Hypothesis test Flashcards
Determine H & H0.
Are these outcomes equally likely?
H: are the counts /frq. of each category as expected?
H0: the probability of each group is exactly equal (or equal)
Determine H & H0.
are groups different from each other?
H: are the means of X different in the two groups
H0: the mean of Xa equals the mean of Xb
Determine H & H0.
did the outcome change?
H:did the mean of outcome X change across the two measurements?
H0: the mean of X1 equals the mean of X2
Determine H & H0.
are these two outcomes correlated?
H: are they the same?
H0: X and Y are uncorrelated (orthogonal)
Determine H & H0.
are these variables related
H: is there a linear relationship between X and Y
H0: the coefficient of alpha in an OLS regression of Y on X (and Z…) is zero
Procedure for a statistical test
1-based on theory + H0 there is a stat of interest that you can calculate with sample
2-use theory to derive distribution of expected values (under H0). some assumption must be made
3- calculate the statistic actual value given sample
4-state likelihood of answer from sampling method, given that the H0 is true, if unlikely = reject H0
What is the null hypothesis (H0)?
-what you are trying to disprove
- strong results, eliminate the possibility of the H0
- no difference, no change, small difference, no effect
reject the null if ( statistical significance)
p-value is small or near zero
type I error for binary decisions
rejecting the null hypothesis when it is true ( false positive)
type ii error
failing to reject the null hypothesis when it is false (false negative)
the probability of a type I error is determined by ____
significance level
- with a 99% significance threshold, type I error is less likely than with a 95% confidence
the probability of a type ii can be computed for a particular test statistic (i.e. H0), if given______
population distribution (parameterization, mean and SD)
sample size (N) and alpha ( chance of type I error)
hypothesis test power
1 - ( the probability of a type ii error)
AKA - the probability that we correctly reject the null, when the null is false
frequentist statistics
developed before computers & calculators ( t-test, chi-square, F test)
bayesian statistics
rapidly developing framework for using prior expectation + evidence to make bets