# Statistical Testing

Abstract There are inherent random fluctuations in the measurement of any quantity. Statistical tests allow decisions to be made from and about measurements. A calculated statistical value less than the critical test value indicates that the null hypothesis is true, and that the difference between two or more quantities is due to random fluctuations within a specified level of confidence. The standard deviation, sigma, is a measure of the magnitude of the random fluctuations. Students t test is used to express whether two numbers are significantly different at a given level of confidence after consideration of the random fluctuation in measurement. Grubb’s test, Z-values, Dixon’s Q-test (but not the t test) can all be used to test the possibility that an extreme measurement is an outlier. The F test, meanwhile, is used to test the equality of two standard deviations.

KeywordsNull hypothesis, Critical value, Uncertainty, Mean, Standard deviation, Confidence interval, Measurement uncertainty, Two-sided, Single-sided, Students t, Z test, Grubb’s test, Dixon’s Q test, Outlier testing, Precision, Expectation value     