# Technologies for Forecasting Tree Fruit Load and Harvest Timing--From Ground, Sky and Time
## 2 Measurement of Fruit Number
### Manual Fruit Count
#### 2.3.2 Sampling Approaches  
Sampling in the context of the estimation of tree fruit load has been described by [PERSON] [14]. These methods provide an estimate of the average number of fruits per tree, with the total orchard fruit load achieved by multiplication of the mean tree fruit load and number of trees in the orchard. In systematic sampling, the orchard total load is estimated by knowing the 'proportion' (inverse probability) of the trees the sample represents. Briefly, several 'uniform random probability-based' sampling strategies are relevant, in which all units of the populations have an equal probability of being selected:  
(i) Simple Random Sampling (RS) with replacement. This procedure is the most inefficient of sampling designs but provides independent samples, which simplifies many statistical analyses. An unbiased estimate of the population mean (e.g., mean fruit load per tree) is obtained. (ii) RS without replacement. This procedure is close to (i) in terms of efficiency. If the population is large, then the probability of choosing a unit of the population more than once is extremely low, and it can be shown that the results obtained from sampling with replacement are very close to the results obtained using sampling without replacement. An unbiased estimate of the population mean is obtained. RS provides no mechanism to improve the sampling effort based on spatial variability, which almost always exists at some level within orchards. The only parameter that can be controlled is the sample size, to ensure that it is large enough to capture the variability of the population, and as Table 3 shows, these numbers can be very large. (iii) Systematic uniform random (SUR) sampling achieves a compromise between the precision of the estimate and effort to obtain samples. This method is superior to RS for spatially heterogeneous autocorrelated populations [14]. Every \(m\)th unit is chosen from a uniform random starting point, where \(m\) is the sampling interval. For example, fruit number could be counted on every 20 th tree, starting from a tree randomly chosen between 1 and 20. Care must be taken to choose a sampling period that avoids a similar periodicity in the population. For example, a sampling period of 20 in an orchard with rows of 100 trees would result in sampling of trees in the same positions within each row. An unbiased estimate of the population total (the total number of fruits in the orchard) is also achieved as sample size x inverse probability, without explicit knowledge of the number of trees in the orchard. Equations (2)-(4) are biased (conservative) for SUR sampling [17]. (iv) Stratified sampling involves dividing the population into relatively homogeneous regions or strata, and then treating each stratum as a population. The advantage of stratified sampling is that different sampling fractions may be used in each stratum with the aim of reducing the estimator variance, allowing decreased sampling effort for the same accuracy of estimation as an unstratified sampling strategy. Stratification on fruit load estimation requires use of a tree attribute with correlation to fruit load. A methodology caveat for any system requiring a randomized selection is that a random number generator or table should be used. This is necessary as humans are poor at random selection [18]. The aim of a good sampling strategy is to capture the spatial variability of the orchard in a small sample number. Under independent sampling, the CE will decrease by a power of n\({}^{-0.5}\) approximately, where \(n\) is the sample size [15]. An efficient sample design will produce low between-sample variance (different realizations of the sampling design should provide similar estimates) and will have a steeper rate of decrease in CE than \(n^{-0.5}\). The use of RS, systematic RS and stratified sampling procedures for tree fruit yield prediction has been described in a number of studies [15; 19; 20; 21; 22; 23]. For example, [PERSON] et al.