I have two data sets of hourly measurements from two different time periods. During each time period, the values drop below a given threshold for different amounts of time.

I would like to develop a statistical basis for determining if the amount of time spent below the threshold during period 1 is significantly different from the amount of time spent below the threshold during period 2.

For example, if the temperature drops below 10 deg C for 15 hours during one week and for 22 hours during another week, the difference in the number of hours below 10 deg C would be 7.

Are there any statistical methods to determine if this difference of 7 hours is a "significant" amount of time? (among the 168 hours that are in a week)


Yes, this is the test for equality of proportions $p_1, p_2$ in two populations given samples of sizes $n_1, n_2$ respectively.

Null is $H_0 : p_1-P_2 =0 $

Alternative is $H_A: p_1 \neq p_2 $ (two-tailed)

The z statistic is

$z= \frac {p_1 -p_2}{\sqrt {p'(1-p')(\frac {1}{n_1}+\frac {1}{n_2})}}$

Where $p$ is the pooled proportion ; $p= \frac {s_1+s_2}{n_1+n_2}$; $s_1,s_2$ are the "successes" and $n_1,n_2$ are the respective number of trials.


EDIT: For the sake of completeness, there is another type of test when you have contingency tables ( included in link), but this is not your case.

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