# Can a t-test be performed here?

#### Sarah20

##### New Member
I have been given data of 13 care hospitals. A mortality ratio of less than 1 indicates fewer deaths than predicted.So below shows the mortality ratio for 8 hospitals with nurse staffing problems, and 5 hospitals without nurse staffing problems. So my question is, can a t-test be performed to test the hypothesis that the 'means' of the 2 population mortality ratios are different between the 2 sets of hospitals at a 5% level of significance?

Hospital Number Mortality Ratio Hospital Number Mortality Ratio
1 0.84 9 0.59
2 0.88 10 0.9
3 0.93 11 0.92
4 1 12 0.96
5 1.04 13 1.1
6 1.13 Mean +/- SD 0.89+/-0.19
7 1.27
8 1.58
Mean +/- SD 1.08+/- 0.24

Note: p value for t=1.46 for 11 DF is not given in the t-table, so it could be assumed to be greater than 0.10.

#### Mean Joe

##### TS Contributor
You can do the t-test if the mortality ratio in BOTH types of hospitals (with staffing problems / without staffing problems) is normal, and if the variance of the ratio in the two types are equal.

Since your calculated sample standard deviations are pretty close, I'd say the equal variance assumption is okay.

A non-parametric alternative to the t-test is the Mann-Whitney test.

Note that the mean for the first column of data is 1.09; I input your data to Excel and got t=1.62. So you might have a calculation error.

You can also use Excel to get a more precise p-value:=TDIST(1.46,11,2) where the first # is your test statistic, second # is your df, third # is 1 (one-tail test) or 2 (two-tail test)

#### Sarah20

##### New Member
actually i redid the calcs and i got what i had typed...im not sure how you went about your calc?

#### Sarah20

##### New Member
So what you're saying is that because the Standard devns are so close a t test can be performed? also, you mentioned using a 1 tailed or 2 tailed test, which one would be better and why? i'm thinking the 2 tailed because of two different sample results but i'm not sure

#### Mean Joe

##### TS Contributor
So what you're saying is that because the Standard devns are so close a t test can be performed?
There are two conditions for the t-test that I usually check: 1) are the two samples normally distributed (can be tested by a Shapiro-Wilk test)? and 2) do the samples have equal variance (can be tested by F test)?

BUT just looking at the data, it looks reasonable not to reject those two assumptions (data on the right has a peak around 0.9 and pretty symmetric, data on the left not so much a textbook example of normality, but it's such a small sample).

also, you mentioned using a 1 tailed or 2 tailed test, which one would be better and why? i'm thinking the 2 tailed because of two different sample results but i'm not sure
Use a 2-tailed test if you are testing for any difference (i.e. not equal) between the group means. Use a 1-tailed test if you are testing for one sample having a larger mean than the other.

to test the hypothesis that the 'means' of the 2 population mortality ratios are different between the 2 sets of hospitals
I'd use a 2-tailed test here.