Purpose:
To provide and unbiased AND low-variance estimate of a population parameter (e.g., density, survival rate) when entire population cannot be measured
To allow researchers/managers to select the sampling strategy that provides the most precision for the amount of effort/cost in obtaining the estimate
Terms:
Statistical Population - the entire collection of elements about which we wish to measure some characteristic
Sample - a fraction of the statistical population such that the sample represents the population
Population unit - each individual element in the statistical population
Estimate - an approximation of some characteristic of the statistical population based on some method of sampling
Bias of Estimate - Difference between the expected value of the estimate and the true value of the population characteristic
Precision/Variance of Estimate - How close repeated estimates are to the expected value
Single-Stage Survey Sampling
Sampling Methods
Simple Random Sample (SRS)
Systematic Sample (SS)
Stratified Random Sample (StrRS)
Cluster Sample (CS)
Simple Random Sample: Every population unit has an equal chance of being in the sample
Systematic Sample: Select population units at regular intervals. The first population unit is selected randomly within the first interval.
Usually more precise than SRS
Values of the variable (e.g., density) may exhibit trends across space so adjacent units tend to have similar values. A systematic sample covers the population evenly while SRS is more patchy.
If the interval in a systematic sample follows some cyclic or periodic property of the population then there will be less precision than SRS.
No unbiased method for estimating the precision or variance from a systematic sample. If the SRS formula is used, variance is generally overestimated.
Many advantages (without disadvantages) can be obtained by cluster or stratified sampling
Stratified Random Sample: Divide population into regions of known size so that variation between strata is maximized and variation within strata is minimized. Then take random samples within each strata.
Applied to patchily distributed organisms, where patchiness is predictable from mappable environmental characteristics
Used when the variability within strata is much lower than the variability found in the population. If this is the case, precision is much better than SRS.
Ensures that the sample is distributed throughout the area
Permits heavier sampling in some areas
Can obtain separate estimates for each strata
Variance/Precision comes from differences within each strata
Cluster Sample: Initial units are chosen at random then all population units in some fixed conformation around the initial are selected.
In contrast to stratification, cluster sampling is most efficient when variability within the cluster is high but among clusters is low
Useful when populations naturally occur in clusters or when the cost of obtaining measurements on population units increases as the distance separating the units increases.
Variance comes from differences between clusters
Influence of Population Unit
Recommendations for population unit shape and size follow the same recommendations for cluster sampling. That is, variation within population units should be maximized and variation between population units should be minimized.
Quadrat vs. Line transect (from McCallum 2000)
