);
c) the final visible output, ie the test result relative to the equality of the n groups means mu (here 4),
d) together with the detailed ANOVA table (with the corresponding probability).

It says that Fc(Calculated with the effective data of the experiments) in last column of ANOVA, line 2, = 20.54*
> Ftable(0.05, v1=3, v2=13), last column, line 3, = 3.41.
—> You should be very confident in rejecting the Ho Hypothesis that the 4 means** are equal at 5% level.

* The complex part, when editing that cell, is the corresponding calculated probability: 3.26*10^(-5)
or 3.26*10^(-3)% (here, a very, very tiny probability that we might however accept that at least two means mu — among the n groups/means, here then among the 4 groups/means — are equal, not knowing though which means mu_i might be considered as equal).

** The n means (relative to the last comparison test — last run of C. MODEL in directory DATA ANOV.1WAY — for the n groups means, here 4 groups/means) may always be found by pressing muANOVA (F-key on the right of ANOVA-Menu-Variable).