Biostats exam 2

Null hypothesis

specific statement about a population parameter made for the purpose of an argument

alternative hypothesis

includes all other feasible values for the population parameter besides those in the null

test statistic

value calculated from the data used to evaluate compatibility to the result expected under the null

general addition rule

pr [ A or B] = pr [A] + pr [B] - pr [A and B]

general multiplication rule

pr [A | B] = pr [B | A] x pr [A]

bayes rule

pr [B|A] = (pr [A|B] x pr [B] )/ pr [A]

Mutually exlcusive

events cannot occur at the same time

pr[A and B] = 0 pr[A or B] = pr[A] + pr [B]

Independence

the occurrence of one event doesn’t inform us about the probability that the 2nd will occur

pr [A and B] = pr [A] x pr [B]

Law of total probability

the total probability of an event is the sum of the probabilities of the different ways it can occur

hypothesis

a clear statement articulating a plausible candidate explanation for observations

hypothesis testing

compares data to what we would expect to see if a specific null hypothesis were true

p-value

probability of obtaining the data (or more extreme) if the null were true

significance level (α)

probability used as criteria for rejecting the null

if the p is low, reject the Ho

NOT the same as biological importance

Type 1 error

Falsely claiming significance; rejecting the null when the null is true

In the power of the researcher cause we set α

pr [reject Ho| true Ho] = α

Type 2 error

Failing to reject a false null

pr [ not rejecting Ho | false Ho] = ß

Statistical Power

probability of correctly claiming significance

pr [reject Ho| false Ho] = 1 - ß = 1 - pr [ type II error]

Standard Error for a proportion

On formula sheet

SE= sqrt (p-hat(1-p-hat))/n

Wald’s Confidence Interval

NOT on formula sheet

p-hat ± 1.96SE

Acresti-Coull CI

On formula sheet

p’ ± sqrt ( (p’ * (1-p’))/ n+4)

where p’ = (X + 2)/(n + 4)

X = number of successes

Binomial distribution formula

On formula sheet

Binomial mean

mu = np

Binomial variance

sigma squared = np (1-p)

Binomial standard deviation

sigma = sqrt(np (1-p))

binomial standard error

SE = sqrt ((p*(1-p))/n

Binomial p-value

2 * sum (pr[ extreme values])