Statistics Toolbox

Sampling -- Two Sample

Introduction

This module provides guidance in setting up sampling plans for two populations; that is, when the interest is comparing a site mean to a pre-defined threshold (action level). An appropriate sample size is calculated, and samples can be located on a map in ESRI shapefile format.

Choose a Dataset : Choose a dataset for analysis

Hypothesis Set-up Options

Null Hypothesis Indicate which type of null hypothesis to be tested on the data. Using "site mean is higher ..." typically implies that the site is "dirty" until proven "clean." Using "site mean is equal to or lower ..." typically implies that the site is "clean" until proven "dirty." Using "site mean equals ..." typically implies that the purpose of the test is to look for any deviations from a specified level ("action level" is typically a conjectured level in this case, rather than a level at which to take remedial action).

	Site mean is higher than background mean
	Site mean is equal to or lower than background mean
	Site mean equals background mean

Action Level The action level is typically the value of the difference in the means at which remedial action needs to be taken (though it may instead signify some other level of interest). If the difference between the site mean and the background mean is higher than the action level, the site would be considered "dirty."

Probability of Type I Error Often denoted alpha and also called the significance level or the probability of false rejection, the probability of Type I error is the probability that the null hypothesis is rejected when it is actually true. If the null hypothesis is "site mean is equal to or lower ..." or "site mean equals ..." then the specified probability of type I error occurs when the actual difference in means is equal to zero. If the null hypothesis is "site mean is higher ..." then the specified probability of type I error occurs when the actual difference in means is equal to the action level. Probability of Type I error must be (strictly) bigger than 0, and for current implementation, must be no greater than 0.25. [Most acceptable standards would use values of 0.1 or smaller.]

Probability of Type II error Often denoted beta and also called the probability of false accecptance (or one minus the power), the probability of Type II error is the probability that the null hypothesis is accepted when it is actually false. If the null hypothesis is "site mean is higher ..." then the specified probability of type II error occurs when the actual difference in means is equal to zero. If the null hypothesis is "site mean is equal to or lower ..." then the specified probability of type II error occurs when the actual difference in means is equal to the action level. If the null hypothesis is "site mean equals ..." then the specified probability of Type II error occurs when the actual difference in means is equal to either the action level or the negative of the action level. Probability of Type II error must be (strictly) bigger than 0, and for current implementation, must be no greater than 0.5.

Standard Deviation The standard deviation of the samples. In general, this value is not known. Utilize external information as much as possible and specify the maximum standard deviation one could expect to observe. Note: if some previous data is available, it can be used to construct an estimate of the standard deviation.

Assume normality If checked, the calculation will assume normality of the data. If not checked, the normality calculation is multiplied by a "fudge factor" of 1.16, a value often considered a reasonable approximation to the required sample size under a nonparametric test. The fudge factor is based on a particular simulation study and is likely not appropriate for particularly small or particularly large samples. Note: the power graph is only an approximation (a possibly bad one) for the nonparametric test.

Map Set-up Options: Click on the + to reveal the advanced options for this topic

Cost Calculation Options: Click on the + to reveal the advanced options for this topic

Existing Data Options: Click on the + to reveal the advanced options for this topic