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Program
Explanation
This page is a simple utility to calculate precision of measurements. This
exercise is particularly important in laboratory research, where the 95%
confidence interval for a measurement and the coefficient of variation
provides quality assessment of the method of measurement.
A common method of assessment is to use duplicated measurements (2 measurements of each sample or subject) and this uses the paired difference as an estimate of precision. The method presented on this page allows for more than 2 measurements being made on each sample or subject, and uses the analysis of variance to partition variances between and within samples. The residual (error or within sample) variance is used to estimate the Standard Deviation of precision. In some methods, the 95% confidence interval is calculated by multiplying the Standard Deviation by 1.96, which is the z value for p=0.025 (2.5% each side of the normal distribution curve). This assumes the measurements are made on a population of infinite size. The calculation on this page uses the two sided t value for p=0.05, using the residual degrees of freedom as sample size. This produces a wider confidence interval than using 1.96, but is more realistic. t will approach 1.96 when sample size approaches infinity. If confidence interval based on population assumption is requred, the value can be divided by t and multiply by 1.96. The model of analysis of variance assumes equal number of measurements are made on each sample or subject. Although minor variations in the number of measurements do not distort the result much, increasing discrepency in measurement numbers, particularly if the number of subjects are small, may produce unreliable results. Reference for One Way Analysis of Variance
