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I have three sets of data, measured by three different devices: A,B and C of air balloon whose fall is influenced by wind. Each data sheet looks like:

A:

Longitude    Latitude    Altitude    Weight    Rotation(about main axis)   Time
    ...       ...           ...       ...       ...                         ...

B:

Longitude    Latitude    Altitude    Weight    Rotation(about main axis)   Time
    ...       ...           ...       ...       ...                         ...

and similarly for C.

Are there standard techniques to compare the error measurement of B and C with respect to A (considered standard)?.

Note that except time, all other parameter can both increase and decrease, and longitude/latitude and rotation are the only parameters that can be positive and negative.

The problem with regression is that I do not have independent/dependent variables. The method of error analysis I generally use is to calculate ${\rm Err}_{x}$, ${\rm Err}_{y}$, and ${\rm Err}_{z}$, and combine them suitably when I have a function explaining something. I do not have 'the function'. (I mean I do not have a function to use 'propagation of error'.)

Precisely, I am trying to measure accuracy of devices B and C

Side note: I could not find an appropriate tag.

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  • $\begingroup$ And where is the question? $\endgroup$
    – sashkello
    Jul 17, 2013 at 7:41
  • $\begingroup$ @sashkello The was small thinking error. I intended what are? but wrote these are. Sorry. $\endgroup$
    – user59756
    Jul 17, 2013 at 7:44
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    $\begingroup$ Can you give examples of results you expect or even hypotheses? This will influence the answer. For example, I suppose combined change over time in longitude and latitude (i.e. speed) might be interesting. Or only change in altitude over time? On the other hand, change in weight over time maybe not? $\endgroup$
    – robert
    Jul 17, 2013 at 8:56
  • $\begingroup$ @robert, thank you for your comment. I expect change in all quantities. Longitude and latitude and altitude definitely change. Weight also change slightly when you consider significant change in altitude. I am merely measuring accuracy of two devices B and C with respect to A(consider standard). Hypothesis would be accurate measurement. I don't know what else? $\endgroup$
    – user59756
    Jul 17, 2013 at 10:19
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    $\begingroup$ For clarification: (1) You want to know how much measurement error there is in the data that come from each device; & (2) A is considered the 'gold standard' / measured w/o error. Is that correct? $\endgroup$ Jul 17, 2013 at 12:49

1 Answer 1

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I would suggest two approaches. First compare relative differences in all measures, and then use linear regression.

  1. Compute relative differences, e.g. $(longitude_{B}-longitude_{A})/longitude_{A}$ for all variables at all time points (assuming the devices measured all variables at the same time points). Then look at the distribution and change over time of the differences.

  2. If the differences increase over time (which might or might not be plausible) you could use linear regression with time as predictor and relative difference in e.g., longitude, as variable you want to explain. This could be done for each variable and pair of devices.

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  • $\begingroup$ Ok, what does linear regression tell me here? Since I need total error, why is linear regression better than averaging the relative difference in specific quantity. $\endgroup$
    – user59756
    Jul 17, 2013 at 14:17
  • $\begingroup$ If you only care about total error then you don't need linear regression. However, if (and only if) the error changes over time I could imagine it would make a lot of sense to include that aspect in your analysis. For example, sensor error could increase over time because the accuracy of the sensors deteriorates over time or because measurements at $t_2$ depend on measurements at $t_1$ (and error accumulates). Whether such a scenario makes sense or not is of course up to you to decide. $\endgroup$
    – robert
    Jul 17, 2013 at 14:33

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