A topic in stats is hypothesis testing. The usual premise: the tester believes they know the mean of a population, but aren’t sure.<\/p>\n
In such a case, a sample is taken from the population, then the sample mean x<\/span> is calculated. Next, the difference between x<\/span> and the supposed population mean \u03bc0<\/sub> is divided by s\/n0.5<\/sup> or \u03c3\/n0.5<\/sup>. This gives a t-score or z-score, whence a p-value can be found.<\/p>\n The p-value means “the likelihood that the same result, or else a more dramatic one, will occur next time.” Dramatic<\/em>, in this case, means “far from zero.”<\/p>\n The reasoning is that if \u03bc0<\/sub> truly is the population mean, then the sample mean x<\/span> should closely match it. Therefore, t<\/strong> or z<\/strong> (whichever statistic is used ) should be close to 0, since it’s based on x<\/span>-\u03bc0<\/sub>. In fact, the closer t or z is to 0, the higher the p-value.<\/strong><\/p>\n A low p-value suggests that x<\/span> and \u03bc0<\/sub> are surprisingly different. A high p-value, on the other hand, suggests that the difference between them is small enough that it’s easy to believe, practically, that x<\/span>\u2248\u03bc0<\/sub>. <\/p>\n Generally, with p-values, “low” means p<0.05, or 5%. Anything above 5% is generally tolerated as believable.<\/p>\n In a coming post I’ll show how to find a p-value from a test.<\/p>\n Source:<\/p>\n Harnett, Donald L. and James L. Murphy. Statistical Analysis for Business and Economics<\/u>, first Can. edition. Don Mills: Addison-Wesley, 1993.<\/p>\n