Glossary

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Glossary Entries
Word(s)	Definition	Image	Caption	Link	Source
alternative hypothesis	A statement that is accepted as true only if there is convincing evidence in favor of it.
ANOVA F-test	a test based on an F statistic to check whether several population means are equal.
binomial random variable	A random variable that counts successes in a fixed number of independent, identical trials of a success/failure experiment.
box plot	For a data set, a diagram constructed using the five-number summary, which graphically summarizes the distribution of the data.
chi-square goodness-of-fit test	A test based on a chi-square statistic to check whether a sample is taken from a population with a hypothesized probability distribution.
chi-square random variable	A random variable that follows a chi-square distribution.
chi-square test	A test based on a chi-square statistic to check whether two factors are independent.
coefficient of determination	A number that measures the proportion of the variability in y that is explained by x.
complement of an event	The event does not occur.
conditional probability	The probability of the event A taking into account the fact that event B is known to have occurred.
confidence interval	An interval with endpoints $\bar{x} \pm E$ , computed from the sample data in such a way that a specified proportion of all intervals constructed by this process will contain the parameter of interest.
continuous	A random variable whose possible values contain an interval of decimal numbers.
critical value	The number or one of a pair of numbers that determines the rejection region.
data list	An explicit listing of all the individual measurements made on a sample.
degrees of freedom	A number that specifies a particular t-distribution and that is computed based on the sample size.
density function	The function $f (x)$ such that probabilities of a continuous random variable X are areas of regions under the graph of $y = f (x)$ .
Descriptive statistics	The organization, display, and description of data.
error	Using $y - \hat{y}$ , the actual y-value of a data point minus the y-value that is computed from the equation of the line fitting the data.
event	Any set of outcomes.
expected value	Its mean.
extrapolation	The process of using the least squares regression equation to estimate the value of y at an x value not in the proper range.
$F$ random variable	A random variable following an F-distribution.
F-distribution	A particular probability distribution specified by two degrees of freedom, df1 and df2.
factors	A variable with several qualitative levels.
five-number summary	Of a data set, the list ${$ xmin, Q1, Q2, Q3, xmax}.
frequency	Of a class of measurements, the number of measurements in the data set that are in the class.
hypothesis	A statement about a population parameter.
Hypothesis testing	A statistical procedure in which a choice is made between a null hypothesis and a specific alternative hypothesis based on information in a sample.
independent	Events whose probability of occurring together is the product of their individual probabilities.
Inferential statistics	Drawing conclusions about a population based on a sample.
interquartile range (IQR)	Of a data set, the difference between the first and third quartiles.
intersection of events	Both events occur.
least squares regression equation	The equation $\hat{y} = {\hat{β}}_{1} x + {\hat{β}}_{0}$ of the least squares regression line.
least squares regression line	The line that best fits a set of sample data in the sense of minimizing the sum of the squared errors.
level of confidence	The proportion of confidence intervals which, if under repeated random sampling were always constructed according to the formula of the text, would contain the parameter of interest.
level of significance of the test	The probability $α$ that defines an event as “rare;” the probability that the test procedure will lead to a Type I error.
linear correlation coefficient	A number computed directly from the data that measures the strength of the linear relationship between the two variables x and y.
most conservative estimate	The estimate obtained using $\hat{p} = 0.5$ , which gives the largest estimate of n.
mutually exclusive	Events that cannot both occur at once.
normal distribution	Assignment of probabilities to a continuous random variable using a bell curve for the density function.
normal random variable	A continuous random variable whose probabilities are determined by a bell curve.
NOVA	Analysis of variance.
null hypothesis	The statement that is assumed to be true unless there is convincing evidence to the contrary.
observed significance or p-value	The probability, if H₀ is true, of obtaining a result as contrary to H₀ and in favor of H_a as the result observed in the sample data.
percentile rank	Of a measurement x, the percentage of the data that are less than or equal to x.
percentile rank	Of a measurement x, the percentage of the data that are less than or equal to x.
population mean	The familiar average of a population data set.
population regression line	The line with equation $y =$ β1x+β0 that gives the mean of the variable y over the sub-population determined by x.
population standard deviation	The variability of population data as measured by the number $σ^{2} = \frac{Σ {(x - μ)}^{2}}{N}$ .
probability distribution	A list of each possible value and its probability.
probability of an event	A number that measures the likelihood of the event.
probability of an outcome	A number that measures the likelihood of the outcome.
Qualitative data	Measurements for which there is no natural numerical scale.
Quantitative data	Numerical measurements that arise from a natural numerical scale.
quartiles	Of a data set, the three numbers $Q_{1}$ , $Q_{2}$ , $Q_{3}$ that divide the data approximately into fourths.
random variable	A numerical value generated by a random experiment.
range	The variability of a data set as measured by the number $R = x_{max} - x_{min} .$
rejection region	An interval or union of intervals such that the null hypothesis is rejected if and only if the statistic of interest lies in this region.
relative frequency histogram	A graphical device showing how data are distributed across the range of their values by collecting them into classes and indicating the proportion of measurements in each class.
sample	The objects examined.
sample data	The measurements from a sample.
sample mean	The familiar average of a sample data set.
sample median	The middle value when data are listed in numerical order.
sample mode	The most frequent value in a data set.
sample standard deviation	The variability of sample data as measured by the number $\sqrt{\frac{Σ {(x - \bar{x})}^{2}}{n − 1}}$ .
sample standard deviation of errors	The statistic $s_{ε}$ .
sampling distribution	The probability distribution of a sample statistic when the statistic is viewed as a random variable.
standard deviation	The number $\sqrt{Σ {(x - μ)}^{2} P (x)}$ (also computed using $\sqrt{[}$ Σx2P(x) ]−μ2), measuring its variability under repeated trials.
standard normal random variable	The normal random variable with mean 0 and standard deviation 1.
standardized test statistic	The standardized statistic used in performing the test.
statistic	A number computed from the sample data.
Statistics	Collection, display, analysis, and inference from data.
tail	The region under a density curve whose area is either $P (X < x)$ or $P (X > x)$ for some number $x*$ .
Type II error	Failure to reject a false null hypothesis.
union of events	One or the other event occurs.
z-score	Of a measurement x, the distance of x from the mean in units of standard deviation.