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Prevalence of helminths in sheep

or How not to work out prevalence!

Let us say you have carried out four surveys for intestinal helminths, each comprising 1000 to 1500 sheep. These indicate prevalences of 17.2, 25.4, 26.1 and 28.3%. This gives an overall mean of 24.3%.

Your colleague disputes your findings. He has performed nine surveys in a similar area. But his sample sizes are much smaller and range from 5 to 24 sheep per survey. His results indicate prevalences of 0.9, 3.5, 4.2, 7.0, 39.1, 9.4, 15.2, 1.7 and 17.4%. This gives an overall mean of 10.9%.

He suggests you should combine your results with his, by taking the mean of your two overall results. That is (24.3 + 10.9) ÷ 2 = 17.6%. However, your results are based on nearly 5,000 sheep, whereas his are from less than 100 sheep. Clearly, his much smaller sample sizes would bias the result.

If you agree to combine your results with his, you should weight each mean to allow for the quality or quantity of information each represents. Or, alternatively, work out the overall prevalence, by dividing the total number of infections by the total number of sheep sampled.