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Sample Size Requirements Calculator |
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Click here for additional information on the USDA NRCS website. Sampling Requirements Three tools were designed to help determine and evaluate sampling requirements. The Sampling Requirements Table and Graph tool and Multi-scale Sampling Requirements Evaluation Tool (MSSRET) are used to estimate sampling requirements for project planning. MSSRET is a Microsoft Excel spreadsheet file that can also be used to determine whether a sufficient number of samples has been collected. The Multi-scale Variance Estimator is another Excel file tool that calculates multi-scale variances for use in MSSRET. These tools are designed to work with studies or projects that have two scales: plot scale and a broader landscape/study/regional scale. The tools refer to state phase and soil map unit component. State phase is the condition of interest that will be compared in a project. Condition, treatment or another classification of interest could be substituted. Sampling requirements are calculated from the magnitude of the difference to be detected (minimum detectable difference, MDD), the variability of the property (measured as variance), and the desired level of precision and acceptable error rates (alpha and power). Minimum detectable difference: The minimum detectable difference (MDD) is the smallest difference that can be detected with a given number and variability of samples. The desired MDD is the difference that one would like to detect between conditions or treatments. It should be based upon differences that are known to be functionally important. Specific, functionally important differences are not well established for most systems. To overcome this knowledge gap, a percent MDD of the grand or overall mean can be used. The grand mean is the average of all state phase/condition/treatment means for that property and depth. The percent MDD is a percentage of that overall mean. Precision and error rates: To detect a difference between state phases, where they occur, sufficient samples are needed to reduce the probability of false-change errors and missed-change errors (Table A2-2). A probability of a false-change error (Type I error) of 0.20 and a probability of a missed-change error (Type II error = 1 – power) of 0.20 are the recommended sampling objectives for inventory. In the MSSRET tools, these default values appear as alpha = 0.2 and power = 0.8. Variance: Variance is a statistical measure of the variability of individual values around the mean. Variance is related to the variability of a property. As variability increases, variance increases. The spatial variability of a property may vary at multiple scales within a map unit component phase. Soils and state phases with high fine-scale variability (between samples within a plot) and high regional-scale variability (between plots within a state phase) have much greater sampling requirements to estimate parameters and detect differences than those that exhibit more spatially uniform values. Variances can be obtained from existing data sets or from collected data (preliminary samples or a partially or fully completed project) with the Multi-scale Variance Estimator. Rho is a measure of that correlation (0 - not correlated, 1 – perfect correlation). It modifies variance in sample requirement formulas. Rho is the square root of r2 in a regression of the two sample times. The more closely the spatial location and sampling conditions are repeated, the greater the value of rho. The Multi-scale Variance Estimator tool is valid when there is equal replication (the same number of samples within every plot). If there is unequal replication, see directions in Figure A2-3 of the Soil Change Guide or seek help from a statistician (http://soils.usda.gov/technical/soil_change/index.html). To use the Multi-scale Variance Estimator worksheet: 1. Enter soil map unit component phase, state phase, property and depth or other appropriate identifiers for record keeping purposes. 2. Enter sample values by plot in the grey area. Samples should be arranged in columns under the appropriate plot number. 3. The variance estimator will report the state phase means, variance within plots, and variance between plots. MSSRET for project planning with multi-scale data This worksheet is intended for one property, depth, and state phase. The worksheet is designed to be interactive and iterative. Enter data into the grey cells on the Pre-project Sampling worksheet and evaluate the output as follows: 1. Enter acceptable error rates and correlations or accept the default values. (The default values for the guide’s sampling protocols are alpha = 0.2, power = 0.8, and rho = 0.0.) 2. Enter the grand property mean (the overall property mean for all state phases/conditions/treatments) for the property and depth increment and residual (within plot) and plot (between plot) variances for the individual state phase/condition/treatment. 3. Use Table 1 to evaluate the number of samples needed per plot for a range of MDDs. This table uses the residual variances given to show the relationship between MDD and samples needed to detect differences at the plot scale. Alter the percent MDDs in the grey cells (D14 to D22) to evaluate specific MDDs of interest. 4. Use Table 2* to evaluate the number of plots needed in that state phase/condition/treatment for a range of MDDs and samples per plot. Alter the percent MDD (C27 to C35) or samples per plot (E26 to K26), in the grey cells, to evaluate specific combinations of interest. *Note: Use Table 2 in the Pre-project Sampling worksheet to determine the most efficient distribution of samples. In some cases, the samples needed per plot as computed in Table 1 can be reduced if the number of plots is increased. In most cases, the most efficient distribution of plots and samples per plot is the one with the lowest number of total samples per project. It is important to balance the cost of analyzing samples with the costs of time and travel to reach plots. In the Pre-project Multi-property worksheet, multiple state phases, properties, and depths can be evaluated for plot- and project- (regional) scale sampling requirements. Identifying information is entered at the top of the worksheet. Scroll down to find the corresponding sampling requirements. Enter data into the grey cells on the Pre-project Multi-property worksheet and evaluate the output as follows: 1. Enter acceptable error rates and correlation or accept the default values. (The default values for the guide’s sampling protocols are alpha = 0.2, power = 0.8, and rho = 0.0.) 2. Enter the identifying information in rows 5 to 7. 3. Enter the grand property means (the overall property means at that depth increment for all state phases/conditions/treatments) in row 8. 4. Enter the residual and plot variances for the individual state phase under the appropriate columns in rows 9 and 10. 5. Use Table 1 to evaluate the number of samples needed per plot for a range of MDDs reported as a percent of the mean. This table uses the residual variances given to show the relationship between MDD and samples needed to detect differences at the plot scale. a. Alter the percent MDDs in the grey cells (C15 to C18) to evaluate specific percent MDDs of interest. 6. Use Table 2 to evaluate the number of plots needed in that state phase for a range of MDDs and samples per plot. a. Alter the percent MDDs in rows 23 to26 and/or enter the samples per plot in D23 to D36. |
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USDA, ARS, Jornada Experimental Range P.O. Box 30003, MSC 3JER, NMSU Las Cruces, NM 88003-8003 Tel: 575-646-4147 Email: ericha@nmsu.edu |