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138 terms

AP Statistics

AP Statistics vocabulary.
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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
systematically recorded information, whether numbers or labels, together with its context
data table
an arrangement of data in which each row represents a case and each column represents a variable
case
an individual about whom or which we have data
variable
holds information about the same characteristic for many cases
categorical variable
a variable that names categories (whether with words or numerals)
quantitative variable
a variable in which the numbers act as numerical values; always has units
units
a quantity or amount adopted as a standard of measurement, such as dollars, hours, or grams
frequency table
lists the categories in a categorical variable and gives the count or percentage of observations for each category
distribution
gives the possible values of the variable and the relative frequency of each value
area principle
in a statistical display, each data value should be represented by the same amount of area
bar chart
shows a bar representing the count of each category in a categorical variable
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
dotplot
graphs a dot for each case against a single axis
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
spread
a numerical summary of how tightly the values are clustered around the "center"
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
bimodal
distributions with two modes
multimodal
distributions with more than two modes
uniform
a distribution that's roughly flat
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
outliers
extreme values that don't appear to belong with the rest of the data
timeplot
displays data that change over time
center
summarized with the mean or the median
median
the middle value with half of the data above and half below it
spread
summarized with the standard deviation, interquartile range, and range
range
the difference between the lowest and highest values in a data set
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
interquartile range
the difference between the first and third quartiles
percentile
the ith ___ is the number that falls above i% of the data
5-number summary
consists of the minimum and maximum, the quartiles Q1 and Q3, and the median
boxplot
displays the 5-number summary as a central box with whiskers that extend to the non-outlying data values
mean
found by summing all the data values and dividing by the count
variance
the sum of squared deviations from the mean, divided by the count minus one
standard deviation
the square root of the variance
comparing distributions
when doing this, consider their shape, center, and spread
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
standardized value
value found by subtracting the mean and dividing by the standard deviation
normal model
useful family of models for unimodal, symmetric distributions
parameter
numerically valued attribute of a model
statistic
value calculated from data to summarize aspects of the data
z-score
tells how many standard deviations a value is from the mean; have a mean of zero and a standard deviation of one
standard normal model
a normal model with a mean of 0 and a standard deviation of 1
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
changing center and spread
doing this is equivalent to changing its units
scatterplots
shows the relationship between two quantitative variables measured on the same cases
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
form
the ____ we care about most is straight
strength
a scatterplot shows an association that is this if there is little scatter around the underlying relationship
correlation
a numerical measure of the direction and strength of a linear association
outlier
a point that does not fit the overall pattern seen in the scatterplot
lurking variable
a variable other than x and y that simultaneously affects both variables, accounting for the correlation between the two
model
an equation or formula that simplifies and represents reality
linear model
an equation of the form y-hat = b0 + b1x
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
regression line
the linear equation y-hat = b0 + b1x that satisfies the least squares criterion
intercept
this, b0, gives a starting value in y-units; it's the y-hat-value when x is 0
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
ladder of powers
places in order the effects that many re-expressions have on the data
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
simulation component
the most basic situation in a simulation in which something happens at random
outcome
an individual result of a component of a simulation
trial
the sequence of several components representing events that we are pretending will take place
response variable
values of this record the results of each trial with respect to what we were interested in
population
the entire group of individuals or instances about whom we hope to learn
sample
a representative subset of a population, examined in hope of learning about the population
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
matching
any attempt to force a sample to resemble specified attributes of the population
sample size
the number of individuals in a sample
census
a sample that consists of the entire population
population parameter
a numerically valued attribute of a model for a population
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
sampling frame
a list of individuals from whom the sample is drawn
sampling variability
the natural tendency of randomly drawn samples to differ
stratified random sample
a sampling design in which the population is divided into several subpopulations, and random samples are then drawn from each stratum
cluster sample
a sampling design in which entire groups are chosen at random
multistage sample
sampling schemes that combine several sampling methods
systematic sample
a sample drawn by selecting individuals systematically from a sampling frame
voluntary response bias
bias introduced to a sample when individuals can choose on their own whether to participate in the sample
convenience sample
consists of the individuals who are conveniently available
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
response bias
anything in a survey design that influences response
observational study
a study based on data in which no manipulation of factors has been employed
retrospective study
an observational study in which subjects are selected and then their previous conditions or behaviors are determined
prospective study
an observational study in which subjects are followed to observe future outcomes
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
factor
a variable whose levels are controlled by the experimenter
response
a variable whose values are compared across different treatments
experimental units
individuals on whom an experiment is performed
level
the specific values that the experimenter chooses for a factor
treatment
the process, intervention, or other controlled circumstance applied to randomly assigned experimental units
principles of experimental design
control, randomize, replicate, block
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
single-blind
when either those who could influence or evaluate the results is blinded
double-blind
when both those who could influence and evaluate the results are blinded
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
randomized block design
randomization occurring within blocks
completely randomized design
all experimental units have an equal chance of receiving any treatment
confounded
when the levels of one factor are associated with the levels of another factor so their effects cannot be separated