6. Hypothesis Testing Flashcards
What IS hypothesis testing?
Asks how unusual it is to get data that differes from the null hypothesis.
If the data would be quite unlikely under H0, we reject H0.
Null Distribution
Distribution of answers we would get if the null hypothesis were true
Assumes that all samples would be random samples, thus with sampling error
How is a Null Distribution used to reject null hyp
If real answer from sample falls in a very unlikely area of the null distribution, evidence that the null hypothesis isn’t true
Doesn’t necessarily PROVE that null hypothesis isn’t true
Hypotheses usually assume…
Samples are random samples
Null Hypothesis
A specific statement about a population parameter made for the purposes of argument
*Don’t necessarily think its true
*Very specific
ex. No difference between mean offspring of two populations - SPECIFIC, means difference is 0
Could also be specific number, not 0
Usually simplest statement
Alternate Hypothesis
Represents all other possible parameter values except those stated in the null hypothesis
Non-specific
Usually the statement of greatest interest
Are scientific hypotheses and alternate hypotheses the same?
NO scientific is what you think is true, alternate hypothesis is anything other than the null hypothesis
Test Statistic
A number calculated to represent the match between a set of data and the null hypothesis
cam be compared to a general distribution to infer probability
P-value
The probability of getting the data OR something as or more unusual, if the null hypothesis were true.
- The measure of uncertainty associated with null hypothesis testing
- Given test statistic, what is the probability of getting test statistic OR any value less likely than it one BOTH tails of the distribution
Ways of calculating P-value
Simulation (computer)
Parametric tests
Permutation - test that lets us ask if two variables are independent of each other, take the data itself randomize association between two variables
Statistical significance
a probability used as a criterion for rejecting the null hyp.
If P-value is less than or equal to alpha (sideways breast cancer symbol) then the null hypothesis is rejected
Significance level
the acceptable probability of rejecting a true null hypothesis
called alpha
for most purposes alpha = 0.05 is acceptable, alpha is somewhat arbitrary
Type 1 error def.
Rejecting a true null hypothesis
type 1 error probability
alpha (significance level)
type 2 error definition
NOT rejecting a false null hypothesis
type 2 error probability
Beta
A test has more POWER the smaller beta is
How to calculate beta
POWER = 1 - beta
Power definition
The ability of a test to reject a false null hypothesis
Power equation
Power = 1- beta
Statement about how power changes
Power increases with more information (i.e. with larger sample size)
Two-tailed tests
A deviation in either direction from proportion expected from null hypothesis would reject the null hypothesis
Each tail is rep. by alpha/2
One tailed test
Used when one tail is nonsensical
ex. comparing grades on multiple choice to those expected by random guessing
Critical value
the value of a test statistic beyond which the null hypothesis can be rejected
Can you accept a null hypothesis?
NO!!!!
