Detecting change in advance tree regeneration using forest inventory data: the implications of type II error

Abstract

Achieving adequate and desirable forest regeneration is necessary for maintaining native tree species and forest composition. Advance tree seedling and sapling regeneration is the basis of the next stand and serves as an indicator of future composition. The Pennsylvania Regeneration Study was implemented statewide to monitor regeneration on a subset of Forest Inventory and Analysis plots measured by the U.S. Forest Service. As management techniques are implemented to improve advance regeneration, assessments of the change in the forest resource are needed. When the primary focus is on detecting change, hypothesis tests should have small type II (β) error rates. However, most analyses are based on minimizing type I (α) error rates and type II error rates can be quite large. When type II error rates are high, actual improvements in regeneration can remain undetected and the methods that brought these improvements may be deemed ineffective. The difficulty in detecting significant change in advance regeneration when small type I error rates are given priority is illustrated. For statewide assessments, power (1-β) to detect changes in proportion of area having adequate advance regeneration is relatively weak (≤0.5) when the change is smaller than 0.05. For evaluations conducted at smaller spatial scales, such as wildlife management units, the reduced sample size results in only marginal power even when relatively large changes (≥0.20) in area proportion occur. For fixed sample sizes, analysts can consider accepting larger type I error rates to increase the probability of detecting change (smaller type II error rates) when it occurs, such that management methods that positively affect regeneration can be identified.

A regeneration indicator for Forest Inventory and Analysis: history, sampling, estimation, analytics, and potential use in the midwest and northeast United States

“…Type I and II errors are inversely related, which challenges the analyst to balance the two error types based on the negative consequences of each. Westfall and McWilliams (2012) demonstrate that when the change in the proportion of adequately stocked forested samples is less than 0.05, it is likely not statistically different from zero (i.e., the null hypothesis of no change is accepted). The problem is exacerbated for substate regions as sample sizes become smaller.…”

“…At the population level, the overall rate of advance regeneration adequacy can be estimated as the proportion of the microplots sampled in the state or subregion that qualify as adequately stocked (Westfall and McWilliams 2012). It is important to consider sample sizes when making population estimates because specifying subsets of the population, either geographically or via classification variables, reduces the precision of the estimate.…”

“…When conducting statistical analyses, hypothesis tests should consider both Type I and II sources of error (Westfall and McWilliams 2012). In this context, the null hypothesis is that no change in the population parameter has occurred, while the research hypothesis is that some specified amount of change has transpired.…”