Biostatistics unit 2 (ch 6-10)

hypothesis testing

comparing data to what we would expect to see if a specific null hypothesis were true. If the data are too unusal, compared to what we expect to see if the null hypothesis were true, then the null hypothesis is rejected 

null hypothesis

a specific statement about a population parameter made for the purpose of argument (interesting to reject)

alternative hypothesis

a statement that includes all other feasible values for the population parameter besides the value stated in the null hypothesis 

test statistic 

a number calculated from the data that is used to evaluate how compatible the data are with he result expected under the null hypothesis 

P-value

the probability of obtaining results as extreme as or more extreme than those observed in a study, assuming the null hypothesis is true

two-sided

a test in which the alternative hypothesis includes parameter values on both sides of the parameter value specified by the null hypothesis (two-tailed) 

null distribution 

the sampling distribution of outcomes for a test statistic under the assumption that the null hypothesis is true

significance level

a probability used as a criterion for rejecting the null hypothesis. If the P-value is less than or equal to alpha, then the null hypothesis is rejected. If the P-value is more than or equal to alpha, then the null hypothesis is not rejected.

type I error

rejecting a true null hypothesis (significance level sets the probaility of committing a Type I error) 

type II error

failing to reject a false null hypothesis

power

the probability that is random sample will lead to rejection of a false all hypothesis (want to reject the null hypothesis)

one-sided test

a test in which the alternative hypothesis includes parameter values on only one side of the value specified by the null hypothesis. null hypothesis is rejected only if the data depart from it in the direction stated by the alternative hypothesis

binomial distribution

the probability distribution for the number of “successes” in a fixed number of independent trials, when the probability of success is the same in each trial 

law of large numbers

larger samples yield more precise estimates 

binomial test

using data to test whether a population proportion(p) matches a null expectation for the proportion 

Agresti-Coull method

a method of determining a confidence interval for a proportion in which first, a number called p’ is calculated

goodness-of-fit test

a method of comparing frequency data to a probability model stated by a null hypothesis

contingency analysis

estimates and tests for an association between two or more categorical variables 

independence of variables

if two variables are independent, then the state of one variable tells us nothing about the probability of the different values of the other variable

relative risk

the probability of an undesired outcome in the treatment group divided by the probability of the same outcome in a control group

reduction in relative risk

one minus the relative risk (ex: vaccine efficacy)

reduction in absolute risk

the risk in the control group minus the risk in the treatment group

odds of success

the probability of success didvided by the probability of failure

odds ratio

the odds of success in one group divided by the odds of success in a second group 

odds

the probability of success divided by the proability of failiure

case-control study

type of observational study in which a sample of individuals with a focal condition (cases) is compared to a sample of subjects lacking the condition (controls) 

chi-squared contingency test

the most commonly used test of association btween two caregoricla variables

Yates correction for continuity 

a modification to the formula used to caluclate chi-sqaured statitici in the case of a 2 × 2 contiguency table 

degree of freedom

a number that specifies which chi-squared distribution to use as the null distribution 

continguency table

a table which gives the frequency of occurrence of all combinations of two (or more) categorical variables

critical value

a value of a test statistic that marks the boundary of a specified area in the tail of the sampling distribution under the null hypothesis

vaccine efficacy 

measures the proportionate reduction in cases among vaccinated persons (ex: relative risk reduction) 

chi-squared test statistic

a statistic that measures the discrepancy between observed frequencies from the data and expected frequencies from the null hypothesis

normal distribution 

a theoretical propability distribution, the familar “bell curve”

standard normal distribution

a normal distribution with a mean of zero and a standard deviation of one

standard normal deviate

a measure of how many standard deviations a particular value is from the mean

central limit theorem 

the sum or mean of a large number of measurements randomly sampled from a non-normal population is approximately normally distributed