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AP Statistics vocabulary.

### context

ideally tells who was measured, what was measured, how the data were collected, where the data were collected, and when and why the study was performed

### data table

an arrangement of data in which each row represents a case and each column represents a variable

### frequency table

lists the categories in a categorical variable and gives the count or percentage of observations for each category

### area principle

in a statistical display, each data value should be represented by the same amount of area

### pie chart

shows how a "whole" divides into categories by showing a wedge of a circle whose area corresponds to the proportion in each category

### contingency table

displays counts and, sometimes, percentages of individuals falling into named categories on two or more variables; categorizes the individuals on all variables at once, to reveal possible patterns in one variable that may be contingent on the category of the other

### marginal distribution

the distribution of either variable alone in a contingency table; the counts or percentages are the totals found in the margins (last row or column) of the table

### conditional distribution

the distribution of a variable restricting the who to consider only a smaller group of individuals

### independence

variables are said to be this if the conditional distribution of one variable is the same for each category of the other

### simpson's paradox

when averages are taken across different groups, they can appear to contradict the overall averages

### distribution

gives the possible values of the variable and the frequency or relative frequency of each value

### histogram

uses adjacent bars to show the distribution of vales in a quantitative variable; each bar represents the frequency (or relative frequency) of values falling in an interval of values

### stem-and-leaf display

shows quantitative data values in a way that sketches the distribution of the data

### shape

to describe this aspect of a distribution, look for single vs. multiple modes, and symmetry vs. skewness

### center

a value that attempts the impossible by summarizing the entire distribution with a single number, a "typical" value

### mode

a hump or local high point in the shape of the distribution of a variable; the apparent locations of these can change as the scale of a histogram is changed

### unimodal

having one mode; this is a useful term for describing the shape of a histogram when it's generally mound-shaped

### symmetric

a distribution is this if the two halves on either side of the center look approximately like mirror images of each other

### tails

the parts of a distribution that typically trail off on either side; they can be characterized as long or short

### skewed

a distribution is this if it's not symmetric and one tail stretches out farther than the other

### quartile

the lower of this is the value with a quarter of the data below it; the upper of this has a quarter of the data above it

### boxplot

displays the 5-number summary as a central box with whiskers that extend to the non-outlying data values

### shifting

adding a constant to each data value adds the same constant to the mean, the median, and the quartiles, but does not change the standard deviation or IQR

### rescaling

multiplying each data value by a constant multiplies both the measures of position and the measures of spread by that constant

### standardizing

done to eliminate units; values can be compared and combined even if the original variables had different units and magnitudes

### z-score

tells how many standard deviations a value is from the mean; have a mean of zero and a standard deviation of one

### 68-95-99.7 rule

in a normal model, about 68% of values fall within 1 standard deviation of the mean, about 95% fall within 2 standard deviations of the mean, and about 99.7% fall within 3 standard deviations of the mean

### normal percentile

this corresponding to a z-score gives the percentage of values in a standard normal distribution found at that z-score or below

### normal probability plot

a display to help assess whether a distribution of data is approximately normal; if it is nearly straight, the data satisfy the nearly normal condition

### direction

a positive ____ or association means that, in general, as one variable increases, so does the other; when increases in one variable generally correspond to decreases in the other, the association is negative

### strength

a scatterplot shows an association that is this if there is little scatter around the underlying relationship

### lurking variable

a variable other than x and y that simultaneously affects both variables, accounting for the correlation between the two

### residuals

the differences between data values and the corresponding values predicted by the regression model; ____ = observed value - predicted value

### predicted value

found by substituting the x-value in the regression equation; they're the values on the fitted line

### slope

gives a value in "y-units per x-unit"; changes of one unit in x are associated with changes of b1 units in predicted values of y

### regression to the mean

each predicted y-hat tends to be fewer standard deviations from its mean than its corresponding x was from its mean

### least squares

this criterion specifies the unique line that minimizes the variance of the residuals or, equivalently, the sum of the squared residuals

### r2

the square of the correlation between y and x; gives the fraction of the variability of y accounted for by the least squares linear regression on x; an overall measure of how successful the regression is in linearly relating y to x

### subset

if data consist of two or more groups that have been thrown together, it is usually best to fit different linear models to each group than to try to fit a single model to all of the data

### extrapolation

although linear models provide an easy way to predict values of y for a given value of x, it is unsafe to predict for values of x far from the ones used to find the linear model equation; predictions should not be trusted

### outlier

any data point that stands away from the others; can be extraordinary by having a large residual or by having high leverage

### leverage

data points whose x-values are far from the mean of x are said to exert ____ on a linear model; with high enough ____, residuals can appear to be deceptively small

### influential point

when omitting a point from the data results in a very different regression model, the point is an ____

### lurking variable

a variable that is not explicitly part of a model but affects the way the variables in the model appear to be related

### re-express data

we do this by taking the logarithm, the square root, the reciprocal, or some other mathematical operation on all values in the data set

### random

an event is this if we know what outcomes could happen, but not which particular values will happen

### random numbers

these are hard to generate, but several websites offer an unlimited supply of equally likely random values

### simulation

models random events by using random numbers to specify event outcomes with relative frequencies that correspond to the true real-world relative frequencies we are trying to model

### response variable

values of this record the results of each trial with respect to what we were interested in

### sample survey

a study that asks questions of a sample drawn from some population in the hope of learning something about the entire population

### bias

any systematic failure of a sampling method to represent its population; common errors are voluntary response, undercoverage, nonresponse ____, and response ____

### randomization

the best defense against bias, in which each individual is given a fair, random chance of selection

### representative

a sample is this if the statistics computed from it accurately reflect the corresponding population parameters

### simple random sample

this of sample size n is one in which each set of n elements in the population has an equal chance of selection

### stratified random sample

a sampling design in which the population is divided into several subpopulations, and random samples are then drawn from each stratum

### voluntary response bias

bias introduced to a sample when individuals can choose on their own whether to participate in the sample

### undercoverage

a sampling scheme that biases the sample in a way that gives a part of the population less representation than it has in the population

### nonresponse bias

bias introduced to a sample when a large fraction of those sampled fails to respond

### retrospective study

an observational study in which subjects are selected and then their previous conditions or behaviors are determined

### experiment

manipulates factor levels to create treatments, randomly assigns subjects to these treatment levels, and then compares the responses of the subject groups across treatment levels

### random assignment

to be valid, an experiment must assign experimental units to treatment groups at random

### treatment

the process, intervention, or other controlled circumstance applied to randomly assigned experimental units

### statistically significant

when an observed difference is too large for us to believe that is is likely to have occurred naturally

### control group

the experimental units assigned to a baseline treatment level, typically either the default treatment, which is well understood, or a null, placebo treatment

### blinding

any individual associated with an experiment who is not aware of how subjects have been allocated to treatment groups

### placebo

a treatment known to have no effect, administered so that all groups experience the same conditions

### placebo effect

the tendency of many human subjects (often 20% or more of experiment subjects) to show a response even when administered a placebo

### block

when groups of experimental units are similar, it is a good idea to gather them together into these

### matched

in a retrospective or prospective study, subjects who are similar in ways not under study may be ____ and then compared with each other on the variables of interest