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Data point variability

I'm looking for a way (column properties?) to tell JMP that the values in a column have inherent error or uncertainty.  For example, an analytical scientist may report the presence of a contaminant at 20 ppm +/- 3, and all the data in the column are +/- 3 ppm.  Can this be done?  I'd prefer that the analytical scientist share all the repeated measurements, but sometimes repeated measurements aren't made, sometimes it's not possible to report, and sometimes the long-term variability or error is well known.  Thanks.

Re: Data point variability

Just my two cents here.

Like all statistical software, there is no way to directly incorporate point variability into the data. Why? Because the variability needs to be estimated every time. For any particular observation, we do not know how much error was "observed". So a value of 20 +/-3, is that normally distributed with a sd of 3? Or is it a range of +/- 3? And what if for that particular setup, at that time was really only +/- 1? So, replication is needed to estimate that error. Further, the error that was seen when a method was created is not necessarily the error that will be seen in the future. Things change. The error needs to be estimated for each study.

 

Also, ultimately, the error is needed for statistical testing (making decisions about a mean, not single points) which means you really need a STANDARD ERROR, not a standard deviation (which is what is usually reported with point variability). The standard error needs the square root of n, so what was n? Should n=1? If the long-term variability is known, then you can build your own tests based on that, but again, you need the STANDARD ERROR, not standard deviation. 

 

Bottom line is what would you do with that information? How do you think it could be incorporated? You could create your own procedures based on what you want to do, but you would likely need to build it.

Re: Data point variabilityDan, in response to "Bottom line is what would you do with that information? How do you think it could be incorporated?" I want my graphical analysis of the data to show error bars. Where I have single data points, or a small set of data for a given set of conditions, the analytical chemists look at the data and say "it's all the same", but based on the few data points available the stats say "they're different". In the back of my mind I say, "they're probably right because they know about the inherent error in their measurement", but since I don't have the data I can't record it and plot it, or do t-test/ANOVA with it.

Re: Data point variability

You can always add a column that indicates the variability for each observation. That column could be used to create your error bars. I have attached a data table with a script that shows this.

 

Please keep in mind that error bars have no standard format. People use them in many different ways. You will certainly need to explain what the error bar represents and how to use it. Error bars based on a single point are certainly not standard and would not be appropriate for comparing data since it does not incorporate the distribution of the data. Error bars assume symmetry which is often not true for distributions of individual points. Comparisons are typically done with means, not data points, so that distributions will be understood (thank you Central Limit Theorem!). 

Re: Data point variability

Thanks Dan.  I don't know a quick way to use the error column to create the error bars in JMP.  I could do it "artificially" in Excel by creating high and low values corresponding to each value, then bring the data over to JMP, but that seems a bit laborious.  Is there a way to use the data in the error column directly?

Re: Data point variability

Yes! Look at the script in the JMP file that was in my last post. I used Graph Builder. Drag the X column (sorry for my poor naming!) to the Y-axis. Drag the Group column to the X-axis. Drag the Error column to the Interval role.

I have attached a small video that shows the steps.