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Level V

## Power analysis - several measurements per individual

Hello everybody,

I have an experiment with several measurements per individual of each sample. I would like to study the impact on the sample size and also the number of measurements per individual on the power and difference that can be detected between two samples. I wanted to use the platform Sample Size and Power - Two Sample Means, but if I am not wrong it doesn't allow to take into account the number of measurements per individual. Is there another tool or maybe script that I could use to investigate this question?

Thanks for your help!

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Staff

## Re: Power analysis - several measurements per individual

Just the number of fruits. The piece of fruit is your sample. The variation across pieces of fruit represents the experimental errors.

You will need to manually add the data columns for the repeated measurements of each fruit (each run). You can add a formula to the response column later to compute the mean of the measurements for analysis of the response.

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Staff

## Re: Power analysis - several measurements per individual

Right, these calculators use the standard deviation of the response. The quantity should represent the natural random variation in the response when no treatment is applied and conditions are always nominal. This variance for a measured response is always the part variance plus the measurement variance. So the standard deviation Y = Sqrt( Var(part) + Var(measure)/n ) where n is the number of replicate measurements for each trial.

A measurement system analysis (MSA) would provide an estimate of both of these variances. See Help > JMP Documentation Library > Quality and Process > Chapter 4: Measurement System Analysis for more information.

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Level V

## Re: Power analysis - several measurements per individual

Thank you very much for your answer.

If I understand correctly, the Measurement System Analysis platform allows to study an experiment and estimate the part of variability due to variability between measurements and variability  between samples.

If I have a rough idea of these values and if I want to conduct a prospective analysis I can use the Sample SIze and Power Platform using the formula that you indicate.

Just to give a dummy example. Let's say that I have samples with 10 objects and each object is measured 3 times. The variance between objects is around 2 and the variance between measurements is around 1.

In that case the global Standard deviation is Y = sqrt (2 + 1/3) =1.53

I will use this value in the Sample Size and Power platform for the field Std Dev and 60 for the sample size. Am I right?

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Staff

## Re: Power analysis - several measurements per individual

Yes, that is the idea of MSA. It is a bit different in your case because you are not measuring a sample of normal parts repeatedly but instead measuring the normal response repeatedly. So if you set up nominal conditions from scratch over and over again, and each time you made multiple measurements, you would have the ability to separately estimate the response variation and the measurement variation. You can do this easily in JMP with the MSA platform, the Fit Least Squares platform, or the Variability Chart platform.

Yes, if you estimated that the response variance is 2 and the measurement variance is 5, then the using the mean of 3 repeated measurements for the response would have a standard deviation = square root( 2 + 5/3 ).

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Level VII

## Re: Power analysis - several measurements per individual

Just a clarification...when you state this "several measurements per individual of each sample" what exactly do you mean.  I don't know what an individual is?  Are you talking about a human?  Or are you talking "parts" as Mark eludes to?  If we are talking parts, then too separate just the measurement repeatability precision, it is assumed you are measuring exactly the same location ion the part 3 times.  If not, you will be confounding within part with measurement repeatability precision.  I also suggest looking at the 3 measurements per treatment with a range chart.  This may indicate unusual measurements within treatment and you would therefore want to be careful about using summary statistics.

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Level V

## Re: Power analysis - several measurements per individual

Hello,

Thanks for your answers @markbailey and @statman.

Just to clarify a bit: I have an experiment with samples of 5 fruits, each fruit is measured 3 times (the measurements are done on 3 parts of the fruits, randomly selected). The objective is to determine if the samples are significantly different or not. In order to prepare the next experiment, I would like to know what would be better (in term of power and difference that can be detected) between increasing the number of measurements per fruit and increasing the number of fruits per sample.

I hope it is clearer

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Staff

## Re: Power analysis - several measurements per individual

Thanks for your explanation. Your situation is analogous to one that calls for a 'three-way control chart.' That is because you have within piece of fruit variation (measurement) and between piece of fruit variation in addition the supposedly fixed effect of fruit variety.

You can summarize the data and use the mean response from each piece of fruit or you can enter it in the model as its own source of variation and estimate this variance. The model would assume that the within piece of fruit variance is the same for all pieces and pool the estimates from all the pieces.

So that is an idea for analysis, but you still need to combine the variances as shown above to obtain the standard deviation for the power analysis.

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Level V

## Re: Power analysis - several measurements per individual

Thanks @markbailey for these additional details.

Just one last question regarding the Power Analysis: for the standard deviation I combine the variance as explained, and for the sample size should I use the number of fruits times the number of measurements or just the number of fruits?

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Staff

## Re: Power analysis - several measurements per individual

Just the number of fruits. The piece of fruit is your sample. The variation across pieces of fruit represents the experimental errors.

You will need to manually add the data columns for the repeated measurements of each fruit (each run). You can add a formula to the response column later to compute the mean of the measurements for analysis of the response.

Learn it once, use it forever!
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Level V

## Re: Power analysis - several measurements per individual

Alright, thanks again for your explanations!
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