Glossary
- Page ID
- 54265
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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 |
|---|---|---|---|---|---|
| (Eg. "Genetic, Hereditary, DNA ...") | (Eg. "Relating to genes or heredity") |  |
The infamous double helix | https://bio.libretexts.org/ | CC-BY-SA; Delmar Larsen |
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Word(s) |
Definition |
Image | Caption | Link | Source |
|---|---|---|---|---|---|
| Axiom | An axiom is a statement that is taken to be true and serves as a starting point for further reasoning. | ||||
| Test Statistic | A test statistic is a function of the data that measures the evidence against the null hypothesis by computing the distance between an estimator and the closest possible parameter value specified by the null hypothesis. | ||||
| Standard Error | The standard error of an estimator is an estimate of how large the estimation error of an estimator may be. | ||||
| Estimation Error | The difference between the value of an estimator computed on a sample and the parameter value for the corresponding population is called estimation error. | ||||
| Estimator | A statistical estimator is a summary computed on a sample that is taken to be the best indication of what a corresponding unknown parameter value may be. | ||||
| Alternative Hypothesis | In statistical hypothesis testing the alternative hypothesis is accepted if the null hypothesis is rejected. The alternative hypothesis is usually denoted mathematically as \(H_1\). | ||||
| Null Hypothesis | In statistical hypothesis testing, the null hypothesis is initially assumed to be true. The statistical testing procedure will then determine how much evidence exists in the data contradicting the null hypothesis. The null hypothesis is usually denoted mathematically as \(H_0\). | ||||
| Statistical Hypothesis | A statistical hypothesis is a statement about the value of a parameter of a population. | ||||
| Scatterplot | A scatterplot is a plot of the individual values of two paired variables where is point is represented by a point on the plot. | ||||
| Outlier | The outliers in histograms are values that seem significantly different compared to the rest of the values on the histogram, usually identified as values far out in either of the tails of a histogram. | ||||
| Tail | In a unimodal histogram the tail of the histogram is the range on each side of the of the peak corresponding to the thinner, tapering end of the histogram where data points are less frequent. | ||||
| Skewness | The skewness of a unimodal histogram indicates whether there is a longer tail to the right of the peak, to the left of the peak, or if the tails are about equal on either side of the peak. If the longer tail is to the left, the histogram is left skewed. If the longer tail is to the right, then the histogram is right skewed. If the tails are about equal, the histogram is symmetric. | ||||
| Modality | The modality of a histogram refers to how many “peaks” the histogram has. A histogram is called unimodal if there is one peak, bimodal if there are two peaks, multimodal if there are three or more peaks, and uniform if the histogram is relatively flat across the classes. | ||||
| Mode | A peak on a histogram is called a mode. | ||||
| Histogram | A histogram of a frequency distribution is a graph whose horizontal axis corresponds to the values of a quantitative variable and whose vertical axis corresponds to the observed frequency, relative frequency, or percentage for each class. The bars of the graph span the corresponding classes. | ||||
| Line Graph | A line graph is a plot of points whose horizontal axis is a variable that has at least an ordinal measurement scale and whose vertical axis is an observation or measurement that has at least an ordinal measurement scale. The points are connected by line segments with respect to the order of the horizontal axis. | ||||
| Pie Chart | A pie chart of a frequency distribution is a circular graph whose “slices” corresponds to the possible outcomes for a qualitative variable. The area of the slice compared to the area of the entire pie is equal to the percentage (or relative frequency) of that response. | ||||
| Bar Graph | A bar graph of a frequency distribution is a graph whose horizontal axis shows the category headings of a qualitative variable. The vertical axis shows the observed frequency, relative frequency, percentage, or numerical summary (mean, median, etc.) for each category, which correspond to the bar heights. The bars are separated by spaces. | ||||
| Cross Classified Frequency Distribution | A cross-classified frequency distribution of two variables is a table that contains the frequencies, relative frequencies, and percentages of the number of times each pair of values occur in an observation of the two variables in the data. | ||||
| Classes | A set of classes for a quantitative variable is a set of non-overlapping ranges that cover all the values of the variable so that each value of the variable falls in exactly one class. | ||||
| Frequency Distribution | The frequency distribution of a set of qualitative data is a table that contains the number of times each category of the data is observed. The individual counts for each category are called the frequencies of the categories. | ||||
| Frequency Distribution (Qualitative Data) | The frequency distribution of a set of qualitative data is a table that contains the number of times each category of the data is observed, the proportion of data that was observed in each category, or the percentage of data that was observed in each category. The individual counts for each category are called the frequencies of the categories. The relative frequencies are computed by dividing each frequency by the total number of observations in the set of data. The percentages are computed by multiplying the relative frequencies by 100%. | ||||
| Range | To compute the range of a set of data, subtract the smallest value in the set of data from the largest value in the set of data. | ||||
| Percentile | The \(p\)th percentile of a set of data is the smallest point for which at least \(p\)% of the data is less than or equal to that point. | ||||
| Variation | A measure of variation of a set of data is a measure that summarizes the set of data with a single value that represents typically how far data points can be found from the location of the data. | ||||
| Median | A median is any point which divides the lower half from the upper half of the data. | ||||
| Science |
Science is the systemic process of obtaining knowledge by deduction and careful observation in the form of testable hypotheses and predictions about the universe |
New Websters Dictionary and Thesaurus 1992 |
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| Deduction | A conclusion is based on deduction if it follows logically from a set of statements that are known to be true. | ||||
| Induction | A conclusion is based on induction if it is generalized from a set of observations. | ||||
| Empiricism | Empiricism is the philosophical theory that knowledge is gained through experience. | ||||
| Experiment | An experiment is any process that produces observations that provide evidence that can be used to determine if a hypothesis is true or not. | ||||
| Response | In an experiment the response is the observed condition that is of interest to the researcher. | ||||
| Factor | In an experiment a factor or treatment is a condition that is hypothesized to have an effect on, or is associated with, the response. | ||||
| Treatment | In an experiment a factor or treatment is a condition that is hypothesized to have an effect on, or is associated with, the response. | ||||
| Designed Experiment | A designed experiment is an experiment where the factors are controlled and set by the researcher prior to observing the outcome. | ||||
| Control Group | In an experiment that compares a standard treatment to a special treatment, the group that receives the standard treatment is called the control group. | ||||
| Treatment Group | In an experiment that compares a standard treatment to a special treatment, the group that receives the special treatment is called the treatment group. | ||||
| Observational Study | An observational study is an experiment where the researcher does not control or set the factors. | ||||
| Confounding | Two or more factors are confounded when the effect of one of the factors cannot be distinguished from the effects of the other factors on the outcome. | ||||
| Case Control Study | A case control study is an observational study that observes data about past differences between two groups. | ||||
| Population | A population consists of all individuals or items that are of interest in a statistical study. | ||||
| Data | Measurements taken on individuals or items in a population are called data. A single measurement is called a datum. | ||||
| Variable | A single measurement that is taken on everyone observed in a population is called a variable. | ||||
| Parameter | A parameter is a quantity or characteristic that can be computed when the whole population has been observed. | ||||
| Applicant Flow | The applicant flow for a position is the collection of individuals who apply for a job or promotion. | ||||
| Extrapolation | Extrapolation refers to making conclusions for populations that are larger than the population that was observed. | ||||
| Nominal Measurement Scale | A variable has a nominal measurement scale if the only possible valid mathematical comparison of two datum is whether they are equal. | ||||
| Quantitative Data | Data observed from a variable that have a natural and unique numeric value are called quantitative data. | ||||
| Ordinal Measurement Scale | A variable has an ordinal measurement scale if the only possible valid mathematical comparisons of two datum is whether they are equal and whether one is greater than another. | ||||
| Ratio Measurement Scale |
A variable has a ratio measurement scale if the possible valid mathematical comparisons of two datum are whether they are equal or whether one is greater than the other. Additionally, differences and ratios between two data are a valid comparison. |
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| Direct Observable | A variable is a direct observable if the observation can be measured directly and easily. | ||||
| Indirect Observable | A variable is an indirect observable if the observation can only be measured through an additional process. | ||||
| Construct | Constructs are variables that cannot be observed either directly or indirectly. | ||||
| Random Experiment | A random experiment is any experiment whose outcome cannot be predicted with absolute certainty. | ||||
| Concept | A concept is a construct that has been clearly defined in terms of ideas that can be observed either directly or indirectly. The process of developing a construct into a concept is called conceptualization. | ||||
| Dimension | A particular aspect of a concept is called a dimension. | ||||
| Probability | The probability that an outcome from a random experiment occurs is a number between 0 and 1, inclusive, that reflects the proportion of time the outcome would occur in a very large number of replications of the experiment under the same conditions for each replication. | ||||
| Indicator | A particular aspect of a dimension is called an indicator. | ||||
| Chance | The chance that an outcome from a random experiment occurs is a percentage between 0% and 100%, inclusive, that reflects the percentage of time the outcome would occur in a very large number of replications of the experiment under the same conditions for each replication. | ||||
| Operationalization | Operationalization is the process of developing the procedures that will result in the empirical observations representing the concepts. | ||||
| Valid Measurement System | A measurement system is valid if the system correctly measures the concept without any systematic bias. | ||||
| Face Validity | A measurement system has face validity if the dimensions and the indicators make sense and are consistent with known research about the subject. | ||||
| Content Validity | A measurement system has content validity if the dimensions and indicators cover the range of meanings within the concept. | ||||
| Criterion Validity | A measurement system has criterion validity if it coincides statistically with other measures of the same concept. | ||||
| Census | Observing every individual or item in a population is called a census. | ||||
| Predictive Criterion Validity | A measurement system has predictive criterion validity if it does a good job of predicting future values of an established measure of a concept. | ||||
| Concurrent Criterion Validity | A measurement system has concurrent criterion validity if it is strongly associated with a value of an established measure of a concept that is observed at the same time. | ||||
| Sample | A sample is any observed part of a population. | ||||
| Construct Validity | A measurement system has construct validity if it behaves the way researchers would expect in how it is related to measures of other concepts. | ||||
| Representative Sample | A sample from a population is representative if the characteristics of the sample are like those of the population. | ||||
| Factor Construct Validity | A measurement system has factor construct validity if a statistical factor analysis indicates that the number of dimensions and the grouping of the indicators within the dimensions is correct. | ||||
| Test-Retest Reliability | The reliability of a measurement system is assessed using test-retest reliability if the same measurement is taken two or more times on the same group of individuals. | ||||
| Internal Consistency Reliability | The reliability of a measurement system is assessed using internal consistency reliability if the association between the dimensions and the indicators within the dimension are all strongly associated with one another. | ||||
| Odds Ratio | If the odds of one outcome is \(m\) to \(n-m\) and the odds of another outcome is \(k\) to \(l-k\), then the odds ratio of the first outcome compared to the second outcome is
\[ \text{odds ratio} = \frac{m/(n-m)}{k/(l-k)} = \frac{m(l-k)}{k(n-m)}. \nonumber \] |
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| Simple Random Sample | A simple random sample is any random method of choosing a sample from a population in such a way such that every individual or item in the population has an equal chance of being selected. | ||||
| Location | A measure of location of a set of data is a measure that summarizes the set of data with a single value that represents the middle or center of the data. | ||||
| Mean | To compute the mean of a set of data, add all the values in the data set and divide by the number of values in the data set. |