CSSS 508: Intro to R - Carnegie Mellon University
CSSS 508: Intro to R
3/08/06
Lab 9: Testing
This lab is just a summary of several common tests used in statistics.
Reading material can be found in Dalgaard: Ch. 4, 7, and parts of 6.
T-Test: (one sample, two sample, paired)
T-tests assume that the data come from a normal distribution. The distribution varies depending on the sample size (the length of the vector(s) of data you’re analyzing).
A smaller sample size will be tested against a t-distribution with larger tails.
That is, when we have a small sample, we are more likely to see an average that is extreme or not representative than when we have a larger sample.
One sample test:
We are testing whether the mean of our sample, mu, is equal to some null hypothesis value. For example: Ho: mu = 0. The null hypothesis, or previously/currently held belief, is that the mean of the population is zero. We have collected some data, hopefully a representative sample of our population, and we’re going to test whether or not we have evidence that zero is incorrect.
There are three possible alternative hypotheses: Ha: mu < 0 ; Ha: mu > 0 ; Ha : mu != 0
The first two are one-sided alternatives; the second is two-sided.
Let’s test some small samples:
x ................
................
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