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Say we want to use a method that requires $n > 30$. (Whether this refers to number of observational units or total observations is sometimes vague.)

We have observations on 10 patients for four time points ($t$). Consequently, we have $n=10$ but $t \cdot n = 40$ observations.

Do we consider the required minimum $n$ for the method met due to the total number of observations or not due to the number of observational units?

Although this is really basic, I have not come across a relevant description of this and wonder if anyone have references to this topic.

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    $\begingroup$ Interesting question. Not hazarding an answer but I would be skeptical of calling the number of observations n, as each observation does not provide independent information (as observations are clustered within units). In RCTs in this setting, people often consider the observations as n but account for the fact that each observation doesn't provide unique information by increasing the required sample size proportional to the intra-class correlation (i.e. the proportion of variation at the unit, rather than observation, level) $\endgroup$
    – Lachlan
    Commented Jan 21, 2021 at 10:43
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    $\begingroup$ "$n\gt 30$" is vague because it's not generally true: it's a rough rule of thumb and almost useless as a practical guide. Any good textbook will discuss such issues, so that's the first place to look. In your case there's no information that would help decide whether ten individuals will suffice: it depends on the method and your requirements for precision and confidence. $\endgroup$
    – whuber ♦
    Commented Jan 21, 2021 at 13:00

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Since I don't know the context, I cannot be sure, but I think it depends on how behaves whatever you are measuring. I think that you will probably run an analysis assuming that your data is uncorrelated. Thus, if you have $n=40$ with $t=1$ your data will very likely be uncorrelated (unless there are relations between the patients that lead to correlations in whatever you are measuring) and therefore well-suited for the analysis. On the other hand, if you have $n=10$ with $t=4$ that means that for each patient, the value that you measure at a certain time might be correlated with the values at different times. Whether this hinders your analysis or not, will depend on the degree of correlation. Thus, if you don't expect much correlation over time (for example, if you think the time intervals that you are using are much longer than the typical time over which the value of interest fluctuates) you can use $n \cdot t$ to decide the total number of observations. If you expect strong correlations in time, it would be better to have $t=1$ and increase $n$.

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