Comparing Time Series Data

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• #53658

Bozzone
Member

I have two sensors from two suppliers that measure temperature, pressure and conductivity of sea water at different depths.

One sensor is the reference so I want to know how the new sensor compares to the reference.

The data is non-normal and varies over time (the sensor is moving up and down through the water).

Is there a statistical tool I can use to analyze the data? I’m using MiniTab.

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#191013

Robert Butler
Participant

1. Data normality is not an issue.

2. While the data you are describing has been gathered over time your question is concerned with agreement and not temporal variation therefore time series issues are not the focus of your concern.

If you want to test for simple agreement – that is to say examine the results for bias or trending you could use the Bland-Altman test.

If you want to treat one as the standard you might be able to build calibration curves but given the fact that you are varying temperature, conductivity, and depth (pressure would be a function of depth) you will have to have multiple independent sample readings at various combinations of these variables and these variable combinations would have to be such that in the data set used for calibration they were independent of one another.

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#191014

Bozzone
Member

Robert,

Thank you for the response. I realized after I posted that what I need to look at is a scatter plot. Pressure is the independent variablle and temperature and conductivity are a function of depth.

I read about how you could run a regression on each data set and compare the regressions using ANCOVA. The data does not fit a linear regression very well, R^2 = 5%.

I found this article that describes using a GLM with a covariate to do the analysis.

I think there may be an error for which column to use as the covairate.

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#191015

Robert Butler
Participant

You say “The data does not fit a linear regression very well, R^2 = 5%.”

a) A regression of what against what?

b) Regardless of the regression – did you plot the data first to make sure that a simple linear fit made sense?

With respect to b) if you tested the sensors over a wide enough range of depth it is very likely that the response across the depth range is not a simple straight line. All measuring devices have a region of linear response and, when the things being measured fall outside their measurement specification range the plot of response against whatever is being measured becomes curvilinear.

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#191016

Strayer
Participant

Also consider stratification. You have more than two variables so your scatter plot can be more meaningful if you use the two most critical variables then stratify them according to additional variables. Search this site or elsewhere for techniques.

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#191022

Kennett
Participant

As I understand your question you have sets of data pairs — one result from your standard and one from the new sensor, so for each parameter just run a paired t-test.

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#191111

Liu
Participant

I agree with you too. If you take one sensor as reference, then what you need to do is to make a 2-sample t-test of both sensors to check p-value. That’s enough!

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#253645

Greg Alexander, PhD, PE
Participant

Paired (as Kennett said), not 2 sample (as Liu said). Normality test should apply to the differences, not to the raw data. Maybe the bias and linearity test would be helpful also.

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