How to test if counts differ across temporal categories? I have a homework question in which data is taken from three months of hospital admission data. It is then split into six 4-hour groups (0000–400, 0400–0800, etc.). The data are given with just the hour group and one column containing a number of admits. We are to draw a conclusion about how nurses should be scheduled based on this data. Is there any statistical or graphical method that would result in a significant conclusion, or is this a trick question, and the answer is that there isn't enough data to make a suggestion with any certainty?
Update: the values for the 4 hour window are for the entire 3 month period. So if the value that corresponded to 00:00-04:00 was 80 that would be 80 patients admitted between 00:00 and 04:00 over the last 3 months. If I did a single sample t-test using the values of column 2 and any values that were outside the CI, could I say that more nurses should be allocated to that hour group? 
 A: Ideally, the data would not be aggregated and you would use time-series methods to model the seasonality over the course of the day.  However, as I gather this is an introductory class, and I generally agree with @NickCox's comment, I suspect this is a much simpler exercise. 
My guess is that they wonder if nurses should be scheduled evenly / uniformly, or if they need higher numbers for some time periods.  You have one row of counts that fall into 6 bins, and you want to know if the numbers are approximately equal in each bin.  You can test that with a chi-squared test for goodness of fit.  Since a month has passed, here is an example worked in R:  
set.seed(9337)                               # (makes the example reproducible)
admits        = rpois(6, lambda=80)          # here I generate counts (the null is true)
names(admits) = c("0000–0400", "0400–0800",  # these are your bins
                  "0800–1200", "1200–1600", 
                  "1600–2000", "2000–0000")
admits                                       # here is what the data look like:
# 0000–0400 0400–0800 0800–1200 1200–1600 1600–2000 2000–0000 
#        74        85        96        75        79        76 
chisq.test(admits)                           # this is the test
# 
#  Chi-squared test for given probabilities
# 
# data:  admits
# X-squared = 4.3897, df = 5, p-value = 0.4948

A: There aren't much relevant statistics you can do with the highly aggregated data you have (especially since you don't have any measure of the variance within each time period), so given how you've described the course and problem I assume that the purpose of the question is not to perform a statistical analysis, but to use the summary statistics you've been given to make a decision. Unless you have more information, your best bet is probably to just schedule more nurses during the times when there are high numbers of patients admitted. If each data point is an average of over a thousand days, the Central Limit Theorem likely means that you can be fairly confident in the accuracy of those averages, unless the day-to-day variance is enormous or there's some trend on the scale of years.
