11 - Are my results significant?

Abstract

This chapter focuses on the the issue of measurement error in terms of hypothesis testing. It concentrates on some important and very widely applicable statistical tests—those associated with the statistics, Z, t, and F. The empirical distributions created by bootstrapping can be used to test the significance of results in more complicated cases. One important statistic is the total error, E that is defined as the sum of squares of the individual errors, weighted by their variance. As the error, E , is derived from noisy data, it is a random variable with its own probability density function, p(E) . A great deal (but not all) of hypothesis testing can be performed using just four probability density functions. Each corresponds to a different function of the error, e, which is presumed to be uncorrelated and Normally distributed with zero mean and unit variance. Probability density function 1 is just the Normal probability density function with zero mean and unit variance. Probability density function 2 is the chi-squared probability density function. Probability density function 3 is new and is called Student's t-probability density function . Probability density function 4 is also new and is called the Fisher-Snedecor F-probability density function .