# 10.3.3. Loss rate per factor including stratification on the operation size

**10.3.3. ****Loss rate per factor including stratification on
the operation size**

The loss calculations and confidence intervals
described above can be used as a means to identify risk factors for colony
loss, by looking for confidence intervals that do not overlap each other. Total
loss of operations reporting or not reporting a particular management type
(e.g. transport of colonies) can be compared using the chi-square test (as in
VanEngelsdorp *et al.*, 2010, 2011, for
example). The loss rates of operations grouped by factors presumed to be
involved in colony mortality (starvation, high varroa infestation etc.) can also be compared. Of course, this
analysis does not give any information on, or account for, interdependencies of
different factors, for which model fitting is needed (as described below).

To account for known or obvious differences among beekeeping operations, a first stratification, for example on operation size, can be accomplished, by classifying operations as hobby, side-line or commercial. Alternatively the number of colonies per beekeeper can be used as a basis for stratification.

Depending on the size of the survey and cultural differences between the target populations, beekeeping operations can be split into three operation size classes, for example

- small operations (≤50 colonies),
- intermediate operations (51-500 colonies),
- large scale operations (> 500 colonies).

If the scale of beekeeping in the survey population is limited mainly to small and intermediate operations, the classes can be split further as:

- small hobbyist beekeepers (≤15 colonies),
- large hobbyist beekeepers (16-50 colonies),
- small-commercial beekeepers (51-150 colonies),
- larger-commercial beekeepers (150-500 colonies).

When comparing several operation size classes, a chi-square test can be
used first to compare all size classes, and if the result of this is
significant, it can be followed up by pairwise multiple comparisons, again
using the chi -square test or a *z*-test
of the difference in two proportions. In each such pairwise test, the
significance level to reject the null hypothesis should be Bonferroni adjusted
(i.e. divided by the number of tests being conducted) to reduce the rate of
false rejections of the null hypothesis that operations of different sizes have
equal rates of loss. It should be borne in mind that the chi-squared test and *z*-test assume independent observations
and therefore have their limitations.

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