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How to do T-test with multiple reponses?

MartinY

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

Accepted answers

txnelson

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

txnelson

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.

txnelson

If you use the "?" tool from the tool bar at the top of the window

or while clicked into a JMP window, you press the ? key, you will get a "?" cursor, that you can move over any object in the window and then click on it. It will open a context sensitive help window. In answering your question, if you click on the Parameter Estimates table, the help screens that pop up will provide you with details of what the Parameter Estimates are. Included in the documentation is:

When X'X is singular, a generalized inverse is used to obtain estimates. This approach permits some, but not all, of the parameters involved in a linear dependency to be estimated. Parameters are estimated based on the order of entry of their associated terms into the model, so that the last terms entered are the ones whose parameters are not estimated. Estimates are given in the Parameter Estimates report, and parameters that cannot be estimated are given estimates of 0.

So for your study, these estimates are not of any interest. You should concentrate on the Effect Tests and any subsequent LSMeans comparisons you perform.

All comments

txnelson

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.

MartinY

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

MartinY

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

txnelson

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

MartinY

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

txnelson

If you use the "?" tool from the tool bar at the top of the window

So for your study, these estimates are not of any interest. You should concentrate on the Effect Tests and any subsequent LSMeans comparisons you perform.

MartinY

Hi Jim:

You have fully answered my question, thank you very much for your time and help.

Martin