Test
Assesses the evidence provided by data about some claim concerning a population.
Significance Test
The claim tested by a statistical test. The test is designed to assess the strength of the evidence against the null hypothesis. A statement of "no difference."
Null Hypothesis (H0)
reject the null hypothesis when it is true (Shawshank - found guilty when really is innocent)
Type I error
probability the test will reject the null at a chosen significance level when the alternative value of the parameter is true
Power
smaller significance levels need a _____
larger sample
1. reject the null or
2. fail to reject the null
Two Decisions of a significance test
The claim about the population that we are trying to find evidence for.
Alternative Hypothesis (Ha)
Failing to reject a null hypothesis when it is in fact false. (OJ Simpson - found not guilty when really is guilty)
Type II error
1-β where β is the probability of making a Type II Error
Power of test
An outcome that would rarely happen if a claim were true is good evidence that the claim is ___________.
Not true
Always do ______ for two-sided tests (unless letting the calculator perform the entire test then it does it automatically)
Always double the p value
An alternative hypothesis that includes either > or <.
One-sided alternative hypothesis
probability of type I error
Alpha
1. increase sample size
2. increase significance level alpha
3. increase the difference between the null and the alternative parameter that it is important to detect
Hypotheses always refer to a ______
population - never a sample
The smaller of n1-1 or n2-1 OR let calculator find it exactly
degrees of freedom for two sample tests
An alternative hypothesis that includes ≠.
Two-sided alternative hypothesis
How many types of error are there?
2 types (I and II)
if you need higher power, you need a ________
larger sample or greater significance level
Why would you reject Ho?
if p is low
1. Random and independent for both samples
2. 10% (Must show for BOTH samples)
3. Large Counts (Must show for BOTH samples) use p-hats in the equations and all 4 values must be at least 10
Conditions for performing a significance test about difference in proportions
The hypothesis testing method for matched pairs data. The standard null hypothesis is H0: μd = 0 where μd is the mean difference between treatments.
matched pairs t procedure for mean
Power + Probability of Type II Error =
1
degree of overlap between the sampling distributions under Ho and H1 (this is a function of both the distance between u0 and u1 and the standard error
Why would you give the Ho a try (fail to reject)?
If p is high