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I am working on an experiment which detects signals as a a function of time. There can be a trigger, but no signal (0) or a trigger with a signal (1). We are interested in how the ratio (likelihood of getting 1) changes over time. In order to study this we need to group the data.

If I group the data points in groups of 100 or 1000, I can of course calculate a standard deviation - but this is dependent on the group size I pick. Is there a better way to calculate this? How?

Here is an image where for each plotted point 100 data points (0 or 1 ) were grouped together.The standard deviation would be 0.04287168. enter image description here

Here 1000 data points are grouped together, so the shift in time is better visible. The standard deviation would be 0.03030996. enter image description here

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    $\begingroup$ you do not have to group it. you can use logistic regression. most possibly with a spline input basis to allow a non linear relationship. Please edit your question to specify in more detail what exactly you want to test - "We are interested in how the ratio (likelihood of getting 1) changes over time." - use 'scientific terms' and the statisticians here can translate it into statistical methodology. $\endgroup$
    – seanv507
    Commented Jun 5, 2023 at 9:27

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