Stats Vocab

pth percentile

value with p% of the observations less than it

5 number summary

minimum, Q1, median, Q3, maximum

outlier

any data value >= Q3 + 1.5IQR, or

interquartile range (IQR)

Q3 - Q1

standardized value / z-score

given an observation x from a distribution with mean m and standard deviation s,

z = (z - m)/s

explanatory variable

independent variable; influences changes in the response variable

response variable

dependent variable; depends on the explanatory variable

parameter

a numerical characteristic of a whole population

statistic

a numerical measurement of a sample (rather than the population)

correlation coefficient (r)

measures the direction and strength of the linear association between two quantitative variables (-1 <= r <= 1)

regression line

straight line that describes how a response variable changes as the explanatory variable changes

square of the correlation (r^2)

the fraction of the variation in the response variable that is explained by the least-squares regression

residual

difference between an observed value of the response variable and the predicted value by the regression line:

residual = observed y - predicted y

lurking variable

a variable that is not among the explanatory or response variables but may influence the relationships among the variables

variance

the square of the standard deviation

Simpson's Paradox

the reversal of an apparent association when some variables are (dis)aggregated/combined

confounding

variables whose effects on a response variable cannot be distinguished from each other

anecdotal data

represent individual cases and are not representative of any larger group of cases

available data

data that are easily accessible/available

sample survey

a study that collects data from a sample representing the larger population

census

a study that collects data from all cases in the population of interest

observational study

a study that observes individuals without influencing the responses

experiment

a study that imposes treatments on experimental units to observe their responses

experimental units / test subjects

the individuals on which the experiment is done

treatment

a change in the explanatory variable

outcome

measured variables that are used to compare to the treatments

elements of experimental design

control, randomization, repetition

block design

forming blocks of experimental units that are similar in some way (ex: gender), then randomizing within each block

matched pair design

an special case of block design, where the blocks consist of two experimental units that share as many attributes as possible (ex: twins)

double-blind study

a study in which neither the experimenters nor the subjects know which treatment any subject has received

simple random sample (SRS)

sampling method where all groups of size n from the population have an equal probability of being chosen

stratified random sample

sampling method that separates the population into different strata based on some attribute (ex: socioeconomic level), chooses an SRS from each strata, and combines these samples according to the makeup of the population

multistage random sample

sampling method that selects successively smaller groups within the population in stages (ex: states -> cities -> districts -> schools -> students)

sample proportion (p̂)

proportion of 'successes' in a sample; a statistic

population proportion (p)

proportion of 'successes' in a population; a parameter that we will never know

bias

center of the sampling distribution is not equal to the true value of the parameter

variability

the spread of the sampling distribution

institutional review board

a board that reviews all planned studies in advance to protect subjects from possible harm

informed consent

giving potential participants enough information about a study to enable them to choose whether they wish to participate

confidentiality

only the researchers can identify responses of individual subjects

anonymity

subjects are anonymous, so their names are not known even to the director of the study

random

individual outcomes of a phenomenon are uncertain, but these outcomes occur a predictable percentage of the time in large numbers of independent trials

probability

the proportion of times the event occurs in many repeated trials of a random phenomenon

independent

the outcome of one trial does not influence the outcome of any other trial

sample space

the set of all possible outcomes of the random phenomenon

event

a set of outcomes

complement of an event A

exactly the outcomes that are not in A

binomial experiment

an experiment with a fixed number of trials for which each trial results in either a success or failure

Central Limit Theorem

a simple random sample of size n from a population with mean μ and standard deviation σ is drawn. when n is large, the sampling distribution of the sample mean x̄ is approximately N(μ, σ/sqrt(n))

standard error

the statistic s / sqrt(n), where s is the sample standard deviation and n is the size of the population

level C confidence interval

an interval centered around the sample mean that is computed from a sample. any level C confidence interval will have probability C of containing the population proportion

Type I error

error occurring when we reject the null hypothesis when in fact it is true

Type II error

error occurring when we fail to reject the null hypothesis when it is in fact false

power of a statistical test

1 - probability of a Type II error (given that the null hypothesis is false)