Power Analysis, Sampling, and Statistics for Apiary Studies
How to decide how many colonies to sample, how to select them representatively, and how to run a transparent statistical workflow for beekeeping research.
Why sample size planning comes before data collection, not after
Statistical power is the probability that a study will detect a real effect of a given size if one truly exists, and it depends jointly on sample size, the expected effect size, the natural variability of the outcome, and the significance threshold chosen. A study run with too few colonies risks an inconclusive result even when a real treatment effect exists, wasting a season's fieldwork on a trial that was never capable of detecting what it set out to test; a study run with far more colonies than needed wastes resources that could have answered a second question instead.
Power analysis performed before data collection begins turns this from guesswork into an explicit, defensible decision: given a realistic estimate of variability (often taken from a pilot study or previous published work) and the smallest effect size that would be practically meaningful to detect, a power calculation returns the minimum sample size needed for reasonable confidence, typically aiming for 80 percent power at a conventional significance level.
Sampling design for surveys of beekeeping populations
Where the goal is not a controlled experiment but a representative survey, for example estimating average overwinter colony loss across a region, the sampling frame (the list or method used to identify possible participants) determines whether conclusions can be generalised. A survey that only reaches beekeepers active on a particular online forum will systematically overrepresent more engaged, often more experienced keepers, and its results cannot be safely generalised to the wider beekeeping population even if the sample size is large.
Stratified sampling, which divides the target population into meaningful groups (by region, operation size, or experience level) and samples proportionally within each, produces more representative and more precise estimates than simple random sampling from an incomplete list, particularly when those strata differ meaningfully in the outcome being measured. Clearly documenting the sampling frame, response rate, and any known biases in the final write-up lets readers judge for themselves how far the conclusions can be generalised.
From raw data to a defensible statistical model
A transparent statistical workflow begins with exploratory checks: plotting the raw data before any modelling, checking for outliers, missing values, and obvious data-entry errors, and confirming the distribution shape of the outcome variable. Choosing a statistical model should follow from the structure of the data, not familiarity with a particular test; count data such as mite drop typically calls for a different model family than continuous, roughly normal data such as colony weight, and repeated measurements on the same colonies over a season require a model that accounts for that non-independence, commonly a mixed-effects model with colony or apiary as a random effect.
Every model's assumptions should be checked after fitting, not assumed to hold: residual plots, checks for overdispersion in count models, and tests of variance homogeneity all take only a few minutes but catch problems that would otherwise produce misleading p-values. Where assumptions are violated, a transformation, a different model family, or a non-parametric alternative should be documented as a deliberate choice rather than silently applied.
Reporting results in a way that supports reanalysis
A reproducible statistical write-up reports not just the final p-value but the effect size with a confidence interval, the exact model specification used, and the software and package versions involved, since a p-value alone tells a reader almost nothing about the practical magnitude or reliability of an effect. Publishing the analysis script alongside the manuscript, ideally version-controlled, lets other researchers verify the exact steps taken and adapt the same approach to their own data.
Multiple comparisons deserve particular care in apiary research, where studies often test several outcomes (mite counts, colony weight, brood area, honey yield) simultaneously; without correction for multiple testing, at least one of several independent tests will appear statistically significant by chance alone roughly one time in twenty, and this should be addressed explicitly, whether through a formal correction method or by clearly distinguishing pre-specified primary outcomes from exploratory secondary ones.
Frequently Asked Questions
What effect size should I use when planning a power analysis if I have no pilot data?
In the absence of pilot data, published estimates from similar studies or conservative, practically meaningful thresholds (for example, the smallest yield difference that would actually change a management recommendation) are reasonable substitutes, and the assumption should be stated explicitly in the methods.
Why can't I just survey whichever beekeepers respond to my online post?
A convenience sample drawn from social media or forum responses systematically overrepresents more engaged or connected beekeepers, so conclusions drawn from it cannot be safely generalised to the wider beekeeping population without acknowledging that limitation.
Do I need a mixed-effects model if I only measured each colony once?
If colonies are grouped within apiaries and apiary-level factors could plausibly affect the outcome, a mixed model with apiary as a random effect is still often appropriate even with a single measurement per colony, since it accounts for non-independence within apiary rather than only within repeated measures on the same colony.
How should I handle testing several outcomes in the same trial?
Pre-specify a small number of primary outcomes in the study plan before data collection and treat any additional outcomes as exploratory, applying a multiple-comparison correction or at minimum being explicit in reporting about which results were confirmatory versus exploratory.
What is the difference between statistical significance and practical significance in an apiary trial?
Statistical significance indicates an effect is unlikely to be due to chance given the sample size, while practical significance asks whether the effect is large enough to matter for real beekeeping decisions; a very large trial can detect a statistically significant but practically trivial difference in colony weight or yield.