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ericatay : Changed level → the specific values that the experimenter chooses for a factor are called the levels of the factor to level → the specific values that the experimenter chooses for a factor
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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 |
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