1. Two-sided p-values (1.4) and Theory-based approaches (1.5)
Stat 217 – Day 10
Two-sided p-values (1.4) and
Theory-based approaches (1.5)

2. Previously Test of Significance
Define parameter of interest (e.g., p = long-run probability someone picks the left front tire)
State competing hypotheses about the parameter (e.g., H0: p = .25, Ha: p > .25)
Assume the null hypothesis is true and generate a “null distribution” of the statistic (e.g., distribution of sample proportions for 35 people picking a tire)
If the observed statistic is in the tail of the null distribution, have evidence against the null hypothesis, in favor of the alternative

3. Evidence against the null hypothesis
p-value is probability of getting a result at least as extreme as the observed statistic when the null hypothesis is true (e.g., about 15% of samples from a process with p = .25 have a sample proportion of or larger)
p-values less than .05 are usually considered strong evidence against the null
Standardized score measures how far the statistic is from the hypothesized value of the parameter (center of null distribution) in terms of standard deviation units (e.g., .343 is 1.28 standard deviations above .25)
Standardized statistics above 2 are usually considered strong evidence against the null

4. Previously
But what if our sample comes from a population rather than a process?
Needs to be a random sample for us to believe it is representative of the population
Modelled the chance variation in our statistic from random sample to random sample

5. Proportion of e-words Samples of n = 10 from process with p = .47
Samples of n = 10 from population with p = .47
Coin Tossing
Gettysburg Address

6. Key Result
When the population size is large compared to the sample size (e.g., more than 20 times larger), then sampling from a population looks pretty much the same as sampling from a process
So we will use the same analysis tools
One Proportion Inference applet

7. Example 2

8. Summary
Can calculate “two-sided” p-values for “not equal to” alternative hypotheses by considering evidence at least as extreme in either direction
When validity conditions are met, can use the normal distribution (Central Limit Theorem) to obtain a “theory-based” p-value
Interpret the p-value exactly the same way

9. To do for Friday Finish Investigation 2
Pre-lab for Lab 2 to be posted soon
Finish reading Chs. 1 and 2