Glossary

Alternative hypothesis (H1)—The opposite of the null hypothesis (H0).

Analysis of variance (ANOVA)—A statistical method that tests the significance of different factors on a variable of interest.

Arithmetic mean—The balance point in a set of data that is calculated by summing the observed numerical values in a set of data and then dividing by the number of values involved.

Bar chart—A chart containing rectangles (“bars”) in which the length of each bar represents the count, amount, or percentage of responses of one category.

Binomial distribution—A distribution that finds the probability of a given number of successes for a given probability of success and sample size.

Box-and-whisker plot—A graphical representation of the five-number summary that consists of the smallest value, the first quartile (or 25th percentile), the median, the third quartile (or 75th percentile), and the largest value.

Categorical variable—The values of these variables are selected from an established list of categories.

Cell—Intersection of a row and a column in a two-way cross-classification table

Chi-square (χ2) distribution—Distribution used to test relationships in two-way cross-classification tables.

Coefficient of correlation—Measures the strength of the linear relationship between two variables.

Coefficient of determination—Measures the proportion of variation in Y that is explained by the independent variable X in the regression model.

Collectively exhaustive events—One in a set of events must occur.

Common causes of variation—Represent the inherent variability that exists in the system.

Completely randomized design—An experimental design in which there is only a single factor.

Confidence interval estimate—An estimate of the population parameter given by an interval with a lower and upper limit.

Continuous numerical variables—Values of these variables are measurements.

Control chart—A tool for distinguishing between the common and special causes of variation.

Critical value—Divides the nonrejection region from the rejection region.

Degrees of freedom—The actual number of values that are free to vary after the mean is known.

Dependent variable—The variable to be predicted in a regression analysis.

Descriptive statistics—The branch of statistics that focuses on collecting, summarizing, and presenting a set of data.

Discrete numeric variables—The values are counts of things.

Dot scale diagram—A chart in which each response is represented as a point above a number line that includes the range of all values.

Error sum of squares (SSE)—Consists of variation that is due to factors other than the relationship between X and Y.

Event—Each possible type of occurrence.

Expected frequency—Frequency expected in a particular cell if the null hypothesis is true.

Expected value—The mean of a probability distribution.

Experiments—A process that uses controlled conditions to study the effect on the variable of interest of varying the value(s) of another variable or variables.

Explanatory variable—The variable used to predict the dependent or response variable in a regression analysis.

F distribution—A distribution used for testing the ratio of two variances.

First quartile (Q1)—The value such that 25.0% of the observations are smaller and 75.0% are larger.

Five-number summary—Consists of smallest value, Q1, median, Q3, and largest value.

Frame—The list of all items in the population from which samples will be selected.

Frequency distribution—A table of grouped numerical data in which the names of each group are listed in the first column and the percentages of each group of numerical data are listed in the second column.

Histogram—A special bar chart for grouped numerical data in which the frequencies or percentages of each group of numerical data are represented as individual bars.

Hypothesis testing—Methods used to make inferences about the hypothesized values of population parameters using sample statistics.

Independent events—Events in which the occurrence of one event in no way affects the probability of the second event.

Independent variable—The variable used to predict the dependent or response variable in a regression analysis.

Inferential statistics—The branch of statistics that analyzes sample data to draw conclusions about a population.

Level of significance—Probability of committing a type I error.

Mean—The balance point in a set of data that is calculated by summing the observed numerical values in a set of data and then dividing by the number of values involved.

Mean squares—The variances in an analysis-of-variance table.

Median—The middle value in a set of data that has been ordered from the lowest to highest value.

Mode—The value in a set of data that appears most frequently.

Mutually exclusive events—events are mutually exclusive if both events cannot occur at the same time.

Normal distribution—The normal distribution is defined by its mean (μ) and standard deviation (σ) and is bell-shaped.

Normal probability plot—A graphical device for helping to evaluate whether a set of data follows a normal distribution.

Null hypothesis—A statement about a parameter equal to a specific value, or the statement that there is no difference between the parameters for two or more populations.

Numerical variables—The values of these variables involve a counted or measured value.

Observed frequency—Actual tally in a particular cell of a cross-classification table.

p-chart—Used to study a process that involves the proportion of items with a characteristic of interest.

p-value—The probability of getting a test statistic equal to or more extreme than the result obtained from the sample data, given that the null hypothesis H0 is true.

Paired samples—Items are matched according to some characteristic and the differences between the matched values are analyzed.

Parameter—A numerical measure that describes a characteristic of a population.

Pareto diagram—A special type of bar chart in which the count, amount, or percentage of responses of each category are presented in descending order left to right, along with a superimposed plotted line that represents a running cumulative percentage.

Percentage distribution—A table of grouped numerical data in which the names of each group are listed in the first column and the percentages of each group of numerical data are listed in the second column.

Pie chart—A chart in which wedge-shaped areas (“pie slices”) represent the count, amount, or percentage of each category and the circle (the “pie”) itself represents the total.

Placebo—A substance that has no medical effect.

Poisson distribution—A distribution to find the probability of the number of occurrences in an area of opportunity.

Population—All the members of a group about which you want to draw a conclusion.

Power of a statistical test—The probability of rejecting the null hypothesis when it is false and should be rejected.

Probability—The numeric value representing the chance, likelihood, or possibility a particular event will occur.

Probability distribution for a discrete random variable—A listing of all possible distinct outcomes and their probabilities of occurring.

Probability sampling—A sampling process that takes into consideration the chance of occurrence of each item being selected.

Published sources—Data available in print or in electronic form, including data found on Internet Web sites.

Range—The difference between the largest and smallest values in a set of data.

Region of rejection—Consists of the values of the test statistic that are unlikely to occur if the null hypothesis is true.

Regression sum of squares (SSR)—Consists of variation that is due to the relationship between X and Y.

Residual—The difference between the observed and predicted values of the dependent variable for a given value of X.

Response variable—The variable to be predicted in a regression analysis.

Sample—The part of the population selected for analysis.

Sampling—The process by which members of a population are selected for a sample.

Sampling distribution—The distribution of a sample statistic (such as the arithmetic mean) for all possible samples of a given size n.

Sampling error—Variation of the sample statistic from sample to sample.

Sampling with replacement—A sampling method in which each selected item is returned to the frame from which it was selected so that it has the same probability of being selected again.

Sampling without replacement—A sampling method in which each selected item is not returned to the frame from which it was selected. Using this technique, an item can be selected no more than one time.

Scatter plot—A chart that plots the values of two variables for each response. In a scatter plot, the X-axis (the horizontal axis) always represents units of one variable, and the Y-axis (the vertical axis) always represents units of the second variable.

Simple linear regression—A statistical technique that uses a single numerical independent variable X to predict the numerical dependent variable Y.

Simple random sampling—The probability sampling process in which every individual or item from a population has the same chance of selection as every other individual or item.

Six Sigma management —A method for breaking processes into a series of steps in order to eliminate defects and produce near perfect results.

Skewness—A skewed distribution is not symmetric. There are extreme values either in the lower portion of the distribution or in the upper portion of the distribution.

Slope—The change in Y per unit change in X.

Special causes of variation—Represent large fluctuations or patterns in the data that are not inherent to a process.

Standard deviation—Measure of variation around the mean of a set of data.

Standard error of the estimate—The standard deviation around the line of regression.

Statistic—A numerical measure that describes a characteristic of a sample.

Statistics—The branch of mathematics that consists of methods of processing and analyzing data to better support rational decision-making processes.

Sum of squares among groups (SSA)—The sum of the squared differences between the sample mean of each group and the mean of all the values, weighted by the sample size in each group.

Sum of squares total (SST)—Represents the sum of the squared differences between each individual value and the mean of all the values.

Sum of squares within groups (SSW)—Measures the difference between each value and the mean of its own group and sums the squares of these differences over all groups.

Summary table—A two-column table in which the names of the categories are listed in the first column, and the count, amount, or percentage of responses are listed in a second column.

Survey—A process that uses questionnaires or similar means to gather values for the responses from a set of participants.

Symmetry—Distribution in which each half of a distribution is a mirror image of the other half of the distribution.

t distribution—A distribution used to estimate the mean of a population and to test hypotheses about means.

Test statistic—The statistic used to determine whether to reject the null hypothesis.

Third quartile (Q3)—The value such that 75.0% of the observations are smaller and 25.0% are larger.

Time-series plot—A chart in which each point represents a response at a specific time. In a time series plot, the X-axis (the horizontal axis) always represents units of time, and the Y-axis (the vertical axis) always represents units of the numerical responses.

Two-way cross-classification table—A table that presents the count or percentage of joint responses to two categorical variables (a mutually exclusive pairing, or cross-classifying, of categories from each variable). The categories of one variable form the rows of the table, and the categories of the other variable form the columns.

Type I error—Occurs if the null hypothesis H0 is rejected when in fact it is true and should not be rejected. The probability of a type I error occurring is α.

Type II error—Occurs if the null hypothesis H1 is not rejected when in fact it is false and should be rejected. The probability of a type II error occurring is β.

Variable—A characteristic of an item or an individual that will be analyzed using statistics.

Variance—The square of the standard deviation.

Variation—The amount of dispersion, or “spread,” in the data.

Y intercept—The value of Y when X = 0.

Z score—The difference between the value and the mean, divided by the standard deviation.