The tutor explains the concept of p-value.

A topic in stats is hypothesis testing. The usual premise: the tester believes they know the mean of a population, but aren’t sure.

In such a case, a sample is taken from the population, then the sample mean x is calculated. Next, the difference between x and the supposed population mean μ₀ is divided by s/n^0.5 or σ/n^0.5. This gives a t-score or z-score, whence a p-value can be found.

The p-value means “the likelihood that the same result, or else a more dramatic one, will occur next time.” Dramatic, in this case, means “far from zero.”

The reasoning is that if μ₀ truly is the population mean, then the sample mean x should closely match it. Therefore, t or z (whichever statistic is used ) should be close to 0, since it’s based on x-μ₀. In fact, the closer t or z is to 0, the higher the p-value.

A low p-value suggests that x and μ₀ 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≈μ₀.

Generally, with p-values, “low” means p<0.05, or 5%. Anything above 5% is generally tolerated as believable.

In a coming post I’ll show how to find a p-value from a test.

Source:

Harnett, Donald L. and James L. Murphy. Statistical Analysis for Business and Economics, first Can. edition. Don Mills: Addison-Wesley, 1993.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.