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I have a series of data points representing the number of OKs for a test. For each data point, I want to calculate by how much its value changed compared to the preceding value, and I need this measure to be relative rather than absolute, as it makes it easier to understand and to compare different series of the same kind.

I thought I could use a simple

${\displaystyle {\text{Percentage change}}={\frac {\Delta V}{V_{1}}}={\frac {V_{2}-V_{1}}{V_{1}}}\times 100\%}$

But the obvious problem with this approach is that the number of OKs can often be 0, and a division by zero is not possible.

Is there a better way to obtain a relative measure of change in this scenario? I am fairly new to statistics and wonder if there is a measure of index I am not yet aware of that would be more appropriate.

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The fact that you are interested in relative change doesn’t mean that you should compute a measure of relative change from the raw data and then analyze that. It is much better to analyze the raw data, possibly covariate-adjusted for the initial value. (This doesn’t address your wish to adjust for the continuously moving preceding value though). Percent changes are not easier to understand, because they are asymmetric measures, e.g. a 100% increase is offset by a 50% decrease.

Were there no zeros in your data you could do a relative analysis by sampling logging the raw values and analyzing all those logs, converting estimates of interest to fold change by taking anti-logs of regression coefficients, for example.

Comparing different series on % change basis may hide important effects such as the effect of the starting value.

When in doubt, graph and analyze the raw data.

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  • $\begingroup$ Thanks for your insights. I've learned valuable things going through your answer. To clarify: --- I focus on the change since the preceding datapoint as I want to see if the number of OKs has changed compared to the last execution, rather than comparing it to the first execution that might have taken place months ago --- I prefer a relative measure to rank tests with varying numbers of OKs, so that those with the strongest change will come on top --- I've used graphs, but now aim to automate the process to highlight significant changes in OKs. Any further suggestions given these points? $\endgroup$
    – Mr Kartofel
    Commented Oct 15, 2023 at 14:15
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    $\begingroup$ ...and to graph the data I would suggest you put V1 on the x-axis and DeltaV on the y-axis and see what pattern your data points form. Hopefully, they do form a pattern! $\endgroup$
    – Niels Holst
    Commented Oct 15, 2023 at 20:06
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    $\begingroup$ Any measure that involves summarizing two measurements with one number (by subtract, ratio, % change, …) makes assumptions such as the variable being perfectly transformed before doing the computation. I would rather depict “change” by looking at whole trajectories and slopes over time. You can even do this using semiparametric ordinal models that only use the ordering of outcome levels. $\endgroup$
    – Frank Harrell
    Commented Oct 16, 2023 at 11:56

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