Glossary Terms
- area in the tails of the distribution
- The proportion of the distribution that falls in the tails of a normal curve. The area in the tail of the distribution associated with a particular z score can be found in Appendix A, column C.
- area under the curve
- The proportion of the distribution that is bounded by a single z score or a pair of z scores. The area under the curve bounded by a single z score can be found in Appendix A, column B.
- arithmetic mean
- Perhaps the most common measure of central tendency, the mean is the mathematical average of the scores in a sample.
- asymptote
- A line which a graph of a function approaches closely but never touches.
- bell curve
- The bell curve is a symmetrical distribution in which there is a single peak at the center and tails that extend equally out to each side. The bell curve represents a normal distribution.
- bimodal distribution
- A distribution with two distinct peaks that lie roughly symmetrically on either side of the center point.
- bin widths
- The widths of the class intervals. The choice of bin width determines the number of class intervals. This decision, along with the choice of starting point for the first interval, affects the shape of the histogram.
- box plots
- One of the more effective graphical summaries of a data set, the box plot generally shows the median, 25th and 75th percentiles, and outliers.
- categorical variables
- Also known as qualitative variables, categorical variables cannot be quantified, or measured numerically. Instead, they are measured on a nominal or ordinal scale.
- central tendency
- The center or middle of a distribution. There are many measures of central tendency. The most common are the mean, median, and mode.
- common logarithmic function
- The function [latex]f\left(x\right)=log\;x[/latex] is the common logarithmic function with base[latex]10[/latex], where [latex]x \gt 0[/latex] (Note: [latex]y=log\;x\;[/latex] is equivalent to [latex]\;x={10}^{y}[/latex]).
- complex conjugate pair
- A complex conjugate pair is of the form [latex]a+bi[/latex], [latex]a-bi[/latex].
- complex number
- A complex number is of the form [latex]a+bi[/latex], where [latex]a[/latex] and [latex]b[/latex] are real numbers. We call [latex]a[/latex] the real part and [latex]b[/latex] the imaginary part.
- complex number system
- The complex number system is made up of both the real numbers and the imaginary numbers.
- complex rational expression
- A complex rational expression is a rational expression in which the numerator and/or denominator contains a rational expression.
- continuous variables
- Variables whose possible values fall along a continuous scale (not broken up into discrete steps), eg. the time it takes to answer a question.
- control (group)
- The group in an experimental study that is not receiving the treatment being tested.
- convenience sampling
- A sampling strategy in which participants are recruited for their easy availability (e.g., college students). A sample obtained through convenience sampling should not be considered a representative sample.
- data
- A collection of values to be used for statistical analysis. Data is the plural form of datum.
- degree of the polynomial equation
- The degree of the polynomial equation is the degree of the polynomial.
- degrees of freedom
- The number of independent pieces of information that go into the estimate. In general, the degrees of freedom for an estimate is equal to the number of values minus the number of parameters estimated en route to the estimate in question.
- dependent variable
- A variable that measures the experimental outcome. In most experiments, the effects of the independent variable on the dependent variables are observed. For example, if a study investigated the effectiveness of an experimental treatment for depression, then the measure of depression would be the dependent variable.
- descriptive statistics
- A set of statistics—such as the mean, standard deviation, and skew—that describe a distribution.
- discrete variables
- A variable that exists in indivisible units. For quantitative variables, it is measured in whole numbers that are discrete points on the scale.
- discriminant
- In the Quadratic Formula, [latex]x=\frac{-b\pm\sqrt{{b}^{2}-4ac}}{2a}[/latex], the quantity [latex]b^2-4ac[/latex] is called the discriminant.
- dispersion
- The extent to which values differ from one another; that is, how much they vary. Dispersion is also called variability or spread.
- event
- Any specific outcome that could happen.
- experimental (group)
- The group in a study that is receiving the treatment being tested.
- experimental research
- Research that involves the use of random assignment to treatment conditions and manipulation of the independent variable.
- exponential function
- An exponential function, where [latex]a>0[/latex] and [latex]a\ne 1[/latex]. is a function of the form [latex]f\left(x\right)={a}^{x}[/latex].
- extraneous solution to a rational equation
- An extraneous solution to a rational equation is an algebraic solution that would cause any of the expressions in the original equation to be undefined.
- factoring
- Splitting a product into factors is called factoring.
- frequency polygons
- A frequency polygon is a graphical representation of a distribution that is similar in appearance to a line graph. Frequency polygons can be grouped or ungrouped.
- greatest common factor
- The greatest common factor (GCF) of two or more expressions is the largest expression that is a factor of all the expressions.
- histogram
- A graphical representation of a distribution that is similar in appearance to a bar chart. It partitions the variable on the x-axis into various contiguous class intervals of (usually) equal widths. The heights of the bars represent the class frequencies.
- imaginary unit
- The imaginary unit [latex]i[/latex] is the number whose square is [latex]–1[/latex]. [latex]i^2=–1[/latex] or [latex]i=\sqrt{-1}[/latex]
- independent variable
- A variable that is manipulated by the experimenter, as opposed to a dependent variable. Most experiments consist of observing the effect of the independent variable(s) on the dependent variable(s).
- inferential statistics
- The branch of statistics concerned with drawing conclusions about a population from a sample.
- interquartile range
- interquartile range (IQR)
- The range of the middle 50% of the scores in a distribution; computed by subtracting the 25th percentile from the 75th percentile. The interquartile range is a robust measure of central tendency.
- interval scale
- A numerical scale in which the distance between scores on the scale is consistent (equal) and for which the zero is relative (rather than absolute)
- lie factor
- The ratio of the size of the effect shown in a graph to the size of the effect shown in the data. This term was coined by Edward Tufte, who suggested that lie factors greater than 1.05 or less than 0.95 produce unacceptable distortion.
- like radicals
- Like radicals are radical expressions with the same index and the same radicand.
- logarithmic function
- The function [latex]f\left(x\right)={log}_{a}x[/latex] is the logarithmic function with base [latex]a[/latex], where [latex]a \gt 0[/latex], [latex]x \gt 0[/latex], and [latex]a\ne 1[/latex].
[latex]y={log}_{a}x\;\text{is equivalent to}\;x={a}^{y}[/latex]
- median
- The median is a popular measure of central tendency. It is the 50th percentile of a distribution.
- mode
- A measure of central tendency, the mode is the most frequent value in a distribution.
- natural base
- The number [latex]e[/latex] is defined as the value of [latex]{\left(1+\frac{1}{n}\right)}^{n}[/latex], as [latex]n[/latex] gets larger and larger. We say, as [latex]n[/latex] increases without bound, [latex]e\approx 2.718281827...[/latex]
- natural exponential function
- The natural exponential function is an exponential function whose base is [latex]e[/latex]: [latex]f\left(x\right)={e}^{x}[/latex]. The domain is [latex]\left(\text{−}\infty ,\infty \right)[/latex] and the range is [latex]\left(0,\infty \right)[/latex].
- natural logarithmic function
- The function [latex]f\left(x\right)=\text{ln}\;x[/latex] is the natural logarithmic function with base [latex]e[/latex], where [latex]x \gt 0[/latex].
[latex]y=\text{ln}\;x\;\text{is equivalent to}\;x={e}^{y}[/latex]
- nominal scale
- A scale in which no ordering is implied, and addition/subtraction and multiplication/division would be inappropriate for a variable. Variables measured on a nominal scale have no natural ordering, even if they are coded using numbers (e.g., for eye color 1 = blue, 2 = brown, 3 = hazel, etc.).
- non-experimental research
- Research that involves observing things as they occur naturally and recording observations as data. Also known as correlational research.
- normal distribution
- One of the most common continuous distributions, a normal distribution is sometimes referred to as a bell-shaped distribution, a bell curve, or a Gaussian curve. If the mean is 0 and the standard deviation is 1, the distribution is referred to as the “standard normal distribution.”
- ordinal scale
- A set of ordered values in which there is no set distance between scale values; for example, asking someone to indicate how much education they completed by asking them to circle one of the following: did not complete high school, high school diploma, some college, college degree, professional degree.
- polynomial equation
- A polynomial equation is an equation that contains a polynomial expression.
- population
- The complete set of observations a researcher is interested in. Contrast this with a sample which is a subset of a population. Inferential statistics are computed from sample data in order to make inferences about the population.
- probability
- The likelihood of a statistical result or the number of outcomes that satisfy specific criteria divided by the total number of possible outcomes.
- proportion
- When two rational expressions are equal, the equation relating them is called a proportion.
- quadratic equation
- Polynomial equations of degree two are called quadratic equations.
- quadratic function
- A quadratic function, where a, b, and c are real numbers and [latex]a\ne 0,[/latex] is a function of the form [latex]f\left(x\right)=a{x}^{2}+bx+c.[/latex]
- qualitative variables
- Also known as categorical variables, qualitative variables cannot be quantified, or measured numerically. Instead, they are measured on a nominal or ordinal scale. Variables that are not qualitative are known as quantitative variables.
- quantitative variables
- Variables that are measured on a numeric or quantitative scale or that can be ordered in some fashion. Ordinal, interval, and ratio scales are quantitative. A country’s population, a person’s shoe size, or a car’s speed are all quantitative variables. Variables that are not quantitative are known as qualitative variables.
- quasi-experimental research
- Research that involves manipulating the independent variable but not randomly assigning people to groups.
- radical equation
- An equation in which a variable is in the radicand of a radical expression is called a radical equation.
- range
- The difference between the maximum and minimum values of a variable or distribution. The range is the simplest measure of variability.
- ratio scale
- A numerical scale in which the distance between scores on the scale is consistent (equal) and for which the zero is relative (rather than absolute).
- rational equation
- A rational equation is an equation that contains a rational expression.
- rational expression
- A rational expression is an expression of the form [latex]\frac{p}{q},[/latex] where [latex]p[/latex] and [latex]q[/latex] are polynomials and [latex]q\ne 0.[/latex]
- rational function
- A rational function is a function of the form [latex]R\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}[/latex] where [latex]p\left(x\right)[/latex] and [latex]q\left(x\right)[/latex] are polynomial functions and [latex]q\left(x\right)[/latex] is not zero.
- rationalizing the denominator
- Rationalizing the denominator is the process of converting a fraction with a radical in the denominator to an equivalent fraction whose denominator is an integer.
- robustness
- Something is robust if it holds up well in the face of adversity. A measure of central tendency or variability is considered robust if it is not greatly affected by a few extreme scores. A statistical test is considered robust if it works well in spite of moderate violations of the assumptions on which it is based.
- sample
- A subset of a population, often taken for the purpose of statistical inference.
- sampling bias
- Sampling bias occurs when participants are not selected at random or when they have an unequal probability of being selected for participation in a study.
- sampling error
- The discrepancy between a parameter and the statistic used to estimate it.
- similar figures
- Two figures are similar if the measures of their corresponding angles are equal and their corresponding sides have the same ratio.
- simple random sampling
- A process of selecting a subset of a population for the purposes of statistical inference in which every member of the population is equally likely to be chosen.
- simplified rational expression
- A simplified rational expression has no common factors, other than [latex]1[/latex], in its numerator and denominator.
- skew
- A distribution is skewed if one tail extends out further than the other, making the distribution asymmetrical. A distribution has a positive skew (is skewed to the right) if the tail to the right is longer. A distribution has a negative skew (is skewed to the left) if the tail to the left is longer.
- spread
- The extent to which values differ from one another; that is, how much they vary. Spread is also called variability or dispersion.
- square of a number
- If [latex]n^2 = m[/latex], then [latex]m[/latex] is the square of [latex]n[/latex].
- square root of a number
- If [latex]n^2 = m[/latex], then [latex]n[/latex] is a square root of [latex]m[/latex].
- standard deviation
- The standard deviation is a widely used measure of variability. It is computed by taking the square root of the variance.
- standard form
- A complex number is in standard form when written as [latex]a+bi[/latex], where [latex]a[/latex], [latex]b[/latex] are real numbers.
- standard normal distribution
- A normal distribution that has a mean of 0 and a standard deviation of 1; also known as the unit normal distribution.
- standardization
- The process of transforming any normal distribution into a standard normal distribution by converting all of the raw scores in the distribution into standard scores (z scores).
- statistics
- A range of techniques and procedures for analyzing, interpreting, displaying, and making decisions based on sample data.
- stem-and-leaf display
- A quasi-graphical representation of numerical data. Generally, all but the final digit of each value is a stem, and the final digit is the leaf. The stems are placed in a vertical list, with each matched leaf on one side.
- stratified random sampling
- In stratified random sampling, the population is divided into a number of subgroups (or strata). Random samples are then taken from each subgroup with sample sizes proportional to the size of the subgroup in the population.
- sum of squares
- The sum of squared deviations, or differences, between scores and the mean in a numeric dataset.
- variability
- The extent to which values differ from one another; that is, how much they vary. Variability can also be thought of as how spread out or dispersed a distribution is.
- variable
- Something that can take on different values. For example, different subjects in an experiment weigh different amounts. Therefore “weight” is a variable in the experiment. Or, subjects may be given different doses of a drug. This would make “dosage” a variable. Variables can be dependent or independent, qualitative or quantitative, and continuous or discrete.
- variance
- The variance is a widely used measure of variability. It is defined as the mean squared deviation of scores from the mean.
- whiskers
- Vertical lines ending in a horizontal stroke that are added to box plots to indicate the spread of the data points. Whiskers are drawn from the upper and lower hinges to the upper and lower adjacent values.
- z score
- The number of standard deviations a score is from the mean of its population. When the scores (or sample means) in the population are normally distributed, the z table can be used to find probabilities for obtaining a given z score.
- zero of the function
- A value of [latex]x[/latex] where the function is 0, is called a zero of the function.
- Zero Product Property
- The Zero Product Property says that if the product of two quantities is zero, then at least one of the quantities is zero.
