How to do T-test with multiple reponses?

[#1]

Martin here:

I want to evaluate two chemicals ( two suppliers) in an adhesive formulation in terms of adhesion.

This would be a classic T-Test. But I have multiple adhesions results to compare.

Adhesions results would be: 28 day, 20 mins; 30 mins;  after immersion; heat aging, etc.

How could this be done in JMP?  In terms of interpretation, do I have to do T-Test individually for each

adhesion?

Thanks!

Martin

[#2]

My question is:  Do you test the same parts at the 3 different times?

While you could do multiple t-tests, this would be a poor way to analyze your data.  And you would be loosing a lot of information in your data.  First, you would be missing out on the determination of a potential chemical vs. time interaction, and secondly, performing multiple t-tests will result in alpha slippage because of performing the multiple tests.

What you really need to do, is to initially analyze your data using a single model, and then from it's results, perform subsequent comparison analyses as indicated.  

The design of the the model to use is initially dependent upon my initial question.

[#3]

Thanks Jim.

I make two formulations, one with chemical #1, the other with chemical #2.

Then I apply adhesives on concrete slabs,  some slabs will be stored in standard conditions, some in water, some in oven. At 28 days I will test adhesion for samples

cured under different conditons: standard; water; oven.

So basically, I have two factors: Chemical #1 and chemical #2.  but I need to evaluate their adhesion across different curing conditions, and the adhesion under different conditons are very different from each other.  I am trying to ascertain whether Chemical #1 and Chemical #2 perform similarly across the board.

Thanks for taking time help me.

Martin

[#4 · Accepted solution]

From what you describe, you have a 2x3 factorial, with replication.  That is, you have samples of both chemicals at each of the 3 conditions of standard, water and oven.  And you have more than one concrete slab with the same combination of chemical and condition.

Given this, you need to run the Fit Model platform, specifying the Model Effects:

     Chemical

     Condition

     Chemical*Condition(Even though you indicate there is no correlation with the conditions, the inclusion of this interaction effect will allow for the testing of such)

along with your measurement variable as your Y (response) variable.

Full documentation, along with interpretation of the reports displayed in the output can be found in the Fitting Linear Models guide.  It is available under the Help pull down menu

     Help==>Books==>Fitting Linear Models

[#5]

Not familiar with linear model, I will ask some silly questions before I read the book you recommend.

Is linear model more for regression model?  here I am not interested in generating a model, probably could not, due to their toal lack of correlation.

Do you have a speific example I can follow?

Martin

[#6]

There is a sample data table with a 2x3 factorial embedded script called "Analgesics.jmp".  Go to the Sample Data Library and open it up, and run the Fit Model embedded script, and you will see the data and the results from the analysis.

     Help==>Sample Data Library

[#7]

Hi Jim:

I attached my results based on the example you recommend.  ( I selected some old results)

My interpretion of the results:

1.  The difference of two chemicals are signifiant

2. The testing conditions of heat aging and standard are statistically signifiant

Here problems start. For adhesion after water immersion Chemical #1 gives 2.596 KN (average) , chemical #2 gives 1.47 KN ( average), in the industry,

This difference is as night and day. Yet, in the summary, testing condition of water immersion is not listed as significant, not even listed.

How can this be solved? 

Thanks

Martin

It is a

[#8 · Accepted solution]

You analysis shows, in the Effect Tests, that your interaction effect of Curing Conditions * Chemical is not significant, and that both main effects of Curing Conditions and Chemical are significant.  Therefore, your main effects can be treated as the overall results.  Because the interaction is not significant, you do not need to test for differences between Chemicals at each level of Curing Conditions.  You can simply state "There is a significant difference between the 2 Chemicals".  The same is true for the significant difference for Curing Condions.  However, because there are 3 levels of Curing Conditions,  you need to determine the sublevel differences of standard vs. water, standard vs. heat and water vs. heat.  These analyses are available under the red triangle for the individual analysis for Curing Condition.  I suggest using LSMeans Tukey HSD.  It is a more concervative test.  It will give you an analysis of which of the Curing Conditions are different from each other. 

[#9]

Thanks for your very detailed explanation.

One remaining problem for me is to understand the table of Parameter Estimates.  Why curing condition " water immersion" is not listed?

and actually Chemical #1 correlation with curing conditon " standard" IS significant, which is in conflict with Effect Tests : Chemical* Coniditon is insignificant.

If I present this table, people will naturally raise these questions.

Should part of JMP output be ignored or they are in conflict with each other?

Thanks

Martin

[#10]

I forgot to mention that there is no correlation among adhesions under three curing conditions.

The three curing conditons are important to predict how adhesives perform in such an environment, but definately the three adhesions are not correlated.

so they do not fit in a model  Adhesion= A* adhesion (SC)+B* adhesion (water)+C*adhesion ( oven). 

Martin