Explanation
This collection of shiny apps is designed to assist researchers with soil sampling design. The apps can compute power for SOC change detection, recommend sample sizes, and maximize precision when compositing is used to reduce the number of assays.
Select an app from the drop down menu above. More information about each app can be found on the corresponding page.
Notation
The apps refer to the following notation for plot parameters:
\(\cdot~~ \mu \): The plot average is the average percent soil organic carbon (%SOC) over the plot.
\(\cdot~~ \sigma_{p}\): The spatial heterogeneity is the standard deviation of %SOC over the plot.
\(\cdot~~ \sigma_{\delta}\): The assay error is the average deviation of the assay from the true SOC concentration. It is closely related to the average percent error in assay. For example, if \(\sigma_{\delta} = 0.1\) we would expect most assays of a single sample to be within about 10% of the true SOC concentration of that sample. If \(\sigma_{\delta} = 0\), there is no assay error.
For more details refer to Spertus (2021) "Optimal Sampling and Assay for Estimating Soil Organic Carbon", available at:
https://www.scirp.org/journal/paperinformation?paperid=107467
Compute power for fixed sample sizes
Given means, spatial heterogeneities, and sample sizes for two plots (or sampling times), this app computes the power of a two-sample t-test where the null is no difference between average plot concentrations. Option to include assay error and adjust the number of assays (which may be less than the sample size when compositing is used). If the assay variability is 0, the number of assays is irrelevant. Assumes independent simple random sampling from each plot. The validity of the test relies on SOC being approximately normally distributed in each plot.
Return sample size needed to achieve a given power
This app computes the total number of samples necessary for a level-\(\alpha\) test to detect a difference (at power \(1 - \beta\)) between two plots with given means and standard deviations. The test is a two-sided, two-sample, unpaired t-test, with uniform independent random sampling, no compositing of cores. Option to include assay variability. Also assumes that %SOC is normally distributed or else that sample sizes are fairly large in order for the t-test to be approximately valid. Finally, this calculator assumes that the sample size is equally allocated to the two plots. In practice, sampling is more efficient when the sample size is allocated more to the plot with higher heterogeneity. Note that the sample size returned is the total for both sampling times.
Plot costs and standard errors across a range of composite sizes
Graph costs and standard errors in %SOC (on the y-axes) against size of composites (on the x-axis). Compositing allows investigators to conduct fewer assays of a given number of samples (\(n\)). Compositing thus lowers costs but raises error when there is assay error. These plots allow us to explore the tradeoff.
Plot sample size needed to achieve a given power
Graph sample sizes necessary to detect an effect of a particular size (x-axis) at a given power. Based on two-sided, two-sample t-test, with uniform independent random sampling, no compositing of cores, and a significance level of \(\alpha = .05\). Also assumes SOC is normally distributed or else that sample sizes are fairly large (results for small sample sizes are suspect).
Plot power across a range of effect sizes
Graph the power (y-axis) of a two-sample t-test against the effect size (x-axis), i.e. the difference in average SOC concentration between the two plots. The null hypothesis is no difference between average plot concentrations. Results assume simple random sampling, and that SOC is (marginally) normally distributed within plots. If SOC is not normally distributed results are approximately correct for large sample sizes.
Compute minimum standard error for a fixed budget
This app takes a budget, costs, and parmeters as inputs and returns the smallest achievable standard error to estimate average SOC concentration. The optimization is over the size of composites. The number of cores (samples) and assays to take is also returned. The currency used for costs and budget does not matter. The plot heterogeneity and mean are in percent SOC (grams SOC per hectograms of soil).
Compute minimum budget for a fixed standard error
This app takes a standard error (estimation variance), costs, and parameters as inputs and returns the minimum budget that needs to estimate average SOC concentration. The number of cores (samples) and the assays to take is also returned.The currency used for costs and budget does not matter (results are scale invariant).