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Find differences between related groups of data containing replicates

AGM

I am trying to assess if there is a difference between the hardness of specimens before and after an experiment and I am considering using MANOVA or a univariate ANOVA to do this.

The data that I have is on several different specimens where each specimen has six hardness values recorded before the experiment and a further six after the experiment is done.

What I want to gain from the analysis is:

1) is there a general difference between the pre and post experiment hardness values.

2) Is there a difference between the pre and post experiment hardness values for specific specimens.

What I need help with deciding is:

1) what type of analysis is the most sensible to use.

2) is there a way for me to account for uncertainty of the measurement device when deciding significance?

Thank you in advance for any help.

Accepted answers

Phil_Kay

Hi,

To be clear:

You have n specimens and you measure hardness on each of these 6 times before and after treatment.
Therefore you have n * 6 * 2 observations of hardness.

Is that right?

I would suggest using Fit Model.

Y = Hardness.

Specimen as a random effect.

Treatment as a fixed effect (the regular flavour of effect) with two levels: before and after.

You would need the data in a stacked form: i.e. 12 rows for each specimen (6 for before, 6 for after).

This "mixed" model will separate the measurement variance from the specimen variance.

This should ensure your significance tests are meaningful.

Hope that helps.

Phil

All comments

Phil_Kay

Hi,

To be clear:

You have n specimens and you measure hardness on each of these 6 times before and after treatment.
Therefore you have n * 6 * 2 observations of hardness.

Is that right?

I would suggest using Fit Model.

Y = Hardness.

Specimen as a random effect.

Treatment as a fixed effect (the regular flavour of effect) with two levels: before and after.

You would need the data in a stacked form: i.e. 12 rows for each specimen (6 for before, 6 for after).

This "mixed" model will separate the measurement variance from the specimen variance.

This should ensure your significance tests are meaningful.

Hope that helps.

Phil

AGM

Hi,

Thanks for responding. Yes, your statements are correct.

Your proposed method works well, in that it gives an answer that makes sense. More importantly it lets me check the assumptions of the analysis and the quality of the fit in a way that I am confident about.

Two further questions, if you don't mind answering them:

1) I am assuming that the personality should be standard least squares, is that correct?

2) Can I assume that the central limit theorem is applicable here? Or, would I need 30 odd measurements per specimen and per treatment to do that?

Thanks

Alec.

Phil_Kay

Hi,

1. Yes, I think you will want to use Standard Least Squares as the personality. I don think that other personalities are supported with random effects.

2. 30 observations is a useful rule of thumb. You can expect the standard deviation of 30 observations to be very close to the standard deviation of the population. The smaller number of observations in your study is accounted for in the hypothesis testing in your analysis.

Hope that helps.

Phil

AGM

Hi,

That helps a lot thank you.

Thanks

Alec.