AP Statistics
AP Statistics vocabulary.
Terms
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- 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
- unimodal
- having one mode; this is a useful term for describing the shape of a histogram when it's generally mound-shaped
- lurking variable
- a variable other than x and y that simultaneously affects both variables, accounting for the correlation between the two
- population parameter
- a numerically valued attribute of a model for a population
- 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
- response variable
- values of this record the results of each trial with respect to what we were interested in
- cluster sample
- a sampling design in which entire groups are chosen at random
- ladder of powers
- places in order the effects that many re-expressions have on the data
- tails
- the parts of a distribution that typically trail off on either side; they can be characterized as long or short
- data
- systematically recorded information, whether numbers or labels, together with its context
- retrospective study
- an observational study in which subjects are selected and then their previous conditions or behaviors are determined
- linear model
- an equation of the form y-hat = b0 + b1x
- treatment
- the process, intervention, or other controlled circumstance applied to randomly assigned experimental units
- scatterplots
- shows the relationship between two quantitative variables measured on the same cases
- skewed
- a distribution is this if it's not symmetric and one tail stretches out farther than 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
- 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
- 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
- parameter
- numerically valued attribute of a model
- 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
- stratified random sample
- a sampling design in which the population is divided into several subpopulations, and random samples are then drawn from each stratum
- 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
- 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
- sample
- a representative subset of a population, examined in hope of learning about the population
- independence
- variables are said to be this if the conditional distribution of one variable is the same for each category of the other
- blinding
- any individual associated with an experiment who is not aware of how subjects have been allocated to treatment groups
- stem-and-leaf display
- shows quantitative data values in a way that sketches the distribution of the data
- outlier
- any data point that stands away from the others; can be extraordinary by having a large residual or by having high leverage
- experimental units
- individuals on whom an experiment is performed
- z-score
- tells how many standard deviations a value is from the mean; have a mean of zero and a standard deviation of one
- level
- the specific values that the experimenter chooses for a factor
- normal model
- useful family of models for unimodal, symmetric distributions
- statistic
- value calculated from data to summarize aspects of the data
- random assignment
- to be valid, an experiment must assign experimental units to treatment groups at random
- representative
- a sample is this if the statistics computed from it accurately reflect the corresponding population parameters
- mean
- found by summing all the data values and dividing by the count
- random numbers
- these are hard to generate, but several websites offer an unlimited supply of equally likely random values
- observational study
- a study based on data in which no manipulation of factors has been employed
- standard normal model
- a normal model with a mean of 0 and a standard deviation of 1
- shape
- to describe this aspect of a distribution, look for single vs. multiple modes, and symmetry vs. skewness
- symmetric
- a distribution is this if the two halves on either side of the center look approximately like mirror images of each other
- simulation component
- the most basic situation in a simulation in which something happens at random
- 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
- 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
- multistage sample
- sampling schemes that combine several sampling methods
- confounded
- when the levels of one factor are associated with the levels of another factor so their effects cannot be separated
- interquartile range
- the difference between the first and third quartiles
- conditional distribution
- the distribution of a variable restricting the who to consider only a smaller group of individuals
- double-blind
- when both those who could influence and evaluate the results are blinded
- case
- an individual about whom or which we have data
- randomization
- the best defense against bias, in which each individual is given a fair, random chance of selection
- statistically significant
- when an observed difference is too large for us to believe that is is likely to have occurred naturally
- principles of experimental design
- control, randomize, replicate, block
- strength
- a scatterplot shows an association that is this if there is little scatter around the underlying relationship
- 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
- regression line
- the linear equation y-hat = b0 + b1x that satisfies the least squares criterion
- matching
- any attempt to force a sample to resemble specified attributes of the population
- population
- the entire group of individuals or instances about whom we hope to learn
- changing center and spread
- doing this is equivalent to changing its units
- intercept
- this, b0, gives a starting value in y-units; it's the y-hat-value when x is 0
- 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
- quantitative variable
- a variable in which the numbers act as numerical values; always has units
- correlation
- a numerical measure of the direction and strength of a linear association
- sample survey
- a study that asks questions of a sample drawn from some population in the hope of learning something about the entire population
- percentile
- the ith ___ is the number that falls above i% of the data
- sample size
- the number of individuals in a sample
- center
- a value that attempts the impossible by summarizing the entire distribution with a single number, a "typical" value
- outlier
- a point that does not fit the overall pattern seen in the scatterplot
- 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
- uniform
- a distribution that's roughly flat
- 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
- variance
- the sum of squared deviations from the mean, divided by the count minus one
- bimodal
- distributions with two modes
- 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
- comparing distributions
- when doing this, consider their shape, center, and spread
- form
- the ____ we care about most is straight
- outliers
- extreme values that don't appear to belong with the rest of the data
- center
- summarized with the mean or the median
- 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
- 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
- response
- a variable whose values are compared across different treatments
- variable
- holds information about the same characteristic for many cases
- median
- the middle value with half of the data above and half below it
- block
- when groups of experimental units are similar, it is a good idea to gather them together into these
- 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
- census
- a sample that consists of the entire population
- 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
- placebo effect
- the tendency of many human subjects (often 20% or more of experiment subjects) to show a response even when administered a placebo
- model
- an equation or formula that simplifies and represents reality
- voluntary response bias
- bias introduced to a sample when individuals can choose on their own whether to participate in the sample
- multimodal
- distributions with more than two modes
- response bias
- anything in a survey design that influences response
- range
- the difference between the lowest and highest values in a data set
- frequency table
- lists the categories in a categorical variable and gives the count or percentage of observations for each category
- 5-number summary
- consists of the minimum and maximum, the quartiles Q1 and Q3, and the median
- completely randomized design
- all experimental units have an equal chance of receiving any treatment
- distribution
- gives the possible values of the variable and the frequency or relative frequency of each value
- predicted value
- found by substituting the x-value in the regression equation; they're the values on the fitted line
- randomized block design
- randomization occurring within blocks
- 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
- data table
- an arrangement of data in which each row represents a case and each column represents a variable
- simpson's paradox
- when averages are taken across different groups, they can appear to contradict the overall averages
- single-blind
- when either those who could influence or evaluate the results is blinded
- 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
- prospective study
- an observational study in which subjects are followed to observe future outcomes
- units
- a quantity or amount adopted as a standard of measurement, such as dollars, hours, or grams
- 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
- categorical variable
- a variable that names categories (whether with words or numerals)
- convenience sample
- consists of the individuals who are conveniently available
- bar chart
- shows a bar representing the count of each category in a categorical variable
- random
- an event is this if we know what outcomes could happen, but not which particular values will happen
- standardizing
- done to eliminate units; values can be compared and combined even if the original variables had different units and magnitudes
- area principle
- in a statistical display, each data value should be represented by the same amount of area
- factor
- a variable whose levels are controlled by the experimenter
- bias
- any systematic failure of a sampling method to represent its population; common errors are voluntary response, undercoverage, nonresponse ____, and response ____
- sampling variability
- the natural tendency of randomly drawn samples to differ
- outcome
- an individual result of a component of a simulation
- timeplot
- displays data that change over time
- nonresponse bias
- bias introduced to a sample when a large fraction of those sampled fails to respond
- standardized value
- value found by subtracting the mean and dividing by the standard deviation
- residuals
- the differences between data values and the corresponding values predicted by the regression model; ____ = observed value - predicted value
- boxplot
- displays the 5-number summary as a central box with whiskers that extend to the non-outlying data values
- placebo
- a treatment known to have no effect, administered so that all groups experience the same conditions
- trial
- the sequence of several components representing events that we are pretending will take place
- systematic sample
- a sample drawn by selecting individuals systematically from a sampling frame
- 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
- rescaling
- multiplying each data value by a constant multiplies both the measures of position and the measures of spread by that constant
- sampling frame
- a list of individuals from whom the sample is drawn
- spread
- a numerical summary of how tightly the values are clustered around the "center"
- 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
- spread
- summarized with the standard deviation, interquartile range, and range
- least squares
- this criterion specifies the unique line that minimizes the variance of the residuals or, equivalently, the sum of the squared residuals
- 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
- dotplot
- graphs a dot for each case against a single axis
- 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
- standard deviation
- the square root of the variance
- influential point
- when omitting a point from the data results in a very different regression model, the point is an ____
- distribution
- gives the possible values of the variable and the relative frequency of each value