Statistical Analysis with R For Dummies (For Dummies (ComputerTech)) by Joseph Schmuller

Author:Joseph Schmuller [Schmuller, Joseph]
Language: eng
Format: azw3, epub
ISBN: 9781119337263
Publisher: Wiley
Published: 2017-03-03T05:00:00+00:00

"z =", z.score,"\n",

"one-tailed probability =", one.tail.p,"\n",

"two-tailed probability =", 2*one.tail.p )}

t for Two

The example in the preceding section involves a situation you rarely encounter — known population variances. If you know a population’s variance, you’re likely to know the population mean. If you know the mean, you probably don’t have to perform hypothesis tests about it.

Not knowing the variances takes the central limit theorem out of play. This means that you can’t use the normal distribution as an approximation of the sampling distribution of the difference between means. Instead, you use the t-distribution, a family of distributions I introduce in Chapter 9 and apply to one-sample hypothesis testing in Chapter 10. The members of this family of distributions differ from one another in terms of a parameter called degrees of freedom (df). Think of df as the denominator of the variance estimate you use when you calculate a value of t as a test statistic. Another way to say “calculate a value of t as a test statistic” is “Perform a t-test.”

Unknown population variances lead to two possibilities for hypothesis testing. One possibility is that although the variances are unknown, you have reason to assume they’re equal. The other possibility is that you cannot assume they're equal. In the sections that follow, I discuss these possibilities.

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