I'm studying the length of stay for patients in a hospital. I have a sample of n=4533 observations. Each of these observations are assigned to an admin group numbered between 1 and 8, based on the reason they were admitted to hospital. Admin group 2 has the characteristics:
n = 193, x̄ = 37.2020725 (days), s.d. = 35.6247163 (days)
This is the highest mean of the 8 admin groups. I want to test whether the difference between the other groups means and this mean is significant. If I combine the other 7 admin groups, I get the characteristics:
n = 4340, x̄ = 25.5078341, s.d. = 31.1011062
I tried to run a t-test to compare these 2 sets of data, but I ended up getting really small values for standard error and degrees of freedom (less than 1). I'm assuming the t-test is inappropriate for this data, perhaps due to the fact that 1 sample size is significantly larger than the other.
Can anyone think of a suitable test to help with what I'm trying to investigate here? Alternatively, should I change my angle and try an ANOVA test (if that is appropriate?), to study whether admin group 2's mean is significantly different from all the other groups' respective means? Hope I made my question clear.