## StatsMiniBlog: Middling differences

Is there a difference between these two non-parametric groups? (For example, the duration of cough after bronchiolitis…)

 Time to cough resolution (days) Rx A: Median 15 days Rx B: Median 15 days

You’d want to see a stats test though, wouldn’t you. So what if it was ..

 Time to cough resolution (days) Rx A: Median 15 days Rx B: Median 15 days Median Difference 1.0 days (95% CI -1.0 to 2.0)

Hang on! You might say. Those medians are identical – how can that median difference be 1.0 ?

Well – there’s a difference between a Median Difference and a the difference between the group medians. The latter is what it sounds like, and is tested with them non-parametric testy things. The former is trickier …

Take the durations of cough and put them side by side.

Now take the difference between those pairings you’ve got.

Now rank the resulting “difference between those pairings”, and take the 50%ile.

That’s the median difference (the median of the differences).

Statisticians, huh?

• Archi

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