2013-02-04_REVISION - C1981008 (3)

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JoEllen Turner 970 - 864 -7682 p.10 8orch Envfrontpgntal Pollution Consulting LLC October 2, 2012 "Greater levels of confidence give larger confidence intervals, and hence less precise estimates of the parameter. Confidence intervals of difference parameters not containing 0 imply that that there Is a statistically significant difference between the populations. Certain factors may affect the confidence interval size including size of sample, level of confidence, and population variability. A larger sample size normally will lead to a better estimate of the population parameter." How to Interpret Confidence Intervals. Suppose that a 90% confidence interval states that the population mean is greater than 100 and less than 200. How would you interpret this statement? Some people think this means there is a 90% chance that the population mean falls between 100 and 200. This is incorrect. Like any population parameter, the population mean is a constant, not a random variable. It does not change. The probability that a constant falls within any given range is always 0.00 or 1.00. The confidence level describes the uncertainty associated with a sampling method. Suppose we used the same sampling method to select different samples and to compute a different interval estimate for each sample. Some interval estimates would include the true population parameter and some would not. A 90% confidence level means that we would expect 90% of the interval estimates to include the population parameter; A 95% confidence level means that 95% of the intervals would include the parameter; and so on. To compare if means are statistically different a t- test/ANOVA test needs to be used: "In statistics, analysis of variance (ANOVA) is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether or not the means of several groups are all equal, and therefore generalizes t - test to more than two groups. Doing multiple two - sample t -tests would result in an increased chance of committing a type 1 error. For this reason, ANOVAs are useful in comparing two, three, or more means. Some popular designs use the following types of ANOVA: • One -way ANOVA is used to test for differences among two or more independent groups (means),e.g. different levels of urea application in a crop. Typically, however, the one- way ANOVA is used to test for differences among at least three groups, since the two - group case can be covered by a t - test. When there are only two means to compare, the t- test and the ANOVA F -test are equivalent; the relation between ANOVA and t is given byF =t 9 Page PLTF 002483