Climate-smart agriculture in Zambia
Cochran's Q
Are these six practices really used at different rates, or is that just how the numbers fell?
Farmers were asked which of six categories of climate-smart practice they used, and could tick as many as applied. The counts come out uneven, and the temptation is to read the ranking straight off the page.
Cochran’s Q is the check on that temptation. It asks whether the six are genuinely used at different rates, or whether the unevenness is the kind you would get by chance alone.
It is built for the case where the same people answer about all six options, which matters here. One household’s six answers are not independent of one another, and a test that assumed they were would overstate its own confidence.
What it cannot do
It tells you the six differ. It will not tell you which beats which, and for that you need McNemar’s test.
The equation
Q = (k − 1) [ k ΣCj2 − (ΣCj)2 ] ÷ [ k ΣRi − ΣRi2 ]
- k
- the number of practices being compared, six here
- Cj
- how many farmers used practice j, the column total
- Ri
- how many practices farmer i used, the row total
The row totals are what make it the right test. A farmer who ticked five of the six is telling you something different from one who ticked one, and Q uses that instead of treating every answer as coming from a separate person.
Further reading
- Cochran, W. (1950). "The Comparison of Percentages in Matched Samples", Biometrika. Read it.The original, and short.
From the Zambia climate-smart agriculture research, built on the Water and Soil Accelerator household survey, which was funded by USAID. The thesis is under examination and the three papers drawn from it are under anonymous peer review, so there is nothing to link to yet.