# Biostatistics, help deciding on a test

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1. Nov 4, 2014

### Mogarrr

1. The problem statement, all variables and given/known data
Refer to Table 2.11.
10.6 What significance test can be used to assess whether there is a relationship between receiving an antibiotic and receiving an antibiotic culture while in the hospital?

Here's my attempt of recreating the table:
$\newcommand\T{\Rule{0pt}{1em}{.3em}} \begin{array}{|c|c|c|} \hline ID & Antibiotic(1=Yes,2=NO) & Culture(1=Yes,2=NO) \T \\\hline 1 \T & 2 & 2 \\\hline 2 \T & 2 & 1 \\\hline 3 \T & 2 & 2 \\\hline 4 \T & 2 & 2 \\\hline 5 \T & 2 & 2 \\\hline 6 \T & 1 & 2 \\\hline 7 \T & 1 & 1 \\\hline 8 \T & 2 & 2 \\\hline 9 \T & 2 & 2 \\\hline 10 \T & 2 & 1 \\\hline 11 \T & 2 & 1 \\\hline 12 \T & 2 & 2 \\\hline 13 \T & 1 & 2 \\\hline 14 \T & 1 & 1 \\\hline 15 \T & 2 & 1 \\\hline 16 \T & 2 & 2 \\\hline 17 \T & 1 & 2 \\\hline 18 \T & 2 & 2 \\\hline 19 \T & 1 & 2 \\\hline 20 \T & 2 & 2 \\\hline 21 \T & 2 & 2 \\\hline 22 \T & 1 & 2 \\\hline 23 \T & 2 & 2 \\\hline 24 \T & 2 & 2 \\\hline 25 \T & 2 & 2 \\\hline \end{array}$

2. Relevant equations

Two tests from this chapter are McNemar's Test and a Chi-Square Test for Independence

3. The attempt at a solution

I have no idea which test to use. Since the problem is asking for a test for association, I would think a chi-square test is appropriate, however the nature of the data makes me question that. I would think that, since we are looking at the same subject in the table, this is a dependent sample. However, the null hypothesis for McNemar's test is that the marginal probabilities are equal or that the probability of each type of discordant pair are equal. The problem isn't asking that, just asking if there is a relationship?

Any help would be greatly appreciated.

2. Nov 4, 2014

### RUber

I would tend to agree with the Chi squared test.
You are testing for dependence.

3. Nov 5, 2014

### Ray Vickson

You could use either a NcNemar or a chi-squared test, but since the sample size is small, those will be inaccurate. If you can, you should try Fisher's exact test. See, eg., http://yatani.jp/teaching/doku.php?id=hcistats:chisquare .

Last edited: Nov 5, 2014
4. Nov 5, 2014

### Mogarrr

I have an exact test for small samples, however I wanted to talk about one more thing concerning this problem. I just learned that McNemar's test can be viewed as a within Chi-Squared Test.

Do you think this data is an example of a within-subject design?