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Biostatistics, help deciding on a test

  1. Nov 4, 2014 #1
    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:
    [itex]\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}
    [/itex]

    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. jcsd
  3. Nov 4, 2014 #2

    RUber

    User Avatar
    Homework Helper

    I would tend to agree with the Chi squared test.
    You are testing for dependence.
     
  4. Nov 5, 2014 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    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
  5. Nov 5, 2014 #4
    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?
     
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