Tasked in the previous section and ask the single question: Are the two sets drawn from the same distribution function, or from different distribution functions? Equivalently, in proper statistical language | 620 Chapter 14. Statistical Description of Data Are Two Distributions Different Given two sets of data we can generalize the questions asked in the previous section and ask the single question Are the two sets drawn from the same distribution function or from different distribution functions Equivalently in proper statistical language Can we disprove to a certain required level of significance the null hypothesis that two data sets are drawn from the same population distribution function Disproving the null hypothesis in effect proves that the data sets are from different distributions. Failing to disprove the null hypothesis on the other hand only shows that the data sets can be consistent with a single distribution function. One can never prove that two data sets come from a single distribution since . no practical amount of data can distinguish between two distributions which differ only by one part in 1010. Proving that two distributions are different or showing that they are consistent is a task that comes up all the time in many areas of research Are the visible stars distributed uniformly in the sky That is is the distribution of stars as a function of declination position in the sky the same as the distribution of sky area as a function of declination Are educational patterns the same in Brooklyn as in the Bronx That is are the distributions of people as a function of last-grade-attended the same Do two brands of fluorescent lights have the same distribution of burn-out times Is the incidence of chicken pox the same for first-born second-born third-born children etc. These four examples illustrate the four combinations arising from two different dichotomies 1 The data are either continuous or binned. 2 Either we wish to compare one data set to a known distribution or we wish to compare two equally unknown data sets. The data sets on fluorescent lights and on stars are continuous since we can be given lists of individual burnout times or of stellar .
