What is the equations to calculate prediction intervals for the next one sample and multiple samples?

[#1]

Hi! 

I have been taking the JMP free courses. In the Decision Making with Data course, the instructor showed the prediction interval table for one sample and five samples (see the attached screenshot) but didn't give an equation to show how to calculate that. I searched online and found this equation: PI = x̂ ± t* (s√(1+1/n)). In this case, what is the n value I should use to calculate for one sample and five samples? And how to calculate the mean and individual PI for the five samples case? It will be highly appreciated if someone can help answer my question. 

[#2]

Here are the summary statistics for the data.

[#3 · Accepted solution]

Hi @DendrogramSteer,

Welcome in the Community !

For your use case, it will be easier to attach the datatable directly, to check the data (and results of prediction intervals).

You can find the statistical details for prediction interval calculations in the JMP Help : Statistical Details for Prediction Intervals (jmp.com).

In the equation, n is the number of samples you already have (in your example, 100) so this number doesn't change if you're using the formula for the prediction interval calculation of the mean for the next sample or for the next 5 samples. The number m refers to the number of samples for which you want to have a prediction interval for the mean.

I hope this answer will help you,

[#4]

Thank you @Victor_G. It is very helpful! I have a follow question though. In this example, the sample size is 5, and there are a total of 20 subgroups which make up 100 samples in total. In this case, should I use 5 or 100 for n? Thank you.

[#5]

Hi @DendrogramSteer,

In the example of STIPS course, there are 100 measurements of diameter values done in 20 subgroups (corresponding to machines used), and the sample size used here is 100 for the prediction intervals of the mean : we want to know, for any machines used, what would be the 95% prediction interval for the mean diameter for the next value : https://community.jmp.com/t5/Learning-Center/Calculating-Prediction-and-Tolerance-Intervals/ta-p/271...

But depending on your objective, you might calculate it with a smaller sample size : Suppose you know that the next piece will be done with Machine 3 (or you are only interested in results from Machine 3), you might be interested to calculate the prediction interval for the mean only for the pieces that were measured with Machine 3. You may in this case use the sample size 5 (for Machine 3) in your calculations and calculate the corresponding prediction intervals just for this machine (due to the lower sample size, your prediction intervals will probably be wider than those calculated with sample size 100).
Another option could be also to calculate prediction (or confidence) intervals for each machine, and see how they differ from each other : has one machine on average significantly smaller measurements of diameter ?

The analysis and choice of parameters values should be guided by your objective.

I hope this answer help you,

[#6]

Yes, that cleared up my confusion. Thank you very much @Victor_G!