# Glossary

- Page ID
- 13577

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Words (or words that have the same definition) | The definition is case sensitive | (Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pages] | (Optional) Caption for Image | (Optional) External or Internal Link | (Optional) Source for Definition |
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(Eg. "Genetic, Hereditary, DNA ...") | (Eg. "Relating to genes or heredity") | The infamous double helix | https://bio.libretexts.org/ | CC-BY-SA; Delmar Larsen |

Word(s) | Definition | Image | Caption | Link | Source |
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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. |
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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. |
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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. |
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confidence interval | An interval with endpoints $\stackrel{-}{x}\pm E$, 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. |
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density function | The function $f\left(x\right)$ such that probabilities of a continuous random variable X are areas of regions under the graph of $y=f\left(x\right)$. |
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Descriptive statistics | The organization, display, and description of data. | ||||

error | Using $y-\widehat{y}$, the actual y-value of a data point minus the y-value that is computed from the equation of the line fitting the data. |
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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. |
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$F$ random variable | A random variable following an F-distribution. |
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F-distribution |
A particular probability distribution specified by two degrees of freedom, $$ |
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factors | A variable with several qualitative levels. | ||||

five-number summary | Of a data set, the list $\{{}_{}$ |
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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 $\widehat{y}={\widehat{\mathit{\beta}}}_{1}x+{\widehat{\mathit{\beta}}}_{0}$ 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 $\alpha $ 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. |
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most conservative estimate | The estimate obtained using $\widehat{p}=0.5$, which gives the largest estimate of n. |
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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 H_{0} is true, of obtaining a result as contrary to H_{0} and in favor of H as the result observed in the sample data._{a} |
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percentile rank | Of a measurement x, the percentage of the data that are less than or equal to x. |
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percentile rank | Of a measurement x, the percentage of the data that are less than or equal to x. |
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population mean | The familiar average of a population data set. | ||||

population regression line | The line with equation $y=$y over the sub-population determined by x. |
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population standard deviation | The variability of population data as measured by the number ${\mathit{\sigma}}^{2}=\frac{\mathrm{\Sigma}{(x-\mathit{\mu})}^{2}}{N}$. | ||||

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 $R={x}_{\text{max}}-{x}_{\text{min}}.$ | ||||

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 $\sqrt{\frac{\mathrm{\Sigma}{(x-\stackrel{-}{x})}^{2}}{n\text{\u2212}1}}$. | ||||

sample standard deviation of errors | The statistic ${s}_{\mathit{\epsilon}}$. | ||||

sampling distribution | The probability distribution of a sample statistic when the statistic is viewed as a random variable. | ||||

standard deviation | The number $\sqrt{{\displaystyle \mathrm{\Sigma}{(x-\mathit{\mu})}^{2}P\left(x\right)}}$ (also computed using $\sqrt{[{\displaystyle}}$ |
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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 $P\left(X<\mathrm{x*}\right)$ or $P\left(X>\mathrm{x*}\right)$ for some number $\mathrm{x*}$. | ||||

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. |