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I have data for a continuous dependent variable that I'd like to test for normality. It is a time variable that measures the time of occurrence of an event within 30 seconds. If no event occurs within that timeframe, the result is n.a.

The time variable has been measured for a variety of different conditions, defined by combinations of states of four independent categorical variables.

Will I have to check for normality in the whole material (i.e. not split into subgroups) or should I check within each group? Can normality be tested for when there is a defined cut off at 30 secs?

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If you just look at the distribution of the dependent variable, then you look at the marginal distribution of that variable, and that is never assumed to be normally distributed. If there is a normality assumptions then that typically refers to the distribution of the residuals.

Timing variables are almost never normally distributed: They are usually skewed and negative values are typically impossible. There are additional problems with observations that have not yet experienced the event. All this is better dealt with survival analysis, which does not assume normality.

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