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I have a dataset for 'time spent' (hours) carrying out 'behaviours' (walking, lying, standing, grazing), during day or night 'periods' of cattle. Time spent is my dependent variable, with behaviours and periods my independent variables.

Sample dataset below. Time spent is shown as decimal hours and is considered proportional as time spent doing behaviours within any day or night period are dependent on one another (can be expressed as % with sum of all behaviours for a given period totalling 100%). Time spent has a non-normal distribution.

My question is whether or not it is OK to use arcsine (or another) to transform time spent to achieve normally distributed data prior to analysis?

I'm hoping to use a statistical test to determine whether day or night has any affect on time spent carrying out behaviours, but I'm not sure which test I can use.

Cow ID Period Behaviour Hours
Cow1 Day Walking 4.41
Cow1 Night Lying 0
Cow1 Day Standing 5.01
Cow1 Night Grazing 3.24
Cow2 Day Walking 4.41
Cow2 Night Lying 2.01
Cow2 Day Standing 5.01
Cow2 Night Grazing 3.24
Kyle
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    Why do you want to transform into a normal distribution? The inferences on transformed data do not necessarily map onto inferences on untransformed data. There are plenty of analytic approaches that do not require normality. What question are you trying to answer with your data? – Alexis Oct 21 '21 at 02:38
  • Also: Welcome to CV, Kyle! – Alexis Oct 21 '21 at 02:38
  • Hi Alexis - maybe I don't need to transform the data, I'm not very good when it comes to statistics. Maybe all I need to do is some sort of pairewise test using only day/night with hours. Then if there's any significance I can do 4 more pairwise tests for each behaviour and day/night? I want to know whether they graze sig more at night than day for example. – Kyle Oct 21 '21 at 10:38
  • logratio transforms (there are variants ...) are often used with compositional data, and is probably what you need. There are a few posts here: https://stats.stackexchange.com/questions/264609/applied-logratio-analysis-where-do-you-learn-it, https://stats.stackexchange.com/questions/267294/how-do-you-interpret-parameters-from-logratio-analysis-of-compositional-data, https://stats.stackexchange.com/questions/259208/how-to-perform-isometric-log-ratio-transformation – kjetil b halvorsen Oct 21 '21 at 13:24

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