Statistics Glossary

Jeff_Perkinson

α	Statisitics:  The probability of making a type I error.  It is related to the confidence by   confidence = (1 -  α ) x 100.   Reliability:  The location parameter for a Weibull Distribution.
antagonism	An interaction of factors producing a poorer response than anticipated by considering the factor levels independently.
attribute data	Data that are not continuous.  Attribute data fit into categories that can be described by numbers or words.  Examples are Pass/Fail and Number of people residing in a home.  See also categorical data.
attributes control chart	A control chart for monitoring attribute data.
average	A term used to indicate either the mean or the median depending on the situation.  Typically it refers to the mean in industrial contexts.
b-coefficient	A number that multiplies a term in a model to define the shape of the response surface.
bathtub curve	A plot of the Hazard Rate for the life of a unit.  Typically units have a higher hazard rate early in life due to defects, a flat and lower hazard rate through the middle of life, and an increasing hazard rate near the end of life, forming a bathtub shape.
binomial distribution	A discrete distribution of pass-fail data that is applicable to  reliability demonstrations.
block	A group of experimental trials.
blocking	A technique that breaks experiments into smaller groups of trials to eliminate the effect of a nuisance factor.
blocking factor	A factor used to divide experimental trials into blocks for blocking.
Box-Behnken Design	An experiment design for collecting data to fit a full quadratic model. Also called a  Face-Centered Cubic Design or an Interaction Plus Star Design.
Box-Cox Plot	A plot of the log of the mean vs. the log of the standard deviation for replicate measurements.  The slope of this line can help determine an appropriate transformation for data to make the standard deviation constant over the region of interest.  The Box-Cox Transformation raises each response to the power of 1 minus the slope of this line (called Lambda).  JMP produces Lambda without the need for making this plot.
Box-Cox transformation	A mathematical operation performed on responses to make the standard deviation of the transformed responses constant over the region of interest.  The Box-Cox Transformation raises each response to the power of 1 minus the slope of  the line (Lambda) in a Box-Cox Plot.
CP	A measure of process potential, it compares the process variation to specification limits.
CPK	A measure of process capability, it compares the process variation to the specification limits taking the process mean into account.
CPL	A measure of the process capability, it compares the process variation below the process average with the specification limit below the process average.
CPU	A measure of the process capability, it compares the process variation above the process average with the specification limit above the process mean.
CR	The reciprocal of CPK.
CDF	Cumulative Distribution Function.  In reliability, the cumulative probability distribution of failing up until and in the next instant at any time t.
c-Chart	An attribute control chart used to monitor the number of non-conformities in a unit.
Censored Data	Reliability data that do not have precisely known failure times.  Also any data that are only known within a range, such as data below the detection limit of a measurement system.
Center Point	An experimental trial in which all factors are set to their middle value.
Central Composite Design	An experiment design to collect data to fit a full quadratic model.  The region of interest is spherical for this design.
Central Limit Theorem	The theorem that states that the distribution of means approaches a normal distribution as the sample size approaches infinity.  It allows us to assume Normal behavior for averages.
Coded Factors	Factors can be coded to a different scale to improve numerical accuracy in calculations.  A common coding for process factors is to to code the high level as +1 and the low level as -1 with intermediate values coded linearly over the range [-1,1].
Coded Responses	Sometimes it is valuable to code responses to make it easier to find a Sweet Spot.  For example, you can code your goal as 1, the unacceptable values as 0, and intermediate response values a linearly over the range [0, 1].  The Sweet Spot will have a maximum value for the coded response regardless of whether you are seeking a maximum, a minimum, or a number in a range.  See also desireability.
Coding	Changing a value to a different value, such as coding a high level as +1 and a low level as -1.
Combined s	An estimate of the standard deviation for the region of interest formed by combining separate estimates of the standard deviation by a technique called pooling.  See also pooled s and pure error.
Combined Standard Deviation	See Combined s above.
Common Cause	An intrinsic cause of variation in a process.  Variation which is part of a process when it is operating normally.
Confidence	The percentage of times a good outcome is achieved when a technique is applied consistently over a long period of time.
Confidence Interval	An interval between a lower and an upper limit in which the long-term mean should lie within the specified confidence.
Confidence Limits	The lower and upper limits for a confidence interval.
Consistent Standard Deviation Estimates	A term used to indicate that the standard deviation is constant over the region of interest.  More precisely, it indicates that the variance is homogeneous.
Continuous	Refers to the property of a factor or response that a level can be found between any two other levels, no matter how small the difference between these other levels.
Contour Plot	A picture of a model that shows contour lines of constant response.
Control Chart	A run chart with limits indicating the normal operation of a process.  Typically these limits are ± 3 times the standard deviation.
Critical Value	A value from a distribution to which a calculated value is compared in a significance test.
Cube	A three-dimensional object that represents the region of interest for a 3-factor process factor experiment.
Cubic Model	A polynomial model containing, at a minimum, a constant term, a term for each main effect, a term for each two-factor interaction between main effects, a term for the square of each main effect, and a term for each 3-factor interaction of the main effects.  The full cubic model also includes terms for the interactions of each quadratic main effect with each linear main effect and terms for the cube of each main effect.
Cycle	A periodic fluctuation, such as a temperature cycle.
D-Optimal Design	An experiment design that minimizes the determinant of the variance-covariance matrix of the solution vector.  The goal is to provide accurate and precise estimates of the b coefficients (or effects).
Degrees of Freedom	The number of values which could be arbitrarily assigned.  For example, if you want to assign data to the categories “pass” “fail high,” and “fail low,” the degrees of freedom is 2, because once data has been assigned to any 2 categories the remainder must be assigned to the third – it cannot be assigned arbitrarily.
Design Cube	A three-dimensional object that represents the region for data collection for a 3-factor process factor experiment.
Desireability	An indication of how well a response meets a goal.  Typically desireability uses coded responses with 0 indicating that the goal is not met at all, 1 indicating that the goal was met perfectly, and intermediate values indicating that the goal is partially met.  For multiple goals the overall desireability is typically calculated as the geometric mean of the individual desireabilities.
Discrete	The property of a factor or response that only certain levels are allowed.
Distribution	The shape data take when plotted on a histogram.
Drift	An increase or decrease over time in a factor level or response.
Effect	The average difference in a response as a factor varies from its high to its low level.  These can be ranked in magnitude to determine the relative importance of  terms in a model.
Experiment Design	A plan for collecting and analyzing data.
Experimental Error	A term encompassing both Systematic Error and Random Response Variation.
External Factor	A factor not being studied in an experiment, but influencing one or more experimental responses.
F	The ratio of two variances, each divided by its degrees of freedom.
FCritical	A value from the F-distribution that is compared to a calculated F statistic in a significance test.  This is used to test for statistically significant differences in variances (standard deviations).
F-distribution	A distribution used to describe variance ratios.
F-test	A test to determine whether a difference between two variance estimates is statistically significant.
Face-Centered-Cubic Design	An experiment design for collecting data to fit a full quadratic model.  Also called an “Interaction Plus Star Design” or a “Box-Benkhen Design.”
Factor	Something over which you have direct control in an experiment that influences a response.
Factor Transformation	A mathematical operation performed on factors to simplify the shape of the response surface.
Factorial Design	An experiment design used to study factors and their interactions.
Failure Rate	The probability of failing at the next instant in time at time t divided by the probability of surviving until time t.  Also called the “Hazard Rate.”
Fractional Factorial Design	A factorial design that studies only some of the possible factor interactions, usually just the 2-factor interactions.
Full Cubic Model	A polynomial model containing a constant term, a term for each main effect, a term for each two-factor interaction between main effects, a term for the square of each main effect, a term for each 3-factor interaction of the main effects,  a term for the interactions of each quadratic main effect with each linear main effect, and a term for the cube of each main effect.
Full Factorial Design	A factorial design that studies all possible interactions.
Full Quadratic Model	A polynomial model containing a constant term, a term for each main effect, a term for each two-factor interaction between main effects, and a term for the square of each main effect.
G-Optimal Design	An experiment design that minimizes the largest variance in the region of interest.  While this may the best type of design for DOE work, it is not yet possible to generate these designs to order.  The I-Optimal design is the next best choice in most situations.
Gaussian Distribution	A distribution of measurement error that is widely applicable to many types of continuous data.  This distribution is bell-shaped.
Gosset	A program written by Ron Hardin (ATT Bell Labs) to implement NJA Sloane's (ATT Bell Labs) algorithm for generating custom, Optimal experiment designs.  ( See  http://www.research.att.com/~njas/gosset/index.html)  This has largely been replaced by the JMP Custom Designer.
Grid Search	A method used for finding a Sweet Spot in which the region of interest is divided into a grid, a response is predicted at each grid point, and the grid point or points meeting the goal are listed as potential Sweet Spots.
Hazard Curve	The PDF / The Survival Curve.
Hazard Rate	The probability of failing at the next instant in time at time t divided by the probability of surviving until time t.
Histogram	A plot of data in categories to form a pile of data.
Homogeneous Variance	A term used to indicate that the variance (standard deviation) is constant over the region of interest.
Hypercube	A multi-dimensional object that represents the region of interest for a four or more factor experiment.
I-Optimal Design	An experiment design that minimizes the average variance of prediction over the region of interest.  The goal is to make accurate and precise predictions.
In-Control	Describes a process which is only subject to common causes of variability.
Interactions	Changes in responses due to changes in factor levels that are dependent on other factor levels.  The effect of factors changing levels together.
Interaction Design	An experiment design for collecting data to fit an interaction model.  Also known as  “Factorial” or “Fractional Factorial” designs.
Interaction Model	A  polynomial model that includes, at a minimum, a constant term, terms for each main effect, and terms for each 2-factor interaction between main effects.  It can also contain higher order interaction terms, such as 3-factor interactions among the main effects.