biostats chapter 4

estimation

process of inferring a population parameter from sample data

sample

influenced by chance so the estimate is never exactly the same as the value of the parameter being estimates

sampling distribution

probability distribution of all the values for an estimate that we may have obtained when we sampled the population; used for precisions

what happens when you increase sample size

reduce the spread of the sampling distribution of an estimate and increases precision

standard error

standard deviation of the sampling distribution of an estimate; reflects precision; smaller means more precise

standard error of the mean

estimated from data as the sample standard deviation

confidence interval

way to quantify uncertainty about the value of a parameter; range of numbers calculated that is likely to contain within its span the unknown value of the target parameter

95% confidence interval

mean ± 2 * SEM; in future experiments done in the same way, there is a 95% confidence the mean will lie in the 95% confidence interval; most plausible of parameter

2SE rule of thumb

calculates the 95% confidence interval

error bars

lines on a graph that extend outward from the sample estimate to illustrate the precision of estimates reflecting uncertainty about the value of the parameter being estimated

essential for drawing inferences

quantifying uncertainty in estimates

repeated sampling

quantification of uncertainty is based on this form a population

properties of repeated estimates

used to quantify the quality of those estimates

accuracy and precision

defined for the collective behavior of all the estimates

accurate

estimates centered on the parameter

precise

close together estimates

bias

systematic or nonrandom error, which would lead to the estimates being off target or inaccurate

sampling error

nonsystemic or random error which would lead to the estimates differing from each other or imprecise; causes individual estimates to differ from the true value but on average they will center on the true in the absence of bias

biased estimator

underestimates to population value

sampling distribution

depend on sample size for each individual estimate; collection of mean estimates

standard error

statistical property that tells us how precise our estimates are; equals standard deviation of the sampling distribution; s/sqrt(n)

error bars

the extent to which we would expect a hypothetical sample to be clustered around the true population parameter; coverage of the sampling distribution; use standard errors to show the precision

95% confidence interval

if the samples are random, 95% of them will contain the parameter based on sampling distribution

2SE rule of thumb

95% confidence interval that is equivalent to the interval spanning 2 standard errors from the mean

wider confidence interval

means larger sampling error

larger sampling error

higher standard deviation and higher sample size

box plot

information about quartiles displayed which characterize the distribution of the date