Hi all

Since I'm not sure if it is a problem of Minitab or not I decided to post this question here.

I'm new in multivariate statistics and I would like to understand a possible "linear correlation" between T values and the model coefficients in two-level factorial designs.

The problem is simple: a two-level factorial design with 2 variables and three replicates. Let's see this example from Minitab manual "Meet Minitab 16" (previous versions of the manual use the same example):

In Minitab example the factor A is the "OrderSystem" and the factor B is the "Pack".

When analysing the factorial design including the interaction and using alpha=0.05, we should get:

As I understood, T values here should be obtained from the Student's t-distribution and If |T| > 2 I should reject the null hypothesis for a factor or interaction.

The last column from this analysis was inserted by me and computes the value Coef/T = 0.193 for both the factors and the interaction and also for the constant.

Since I could not reproduce all the factorial design calculations by hand yet and I'm also unable to reproduce a factorial design in R I would like to know the general expression for this T value estimator. From these examples and anothers that I've "googled" and also from my own experimental data I believe that these T values in some conditions could behaves like a linear function of the coefficients but to me it appears to be totally wrong.

If I calculate all the contrasts, the mean over all the experimental data and the standard deviation of the sample, could I calculate this T value estimator or do I need to know anything else?

Could anyone suggest me a good reference to understand how to reproduce all these calculations by hand?

Thank you guys for your attention!

Regis

Since I'm not sure if it is a problem of Minitab or not I decided to post this question here.

I'm new in multivariate statistics and I would like to understand a possible "linear correlation" between T values and the model coefficients in two-level factorial designs.

The problem is simple: a two-level factorial design with 2 variables and three replicates. Let's see this example from Minitab manual "Meet Minitab 16" (previous versions of the manual use the same example):

HTML:

```
<pre>
A B Hours
-1 -1 14.72
1 1 9.62
-1 1 13.81
1 1 7.97
1 -1 12.52
-1 1 13.78
-1 -1 14.64
1 1 9.41
-1 -1 13.89
-1 1 13.89
1 -1 12.57
1 -1 14.06
</pre>
```

When analysing the factorial design including the interaction and using alpha=0.05, we should get:

HTML:

```
<pre>
Estimated Effects and Coefficients for Hours (coded units)
Term Effect Coef SE Coef T P Coef/T
Constant 12.573 0.1929 65.20 0.000 0.193
OrderSystem 3.097 1.548 0.1929 8.03 0.000 0.193
Pack -2.320 -1.160 0.1929 -6.01 0.000 0.193
OrderSystem*Pack 1.730 0.865 0.1929 4.49 0.002 0.193
S = 0.668069 PRESS = 8.0337
R-Sq = 93.79% R-Sq(pred) = 86.02% R-Sq(adj) = 91.46%
</pre>
```

The last column from this analysis was inserted by me and computes the value Coef/T = 0.193 for both the factors and the interaction and also for the constant.

Since I could not reproduce all the factorial design calculations by hand yet and I'm also unable to reproduce a factorial design in R I would like to know the general expression for this T value estimator. From these examples and anothers that I've "googled" and also from my own experimental data I believe that these T values in some conditions could behaves like a linear function of the coefficients but to me it appears to be totally wrong.

If I calculate all the contrasts, the mean over all the experimental data and the standard deviation of the sample, could I calculate this T value estimator or do I need to know anything else?

Could anyone suggest me a good reference to understand how to reproduce all these calculations by hand?

Thank you guys for your attention!

Regis

Last edited: