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In a crossover trial involving 50 patients, two dialysis treatment schedules were compared.Ten patients complained of vomiting on both schedules, 30 on neither, nine on treatment A only and one on treatment B.

(a) What are the proportions of patients vomiting on each treatment?

(b) Perform a significance test comparing these two proportions and interpret the results.

For (a), I think it is 19/50 and 11/50

For (b), I think I have to use McNemar test: (19-11)^2/(19+11)=2.31.

But I'm not sure, can you please check if my answer is right.

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The way to check is to create the contingency table:
\begin{array}{rccl} &\text{treatment B} &\text{vomiting} & \\ \text{treatment A vomiting }\ \ &{\rm yes} &{\rm no} &{\rm sum} \\ {\rm yes} &10 &9 &? \\ {\rm no} &1 &30 &31 \\ {\rm sum} &? &39 & \end{array} An overview of McNemar's test, it's justification, and the formulas can be found here, and below that here. (To provide a hint, your formula is incorrect.)

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  • $\begingroup$ Can you make it the rest of the way yourself, now? $\endgroup$
    – gung - Reinstate Monica
    Commented Jun 21, 2016 at 20:00
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    $\begingroup$ To add a hint for the general problem of paired binary data: concordant results are effectively thrown away with McNemars... our attention is only on discordant pairs (those on the off-diagonal of the contingency table). $\endgroup$
    – AdamO
    Commented Jun 21, 2016 at 20:23
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    $\begingroup$ Ou, so the right formula then is (9-1)^2/(9+1)=6.4>>3.84, which means that we should reject the null hypothesis. Thank you! $\endgroup$
    – Art
    Commented Jun 21, 2016 at 20:57
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    $\begingroup$ You're welcome, @Art. Good luck with your course. $\endgroup$
    – gung - Reinstate Monica
    Commented Jun 21, 2016 at 21:06

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