Definitions
of Concepts and Terms that we use will appear here in alphabetical order
Click
on a letter to jump to words starting with:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
This
glossary is in its early stages – we will be filling in the gaps very soon.
|
@Risk |
An Excel Add-In, produced by
Palisade Corporation, to facilitate Monte Carlo simulations in a
spreadsheet. With @Risk the whole
simulation process can be managed. |
|
Accept
or Reject the Null Hypothesis |
The outcome or conclusion of a test
of a hypothesis, when we decide whether the sample data tends to confirm
(accept) or provide evidence against (reject) the hypothesis. |
|
Additive
Model |
|
|
Additivity |
The additivity property implies the
parts of a whole may simply be added together to give the value for the
whole. |
|
Adjusted
R-squared |
A measure of how well a multiple
regression model fits to the data.
The proportion of the total variance of the dependent variable values
explained by the independent variables in the model. |
|
Aggregate
Planning Model |
A model combining the effects of the
availability of a workforce on production levels, inventory and plant
capacity. The model is used over a
period of time so variables to link inventory variables over time are also
needed. |
|
Alternative
Hypothesis |
That which is to be true if the null
hypothesis is not true. |
|
Analysis
ToolPak (in Excel) |
A set of programs that come with
Excel that can be used to do many statistical calculations. Found under the Tools menu. Can be rather limited, using a statistical
package (like SPSS or S-plus) or an add-in (like StatPro) is usually easier
and better. |
|
Analytical |
vs Numerical approaches |
|
ANOVA
Table |
A display of the calculations and
testing of an Analysis of Variance test. |
|
Array |
A range, in Excel
terms. A block of cells in the
spreadsheet. |
|
Array Function (in Excel) |
A function which operates
on an array, filling in a whole range or array at once, according to the
formula in the function. |
|
Assignable
Cause |
Where a process is ‘out-of-control’
and the reason for that out of control condition can be traced back to cause
that is within the operator’s control. |
|
Attribute |
A characteristic of an
observation, that it either has or doesn’t have (e.g is Blue or not, is Old
or not). |
|
Attribute
Sampling |
Sampling in which we are interested
in recording a variable which is equal to 1 if the unit in the sample has a
particular attribute, and is equal to 0 if the unit doesn’t. |
|
Australia's Population by year by sex |
The age distribution of Australians is
changing. The proportion of older
Australian's in the population is increasing. A graphical representation of the ages of male and female
Australians used to form a pyramid.
What would you call the shape now?
How do we think it will change in the future? See a powerpoint show with one second per
year from 1971 to date using data from the Australian Bureau of Statistics in
Australia's Age
pyramids. |
|
ARMA(p, q) Autoregressive-moving average process |
An autoregressive-moving average
process is a time series where the latest observations depends both on
previous observations in the series and on averages of previous random
disturbances. An ARMA(p, q) for a
time series Xt can
be defined by
|
|
Autocorrelation |
Correlation of a time series values
with previous (lagged) values of the series. |
|
Automatic forecasts |
Parzen's ARAR models performed extremely well in the
various Makridakis forecasting competitions for instance in Makridakis, S.,
Anderson, A., Carbone, R., Fildes, R., Hibbon, M., Lewandowski, R., Newton,
J., Parzen E., and Winkler, R. (1984), The Forecasting Accuracy of
Major Time Series Methods, John Wiley, New York. They are best suited to strongly seasonal
data. For some examples see the Word
documents: Forecasts of monthly sales
of red wine
by Australian winemakers and Quarterly electricity
demand. |
|
Average
Run Length (ARL) |
The ARL is the average number of
‘in-control’ signals that are generated between two ‘out-of-control’ signals,
e.g., with 3-sigma Control Limits this is 1/0.0027 b 370. It is useful for designing control charts for
particular shifts in the process mean. |
|
Backward
Variable Selection |
In multiple regression, the
approach of starting with all variables in the model and one by one dropping
those not significant. |
|
Bayes'
Rule |
Where a number of uncertain
outcomes are linked probabilistically, i.e., are not independent, Bayes’ Rule
provides a way of calculating the probability of an outcome if we already
know the result of other outcomes. (Section 6.7) |
|
Between
Sample Means Variation |
When we have a number of mean
(average) values of a variable, one for each category of another variable,
this is the overall variance of those means. |
|
Bimodal
Data |
Data where the frequency plot has
two peaks, that is, two separate values in the data are more frequent than
any others. |
|
Binary
Variable |
A variable that can only take on
two values, 0 and 1 usually. |
|
Blending
Model |
The aim of these models is to produce
an output blend given an input range of raw materials that satisfies demand
and blend specifications. |
|
Box-Jenkins |
|
|
Boxplot |
A graph of a set of data based on
the median and quartiles. To show the
distribution of the data set. |
|
Capital
Budgeting Model |
These are applied in situations
where a number of investment options are available subject to the constraint
of the amount of available capital and other considerations. |
|
Case |
An item in a set of data, on which we
have one or more values of variables (often represented as a row in a data
spreadsheet). Also called an
observation. |
|
Cash
Balance Model |
A model that may be used for
tracking ‘cash balance’ or ‘cash flow’ over time. |
|
Categorical
Data |
Data in which the observations are
just which category each case falls into.
The counts, or frequencies, of cases in each category are
analysed. E.g. colour of eyes – blue,
green, brown, etc are the categories. |
|
Categorization
Analysis |
A way of trying to predict which
category a case will fall into, based on the values of other variables. |
|
Causal
Methods |
|
|
Causes
of Problems |
When an ‘out-of-control’ signal
occurs, the reasons for this signal are investigated. These are then usually as5cibed to being
assignable, i.e., with operator control, common, i.e., process caused and
hence uncontrollable. |
|
Central
Limit Theorem |
A fundamental theorem in Statistics
that specifies that under very general conditions that the process of average
of data produces numbers (the averages) that eventually (the larger the
sample) conform to the Normal distribution. |
|
Central
Location |
The centre of a set of data, or a
distribution. Mean and median are
commonly used measures of the centre. |
|
Certainty
Equivalent |
This is the certain dollar amount
that is equivalent to a risky venture.
Used to construct or evaluate Utility Functions. |
|
Chart
Wizard (in Excel) |
A tool in Excel that can help to
make drawing graphs (charts) of data easier. |
|
Chi-Squared |
A particular distribution used in
goodness of fit tests. |
|
Chi-Squared
Goodness-of-Fit Test |
A test of how well (or not) a set
of observed frequencies match to a set of frequencies expected from some
hypothesis or theory. |
|
Cluster
Analysis |
A way of analysing data on a number
of variables to determine how the cases group (cluster) together. |
|
Consumer
Price Index (CPI) |
An overall, average measure of how prices
have changed from time to time. Based
on the spending habits of an average consumer. |
|
Contingency
Table |
A table of frequencies broken down
by two categorical variables. It
shows the frequencies of each category of one variable, as spread over the
categories of the other variable. Can
be extended to three or more variables. |
|
Continuous
Variable |
A variable which has measured
values for each case (that is, not categorical or discrete data). The possible values for each case is
infinite, that is, one of a continum.
E.g. how much time you have spent at university |
|
Correlation |
A measure of the extent of linear
relationship between two variables. |
|
Covariance |
A measure of the extent to which two
variables vary together, rather than independently. |
|
Cross-sectional
Data |
Data collected all at a particular
point in time. |
|
Cluster
Sampling |
A sampling method whereby the
sampling unit is a cluster or a collection of smaller units. The smaller units are the ones to be
sampled. Cluster are constructed so
that they individually mirror the total population. |
|
Coefficient
of Determination (R-squared) |
A measure of how well a multiple
regression model fits to the data. The
proportion of the total variation of the dependent variable values explained
by the independent variables in the model. |
|
Coincident
Indicator |
|
|
Combining
Forecasts |
|
|
Common
Causes |
Common causes of problems are due to
systems, environmental, or other factors that operate on the system itself,
outside the control of those working within the system. |
|
Conditional
Probability |
Consider the situation of say, two
events, which are not independent.
The conditional probability of one event is the probability of that
event after the outcome of the first event is known. |
|
Confidence
Interval Estimation |
Using sample data to estimate a
range which has a certain (specified) percentage probability (confidence) of
having the true, unknown parameter value within the range. |
|
Confidence
Level |
The probability that the Confidence
Interval has the true, unkown, value within it. |
|
Constant
Elasticity Relationship |
If an independent variable X changes
by a percentage amount then the dependent variable will change by the
elasticity value times the percentage change in X. No matter what the value
of X started from, the elasticity value is unchanging. |
|
Constant
Error Variance (Homoscedasticity) |
The variance does not change as any
of the relevant variables change. |
|
Constraints |
These are the limitations on
available resources. |
|
Contingency
Plan |
An alternative plan to the main
plan in case of failure of the main plan. |
|
Control
Charts for Attributes |
A Control Chart for monitoring the
proportion of defectives in a process.
The underlying distribution is Binomial, although the Normal
approximation is often used to calculate the 3-sigma limits. |
|
Convenience
Sample |
A sample chosen, not at random, but
for the ease and convenience with which it can be selected. |
|
Correlations |
|
|
Correlogram |
|
|
Covariance |
|
|
Cp |
A measure of ‘potential’
capability, i.e., if the process remains centred on the target value. Cp=1, means that the process is
‘potentially’ capable. |
|
Cpk |
A measure of the ‘actual’
capability, i.e., using the actual mean.
Cpk=1 means that the process is ‘capable’. |
|
Crosstabs |
A contingency table (or pivot table
in Excel). |
|
Data |
An unanalysed collection of basic
information, on some number of cases and variables. |
|
Data
Mining |
Using a variety of techniques to
try and find patterns, trends and relationships between variables in a set of
data. Typically computerised. |
|
Data
Warehousing |
Combines information from a number
of sources for the purpose of discovering interrelationships or patterns in
the data |
|
See DEA |
|
|
Decision analysis |
The study of decisions |
|
Decision
Making under Uncertainty |
Decision making where the outcomes
are not known before making the decision. |
|
Decision
Outcomes |
The alternative outcomes that may
result from a decision. |
|
Decision
trees |
A diagrammatic method of analysing
a decision problem as a ‘tree’. The
elements of this tree are decision, probability and end nodes. Outcome values, values, costs and probabilities
are entered into the tree and used to calculate the value of alternative
decisions. |
|
Decision Support System (DSS) |
A system that provides a decision
maker with a variety of tools and data sources to facilitate the decision
making process. |
|
Design of Experiments |
|
|
Defect |
A non-conforming product, i.e., it
does not meet specifications. |
|
Defective
Component (p2_2.xls,q2) |
Those items or things in a
collection which have a particular defect (thing wrong with them). |
|
Degree
of Belief Probability |
These are subjective probabilities
based on personal assessment of the likelihood of outcomes. They often used in situations where probabilities
cannot be calculated from past experience or logical deductions. |
|
Degrees
of Freedom |
A parameter of a distribution that
provides an idea of how spread out the distribution is. Based on the sample size in t-tests, based
on the number of cells in a chi-squared test. |
|
Deming's
14 Points |
W Edwards Deming devised 14 rules
to be adopted by management for an organisation to be a truly TQM. |
|
Deming's
Funnel Experiment and tampering |
One of Deming’s key insights was
the effect of reacting to or making decisions on the basis of ‘noise’. This experiment shows that variability
becomes worse when decisions are made reactively to random fluctuations. |
|
Dependent
variable |
A variable the values of which are
considered to depend on the values of other variables. |
|
Deseasonalise
Data |
|
|
Discrete
Variable |
A variable which can only take on one
of a finite set of values for each case.
E.g. how many years of university you have completed. |
|
Distribution |
The values a variable can take on,
together with the frequency or probability of each value. Can be expressed as a table or formula. |
|
Divisibility |
The divisibility property means
that the level of activities can measured on a continuous scale. |
|
Dummy
Variable |
A variable which takes the value 1
if an observation has a certain attribute, and 0 if it does not. |
|
Durbin-Watson
statistic |
A statistic used to test if errors
from a regression model are autocorrelated. |
|
Dynamic
Financial Model |
This is a generalisation of the
usual Cash Flow Model in that additional borrowings may be made over the
period of time. |
|
Econometrics |
Econometrics is
formed from two Greek words Economic
theory is the study
of how and why variables in the economy are related. Statistics involves the measurement of variables
and the relationships using limited data, or information, and drawing
conclusions from them. Starting from
the relationships postulated by economists (economic theory) we
express them in mathematical terms (mathematical economics). We obtain data (economic
statistics) and use specific methods (econometric methods) in order
to obtain numerical estimates of economic relationships (called models). A good
description of the scope and division of econometrics is given in A.
Koutsoyiannis, Theory of Econometrics, Macmillan (pp. 3-10) and details of methodology are given
in the same text (pp. 11-30). |
|
Empirical
CDF |
The cumulative frequency
distribution derived from the actual observations and their frequencies in a
set of data. For each value of the
variable, it shows the number of observations less than or equal to the value. |
|
Error
Term |
That part of the value of a
dependent variable not explained by the independent variables. Hence, the difference between the observed
value of the dependent variable and the value expected from the model. |
|
Expected
Monetary Value (EMV) |
The mean of the probability
distribution of possible monetary outcome.
For discrete outcomes, this is calculated as the weighted average of
the possible monetary values, with the weights being the probabilities of the
values. (section 6.2.2) |
|
Expected
Utility Maximizers |
These are decision makers who
maximise their expected utilities, i.e., taking into account risk seeking or
risk averse behaviour. |
|
Expected
Value of Perfect Information (EVPI) |
Given the uncertain nature of the outcomes
of some decisions, this is the additional EMV that is created if the outcome
is known before the decision is made. (section 6.6.2) |
|
Expected
Value of Sample Information (EVSI) |
Additional information, such as
extra tests or research, may have an impact on the EMV of a decision. The change in the EMV is the Expected
Value of Sample Information. Bayes’ Theorem is an important component in this
calculation. |
|
Experimental
Design |
Ways of setting the values of the
explanatory, treatment and blocking variables in an experiment. |
|
Explanatory
variable |
Independent variables. Those variables in a regression model on
which the dependent variable is held to depend (i.e. which help to explain
the value of the dependent variable). |
|
Exponential
Smoothing |
|
|
Exponential
Trend |
|
|
Exponential
Utility |
The Exponential function is one
form of the Utility function. It is
parametrised by a single parameter, the risk
tolerance, and is usually used to describe Risk Averse behaviour.
(section 6.8.3) |
|
Exptrapolation
Methods |
|
|
Extrapolation |
Extending a pattern in a time
series (such as a trend) or regression model beyond the range of the data (or
time period of the observations). |
|
F
distribution |
The theoretical distribution of the
ratio of two variances. Used in
Analysis of Variance tests. |
|
Feasible
Region |
The feasible region is the area
where all of the constraints are satisfied. |
|
Financial
Planning Model |
A model used for planning capital
budgeting and cash flow over time. |
|
Finite
Population Correction (fpc) |
The calculation of variances is
based on either an infinite population or a sampling with replacement for
finite populations. In a finite
population, where the sampling is done without replacement, a finite
population correction needs to be applied to the variance calculation. |
|
Fitted
Value |
The expected value of the dependent
variable, calculated by putting values for the independent variables into the
regression model estimated. |
|
Fixed
Cost Model |
The feature of a fixed cost model
is that an additional one-off cost is incurred if a particular option is
chosen, e.g., using a particular production plant, or a machine setup cost. |
|
Folding
Back on the Tree |
The process of calculating the
optimal decision on a Decision Tree.
It works from the right to the left of the tree. |
|
Forecast
Error |
|
|
Forecasting |
|
|
Forecast method selection |
A survey of forecasting methods (see for instance, Nigel
Meade, Evidence for the Selection of Forecasting Methods, J. Forecast., 19,
515-535) concludes that ·
the
characteristics of the data series are an important factor in determining the
relative performance of methods and ·
statistically
sophisticated or complex methods do not necessarily produce more accurate
forecasts than simple ones. Meade shows in this paper that
summary statistics can be used to select a good forecasting method (or set of
methods) although not necessarily the best. |
|
Forensic Statistical Analysis |
|
|
Formulating
the Model |
The process of abstraction of a
problem from real life into a mathematical form. |
|
Forward
Variable Selection |
In multiple regression, the
approach of starting with only one independent variable in the model and one
by one adding in others, keeping those significant. |
|
Fractionally integrated ARMA models ARFIMA(p,d,q) |
Brodsky, Julia and Hurvich, Clifford M., ‘Multi-step Forecasting for
Long-memory Processes’, J. Forecasting, 18, 59-75 (1999) with
the ARMA model with adaptive parameters proposed by Tiao, G.C. and Tsay,
R.S., ‘Some advances in non-linear and adaptive modelling in time series’ J.
Forecasting, 13, (1994), 109-131. |
|
F-Ratio |
A ratio of two variances, used to
test whether they are equal. Also
used in Analysis of Variance to test whether a set of means are all equal. |
|
Frequency
Table |
A table of values of a variable and
the number of cases (frequency) of each value. |
|
Fuzzy
Logic |
A logical system in which things
are not just True or False, but can have degrees of truth (a bit like
probability of having a characteristic). |
|
Genetic
Algorithm |
A method of optimisation that uses
a genetic code to formulate the problem, a ‘fitness’ criterion to judge the
quality of a solution, an evolutionary heuristic to select the current
‘fittest” best set from a new ‘generation’ of solutions. Generations are
created from an older one by random mutation of individuals or mixing the
genetic codes of pairs. |
|
Global
Maximum (Minimum) |
In some optimisation problems a
number of local maxima may be present (like small hills in a landscape). However, the aim of the optimisation
process is to find the largest of these, the Global Maximum. In LP Models, there is only one hill and
therefore one maximum. |
|
Glossary |
|
|
Grand
Mean |
The overall mean of all the
observations, in an experiment or analysis of variance data set, over all the
levels of the design variables. |
|
Graphical Excellence |
Principles of graphical excellence are clearly
explained in Edward R Tufte's books, the first of which is The
Visual Display of Quantitative Information, Graphic Press, Cheshire,
Connecticut published in 1983.
Envisioning Information (1990) and name? followed and they are
fascinating as well as informative. A
powerpoint lesson on graphical excellence is available from Graphical_Excellence.ppt. |
|
Graphical
Solution Method |
For two dimensional LP problems, it
is possible to solve for the optimum graphically. |
|
H1 |
The alternative hypothesis. |
|
Ha |
The alternative hypothesis. |
|
Ho |
The null hypothesis. |
|
Histogram |
A graph of a frequency table,
showing each value of a variable and a bar whose height represents the
frequency of that value in the data set. |
|
Holt's
Method |
|
|
Hypothesis
Testing |
Analysing a sample of data to test
whether or not it tends to confirm or deny a particular hypothesised value
for a variable parameter. |
|
In
Statistical Control |
A process that has all of its data
within its control limits. |
|
Independent
Samples |
Two (or more) samples selected
independently of each other, that is, with no association between the
selection of one sample and the selection of the other sample. |
|
Independent
Samples Test |
Testing whether the parameter (e.g.
mean0 value from one sample is the same or not as the parameter value from
another, independent, sample. |
|
Independent
variable |
Explanatory variables. Those variables in a regression model on
which the dependent variable is held to depend (i.e. which help to explain the
value of the dependent variable). |
|
Indifference
Value |
The indifference value is the
certain (“for sure”) value that a decisionmaker thinks is the same as a risky
venture. |
|
Infeasibility |
The infeasibility property describes
whether or not a solution satisfies all of the problem constraints. |
|
Influence
Diagram |
A method for describing the
elements of a decision. It displays
decisions, uncertain outcomes, intermediate calculations and payoffs. |
|
Influential
Point |
An observation, in a regression
model, which has a particularly strong impact on the parameter estimates,
that is, which the results are especially sensitive to. |
|
Inspection |
The management process of ‘weeding’
out all of the defective products. |
|
Integer
Programming Models |
Integer Programming (IP) Models
contain one or more variables which can only have integer variables. |
|
Interaction
term |
A term added to an Analysis of
Variance analysis, or to a regression model, to account for the effect of one
variable being determined by the value of another variable. |
|
Interquartile
Range (IQR) |
The difference between the upper
quartile and the lower quartile. It
thus represents a range which has half the observations in it. |
|
Inventory Control |
|
|
ITSM |
Interactive Time Series Modelling, a computer
package for univariate and multivariate time series modelling and forecasting
is distributed with Brockwell, P.J. and Davis, R.A. (1996), Introduction
to Time Series and Forecasting, Springer-Verlag New York Inc. |
|
Joint
Probability |
The probability distribution of two
or more events, e.g., the probability distribution of wind and sunshine on
any day. (section 4.7) |
|
Judgemental Methods |
|
|
Judgemental
Sample |
A sampling method based on the
judgement of the selector, i.e., it is not random. |
|
Key Performance indicators (KPI’s) |
|
|
Kurtosis |
A measure of how flat, or peaked, a
distribution is. |
|
Lag |
|
|
Leading
Indicator |
|
|
Learning
Curve Model |
|
|
Least
Squares Estimation |
|
|
Least
Squares Line |
|
|
Level |
|
|
Likelihood |
Often used in the same way as
probability, but also has a more technical statistical interpretation. |
|
Likert
Scale |
A scale of (typically 5 or 7) attitudes,
in order from one extreme to the other, from which a survey respondent is
asked to chose one. E.g. Do you
approve of the current Prime Minister?
Chose one of: highly approve / approve / neither approve nor
disapprove / disapprove . highly disapprove. |
|
Lilliefors
Test |
A test of the hypothesis that a set
of data is from a Normal distribution. |
|
Line
of Best Fit |
|
|
Linear
Dependence |
|
|
Linear
Programming (LP) |
Linear Programming is a modelling process
that aims to optimises a specific quantity, such as profit. The features of an LP are that : · It has an objective
function that is to be optimised, · It has a number of
resource or other constraints, · All relationships are
described by linear equations. A Microsoft Word lesson on linear programming
formulation is available in LP_Intro.doc. |
|
Linear
Relationship, positive & negative |
A relationship between two variables
(say Y and X) such that one is a linear function of the other (so that Y = a
+ bX). The scatterplot graph of Y
against X will then give points on a straight line. If the line slopes up, so that as X increases Y increases also,
it is termed a positive relationship.
If the line slopes down, so that as X increases Y decreases, it is
termed a negative relationship. The
relationship may be only approximate (correlation provides a measure of the
extent of the linear relationship). |
|
Linear Programming |
Brief explanation needed here. |
|
Linkage
Analysis |
Used to find things that tend to go
together. E.g. people who buy
cigarettes also tend to buy matches, buying cigarettes and matches are things
which are linked. |
|
Local
Maxima |
Maximum values that are not the
overall maximum – the global maximum, hills in a mountainous landscape. |
|
Logistics
Model |
A model that links supply and
demand at different locations with shipping costs to minimise the overall
cost. |
|
Lower
Control Limit (LCL) |
The lower part of the set of
control limits. |
|
Lower
Specification Limit (LSL) |
The lower part of the set of
specification limits. |
|
Managerial
Economics Model |
These are models where economic considerations
also play a role, e.g., using price/demand functions. These models are often non-linear. |
|
Market
Share Model |
A model that incorporates
competition in a market and calculates the relative shares of the competitors |
|
Mathematical
Programming Models |
The generalisation of LP models to
models with functions that may not be linear. |
|
Maximum
Probable Absolute Error |
This is the quantity of a
characteristic such that there is a 95% probability that the sampling error will
not be greater than this quantity. |
|
MA MA(q) Moving average |
A moving average process is a time
series where the latest observation depends principally on averages of
previous random disturbances. An MA(q),
a moving average of order q for a time series Xt can be defined by
|
|
Market Research |
|
|
Matrix Plots |
With multivariate data, an examination of the plot of
each variable in the set against every other variable in the set can be
revealing. One example is given in Psychology. |
|
Maximum |
The largest value of a variable
seen in a set of data. |
|
Mean |
A measure of central tendency – the average value of a
variable in a set of data. Calculated
by adding all the values observed (counting each value as often as it is observed)
and dividing the total by the number of observations. (See also
median and mode) A powerpoint lesson
on basic statistical summary measures is available in Summary_measures.ppt. |
|
Mean
Absolute Error (MAE) |
|
|
Mean
Absolute Precentage Error (MAPE) |
|
|
Measurement
Error |
The error contribution resulting
from the measurement instrument, e.g., poorly framed questions. |
|
Measure
of Association |
A measure of how two (or more)
variables are related, as distinct from independent. E.g. correlation. |
|
Measure
of Dispersion (q15) |
A measure of how spread out a set
of data (or a distribution) is. E.g. variance,
inter-quartile range. |
|
Median |
A measure of central tendency – the middle
observation – half the observations in the data set exceed the median and
half fall below the median. (See also
mean and mode) A powerpoint lesson on
basic statistical summary measures is available in Summary_measures.ppt. |
|
Minimum |
The smallest value of a variable
seen in a set of data. |
|
Minimum
Cost Network Flow Model |
This is a general set of models
where goods flow to demand nodes from supply nodes. Capacity restrictions may apply on some or all of the
arcs. The objective is to minimise the
overall cost of supply. |
|
Mode |
A measure of central tendency – the most frequently
occurring value. (See also median and
mean) A powerpoint lesson on basic
statistical summary measures is available in Summary_measures.ppt. |
|
Model |
|
|
Modelling
the Price of a Stock |
A model of changes in a stock price
using Black Scholes’ theory. |
|
Moving
Averages |
|
|
MSE |
|
|
MSR |
|
|
Multicollinearity |
|
|
Multiple
Regression |
|
|
Multiplicative
Model |
|
|
Multiplicative
Relationship |
|
|
multi-stage
decision problem |
A decision problem which has more
than one decision to be made. (section 6.6) |
|
Multistage
Sampling |
A sampling process which is done in
stages. Sometimes what happens in one
stage will determine what is done in a subsequent stage. |
|
Naïve
Forecasting Model |
|
|
Negatively
Skewed data |
Data for which the frequency distribution
is not symmetrical, but extends further (to more values) below the centre
(mean/median/mode) than above it. |
|
Neural
Networks |
A form of modelling complex
relationships between variables, based on an analogy with the working of the
brain. Between the input
(independent0 variables and the output (dependent) variables are a range of
intermediate variables. |
|
Nightingale, Florence |
Florence Nightingale (1820 – 1910) was an accomplished
statistician and she invented several graphical displays to support her
theories that poor medical practices, poor nutrition and lack of nursing were
the principle causes of deaths in the Army.
For example, see her Coxcomb. |
|
Nominal
Data |
Data falling into categories, and
there is no meaningful order to the categories. E.g. colour of eyes.
Compare with Ordinal data. |
|
Nonlinear
Relationship |
A relationship between variables
which, when graphed, is a curve and does not approximate a straight line. |
|
Nonlinear
Transformation |
|
|
Nonnegativity |
The Nonegativity property specifies
that variables cannot be negative for an LP Model. |
|
Nonnormal
Distribution |
A distribution which is not the
Normal distribution. |
|
Nonresponse
Bias |
Non responses sometimes are not
random but have a well defined characteristic, e.g., people not home during
the day, and these may have an impact on the characteristic being measured. |
|
Nonsampling
Error |
The error contribution resulting
from sources other the sampling process. |
|
Nontruthful
Responses |
Responses which are not truthful
particularly to questions that some people may find threatening. |
|
Normal distribution |
|
|
Numerical
Data |
Observations on variables made up
of numbers. |
|
Nuisance
Parameter |
A parameter which is not the one we
are interested in, but which we need to know the value of to test a hypothesis
about the parameter we are intested in, or carry out some other analysis. |
|
Null
Hypothesis |
The hypothesis that we are testing
in a hypothesis test. It specifies a
particular value for the parameter of interest. |
|
Objective
Function |
The mathematical description of the
quantity that is to be optimised. |
|
Observable
Trend |
A clear, fairly obvious trend,
usually seen in a time series graph of data. |
|
Observation |
An item in a set of data, on which
we have one or more values of variables (often represented as a row in a data
spreadsheet). Also called a case. |
|
Odds
ratio |
The probability of an event,
divided by the probability the event will not happen. |
|
One-sided
Confidence Interval |
A confidence interval with an upper
limit, but no lower limit; or, vice versa, a confidence interval with a lower
limit, but no upper limit. |
|
One-tailed |
Refers to either the upper, or
lower, tail of a distribution, used in finding one-sided confidence intervals
or carrying out one-sided hypothesis tests.
A hypothesis test where the alternate hypothesis specifies a single
direction only, that is, the null hypothesis can only be false if the test
statistic is too big, but not too small (or vice versa). |
|
One-Way
Analysis of Variance (ANOVA) |
A test, simultaneously, of whether
three or means are all equal, or have some differences. |
|
Operations Research |
Operations
Research is
a philosophy used to develop models of systems or processes in a manner that
will facilitate improving the performance of the system or process. It can be applied in the management and
improvement of all types of private and public sector enterprises. Operations Research provides the basis
for a Decision Support Service for all levels of management. To
read more, including some historical details, see OR_Intro.doc. |
|
Optimisation |
vs Heuristics |
|
|
|
|
Optimal
Solution |
The solution to the LP problem that
satisfies all of the contraints and optimises the objective function. |
|
Optimal
Strategy |
The strategy that maximises or
minimisers a particulat objective, such as EMV or Expected Utility. |
|
Optimisation
Modelling |
The modelling process to develop
optimal solutions to problems. |
|
Ordinal
Data |
Data falling into categories, where
there is a meaningful order to the categories. E.g. Do you approve of the current Prime Minister? Chose one of: highly approve / approve /
neither approve nor disapprove / disapprove . highly disapprove.. Compare with nominal data. |
|
Out
of Statistical Control |
A process that has some of its data
outside of the 3-sigma limits or not satisfying a number of statistical
criteria to remain within control. |
|
Outlier
(mild, extreme) |
A value for a variable which is
noticeably apart from the rest. A
value more than three standard deviations from the mean, or one outside the
outer hinge of a boxplot, can be called an extreme outlier; a value more than
two standard deviations from the mean, or outside the inner hinge of a
boxplot, can be called a mild outlier. |
|
Paired
samples |
Two samples in which the units in one
sample are each closely linked to a similar unit in the other sample. |
|
Pareto Distribution |
|
|
Partial
F-Test |
|
|
Payoff
Table |
A decision may have a number of
different alternatives, and each alternative a number of different
outcomes. The values resulting from
the combination of alternatives and outcomes is often represented in a payoff
table. |
|
p-Chart |
Also the control chart for
attributes, i.e., for proportions. |
|
Percentile |
That value of a variable which has a
given percentage of the observations below it. For example, the 5th percentile has 5% of values
below it, the 75th percentile has 75% of values below it. |
|
Pivot
Tables |
Contingency tables produced in
Excel. The pivot table tool in Excel
has a flexibility and power that make this a very useful tool. |
|
Point
Estimate |
An estimate of a population
characteristic based on a sample. |
|
Pooled
Standard Deviation |
An overall standard deviation calculated
by combining two or more standard deviations, usually from sub-groups or
samples. |
|
Population |
The full set from which a sample is
chosen, and hence to which the sample inference statistics apply. |
|
Portfolio
Optimisation Model |
Given a set of investments, a
portfolio optimisation model selects those investments that has a minimum
variance and an acceptable expected return.
These models are often quadratic optimisation problems. |
|
Positively
Skewed Data |
Data for which the frequency
distribution is not symmetrical, but extends further (to more values) above
the centre (mean/median/mode) than below it. |
|
Poster presentations |
Poster presentations are often used at conferences
to enable researchers to communicate ideas flexibly to people attending. An effective poster should have certain
attributes. A Poster about producing
posters is available in Poster.rtf. |
|
Posterior
Probability |
The probability resulting from a
Bayes’ Calculation |
|
PrecisionTree
Add-in |
An Excel Add-In supplied with Albright, S. C., Winston, W. L. &
Zappe, C (1999), Data analysis and decision making with Microsoft Excel, Duxbury Press, Brooks-Cole, Pacific Grove,
Ca. that may be used to evaluate
decisions using decision trees or influence diagrams. |
|
Prediction
Interval |
|
|
Principle
of Parsimomy |
|
|
Prior
Probability |
The conditional probability of
events that are used in a Bayes’ calculation. |
|
Probability
Sample |
A sample which is selected
according to a random mechanism such as a set of probability tables. |
|
Process
Capability |
The state of a process which
determines how well it is able to meet specifications when operating in its
natural state. |
|
Process
Capability Analysis |
An analytical process to determine
how well a process can meet it specifications when operating normally. |
|
Process
Capability Indices |
Indices which numerically show well
a process can meet its specifications when operating normally. If the Process Capability Indices have a
value of 1.0 or better, then the process is called ‘capable’. Typical indices are Cpk and Cp. |
|
Process Business Process Re-engineering |
|
|
Product
Mix Model |
A factory, say, may be able to make
a number of different products. A
Product Mix model has as its output the quantities of each of the products to
be made subject to the given
constraints that optimise the objective function |
|
Proportional
Sample Sizes |
Sample sizes in strata that are
determined on the basis of the overall strata sizes. |
|
Proportionality |
The proportionality property means that
if the level of an activity is multiplied by a constant factor, then the
contribution of this activity to the objective or to any of the constraints
in which this activity is involved is multiplied by the same factor. |
|
p-value |
The probability that, if the null
hypothesis were true, a value of the test statistic as extreme or more as
that observed would have occurred. A
small value is taken to indicate that the null hypothesis is to be rejected. |
|
Quadratic
Loss Function |
A quadratic function, first
introduced by Taguchi, who formulated it as measuring societal loss when a
product is off-target. The quadratic
function achieves its minimum when the product quality characteristic has its
distribution centred on its target specification. |
|
Quality Assurance |
|
|
Quality Control (QC) |
The section of an organisation, or
the process which has as its brief to monitor the quality characteristics of
products. |
|
Quality
Function Deployment (QFD) |
QFD is a planning tool whose
purpose is to design quality into a product or service by starting from
customer needs. It then translates
these through a number of iterations into product and process specifications. |
|
Quantile-Quantile
(Q-Q) plot |
An informal, graphical test of
whether an observed distribution is Normal or not. |
|
Quartiles |
The 25th and 75th
percentiles of a variable. That is,
the upper quartile has 75% of values below it, the lower quartile has 25% of
values below it. |
|
Queueing Theory |
|
|
Random
Numbers |
Numbers, supposedly without any
structure, but which are representative of the full range of possible
values. They are the basic inputs to
simulation studies. |
|
Random
Samples |
A sample selected by a random
selection process. |
|
Random
Selection |
Selection of a sample from a
population that is done randomly.
Technically, selection of a sample such that each possible sample is
equally likely to be chosen, and each unit of the population equally likely
to be in the sample. |
|
Randomized
Experiment |
An experiment in which subjects or
objects are randomly assigned to groups, which we are going to test for
differences in. |
|
Randomized
Responses |
A response whose answer is randomized
to counteract the effect of nontruthful responses. In this way whilst the individual response may be unreliable,
the overall estimate is unbiased. |
|
Rational
Subsample |
Rational subsamples are designed so
that only common cause variation exists within a sample. Assignable cause variability, if it exist
occurs as variation between samples.
For example, samples are taken and analysed separately from different
machines (not pooled) and separately for operators. |
|
Range |
The difference between the minimum
and maximum values of a variable. |
|
Ratio-to-Moving-Average |
|
|
Red
Bead Experiment |
Demings’ ‘Paddle stick’ experiment
that is used to demonstrate the variability inherent in sampling proportions of
red beads (defects) from a boxed with both red and white beads, as well as,
how the imperfect manufacture of the ‘paddle stick’ leads to results which
deviate from the theoretical Binomial distribution. |
|
Regression Analysis |
The term
regression comes from one of the first applications of the technique, carried
out by Francis Galton (Family Likeness
in Stature, Proceedings of the Royal Society of London, 1886, pp. 42-72.) in a series of papers studying the
relationships between the heights of children and their parents. He found that the child of a tall parent
(or parents) tended to be tall, but not quite as tall as the parent(s), and
that the child of short parent(s) tended to be short, but not quite as short as
the parent(s). There was a tendency for
children’s heights to regress towards the population average height. It is unfortunate that the name is not descriptive
of the technique itself but it is over one hundred years too late to complain
of the term regression. |
|
Relationship
between variables |
Variables can be related, or
associated, in various ways. The idea
is that knowing the value of one variable gives you information about the
likely value of the other variable. |
|
Rejection
Region |
Those values of a hypothesis test statistic
that, if seen, would lead to the rejection of the null hypothesis. |
|
Research
Hypothesis |
The hypothesis which a research
project is set up to test. |
|
Residual
Value |
|
|
Response
Variable |
|
|
Rework |
The process of correcting the defects
of products. |
|
Risk
Attitude |
The term that describes whether a
decision maker is ‘risk seeking’, ‘risk averse’, or ‘risk neutral’ in respect
of EMV. |
|
Risk
Averse |
The Risk Attitude where a
decisionmaker trades off some of the EMV for a less risky venture. |
|
Risk
Profile |
The probability distribution of the
outcomes of a decision. |
|
Risk
Seeker |
The Risk Attitude where a
decisionmaker trades off some of the EMV for a more risky venture. |
|
Risk
Tolerance |
The parameter that specifies the Exponential Utility
Function. It is approximately equal
to the dollar amount, R, such that the decisionmaker is indifferent between, ·
Obtaining no payoff at all, ·
Obtaining a payoff of $R or the loss of $R/2, depending on the flip of
a fair coin. |
|
RiskView |
RiskView is a part of the Decision
Tools Suite that shows the graph of any input probability distribution. |
|
Robust
to Violations of Normality |
Many tests and analyses involve an inherent
assumption that the data is normal in distribution. An analysis is robust if it is not too sensitive to departures
from this assumption, that is, if it is still reasonably accurate even if the
data is not exactly Normal. |
|
Rolling
Planning Horizon Model |
This is an Aggregate Planning Model
where the time horizon is fixed at a certain number of periods ahead. |
|
Root
Mean Square Error (RMSE) |
|
|
R-squared |
|
|
Runs
Test |
|
|
6-Sigma |
The number of standard deviations
(plus or minus) from the mean. Also
an approach to statistically control a process to within 6-sigma, i.e., so
that only .002 ppm lie outside of the control limits (Motorola). |
|
Sample |
A sub-set (part0 of a population,
chosen out of the population, usually as in some way representative of the
population. |
|
Sampling |
The process of obtaining sampling
units. |
|
Sampling
Distribution of the Sample Mean |
The distribution of the sample
mean, e.g., normal, or t-distribution. |
|
Sampling
Distributions |
The distributions resulting from
the sampling process, the normal, t-distribution, chi-squared,
F-distribution. |
|
Sampling
Error |
The error contribution resulting
from the sampling process. As the sample
size becomes larger the sampling error becomes smaller. |
|
Sampling
Frame |
The list of all units from a
population from which a sample is to be drawn. |
|
Sampling
Interval |
In a systematic sample, the gap between
selecting units, e.g., every 10 for a one tenth sample. |
|
Sampling
Unit |
The basic unit in a population that
can be selected. |
|
Seasonal
Adjustment |
A means of taking out the effect of
regular seasonal impacts on a time series of data, to enable the trends to be
seen more clearly. There are a number
of techniques for doing this. |
|
Seasonal
Pattern |
A regularly repeating pattern in a
time series, that repeats every year. |
|
Sensitivity
Analysis |
A standard part of many analysis to
see the impact that the numerical assumptions have on the outcome. They are often done as ‘what-if’
questions. |
|
Sensitivity
Graph |
A graph that shows how the solution
changes with changes in particular numerical assumptions. |
|
Set
Covering Model |
In a set-covering model, each
member of a given set must be ‘covered’ by an acceptable member of another
set. The objective is to minimise the
number of members of the second set to cover all of the first set, e.g., fire
stations covering city areas, or the location of hubs for airlines. |
|
Seven-Step OR methodology |
One version is … Another description is given in OR_Intro.doc. |
|
Shadow
Price |
The value, in objective function
terms, that results from relaxing a constraint by one unit. |
|
Shewhart
Chart |
The process control charts first
formulated by Walter A Shewhart. This generally refers to the X-bar, R
charts |
|
Sigma-hat |
The unbiased sample estimator of
the population standard deviation. |
|
Significance
level of the Test |
The (chosen) probability of a type
I error. |
|
Simple
Exponential Smoothing |
|
|
Simple
Random Sample |
A random sampling process which
takes no account of any population characteristics, but gives each population
unit an equal chance of being selected. |
|
Simple
Regression |
|
|
Simplex
Method |
The mathematical technique for
solving LP problems. |
|
Simulating
Correlated Values |
Where there are multiple input
variables to be simulated, it is often unrealistic that these variable be
independent of each other. In this
case correlated values need to be simulated.
@Risk is able to generate these values. |
|
Simulation
Model |
A model that has one or more input
variables that are subject to a probability distribution. |
|
Simulation |
Deterministic/Stochastic Discrete Event
Continuous Replicative |
|
Single-stage
decision problem |
A decision problem with only one
decision to be made. |
|
Skewed
data |
Data that has a frequency
distribution that is not symmetrical, or evenly balanced, about the
centre. See positively and negatively
skewed. |
|
Skewed
to the Left |
Data for which the frequency distribution
is not symmetrical, but extends further (to more values) below the centre
(mean/median/mode) than above it.
I.e. negatively skewed. |
|
Skewed
to the right |
Data for which the frequency
distribution is not symmetrical, but extends further (to more values) above
the centre (mean/median/mode) than below it.
I.e. positively skewed data. |
|
Smoothing
Constant |
|
|
Smoothing
Method |
|
|
Solver
Add-In |
The add-in, developed by Frontline Systems,
that is available with Excel for solving LP and other problems. |
|
SolverTable
Add-In |
The add-in used in conjunction with
Solver to solve for a range of alternative assumptions. Used for performing Sensitivity Analysis. |
|
Sources
of Estimation Error |
Identified reasons contributing to
statistical variability |
|
Span |
|
|
Special
causes |
Another term for assignable causes. |
|
Spider
Graph |
A graph that shows how the base solution
changes, in percentage terms, with changes to particular numerical
assumptions. |
|
Spurious
Correlation |
|
|
SSE
(sum of squared errors) |
|
|
SSR
(sum of squares due to regression) |
|
|
SST
(total sum of squares) |
|
|
Stacked
Boxplot (side-by-side Boxplots) |
A set of box plots of a variable,
with one boxplot for each category value of a second variable. The boxplots are stacked, or drawn side by
side, to enable easy comparisons. |
|
Standard deviation |
A measure of variation in data, the square root of
the variance. A powerpoint lesson on
basic statistical summary measures is available in Summary_measures.ppt. |
|
Standard
Error of Estimate |
|
|
Standard
Error of the Mean |
The standard deviation of the
sample mean. |
|
Static
Workforce Scheduling |
A model that allocates the number
of employees required on different days, say, subject to demand and work constraints. |
|
Statistical
Inference |
The process of drawing conclusions
on population characteristics on the basis of using statistical samples. |
|
Statistical
Model |
|
|
Statistical
Process Control (SPC) |
SPC is the method of monitoring the
output quality of a process by using statistical means, in particular,
control charts. |
|
Statistically
Significant at the alpha level |
The p-value is less than
alpha. The hypothesis test at the
level alpha leads to a reject the null hypothesis conclusion. |
|
Statistics Statistical Analysis |
|
|
Statistical Decision Theory |
Decision Analysis |
|
Statistical Process Control |
|
|
StatPro |
This Add-In to Excel enables one to carry out basic statistical
analyses and produce simple but effective graphical summaries of data. In particular the box plot feature is
excellent. A good book with which
StatPro is distributed is Albright, S. C., Winston, W. L. & Zappe, C
(1999), Data analysis and decision making with Microsoft Excel, Duxbury Press, Brooks-Cole, Pacific Grove,
Ca. It also contains other Add-Ins
including @Risk and decision tree software. |
|
Steady state |
|
|
Stochastic Optimisation |
|
|
Straightline
Relationship |
|
|
Stratified
Sampling |
A sampling process which firstly
divides the population on a basis of a particular characteristic and then
takes a random sample from each strata. |
|
Stratify
(with Pivot Tables) |
Create strata from a particular
characteristic |
|
Subpopulation
Strata |
A sub-division of a population
which shares a common charcteristic. |
|
Subsample |
A sample taken from a sample. |
|
Supply Chain |
|
|
Survey |
The process of going out and asking
a set of questions (by mailed out questionnaire, interviews, via telephone,
etc) or inspecting, to collect data, from a sample. |
|
Symmetrical
Distribution |
A frequency distribution that is
evenly balanced on either side of the centre (mean/median/mode). |
|
Systematic
Relationship |
A relationship between variables
that persists and continues. |
|
Systematic
Sampling |
A sampling process which samples
from a population based on a systematic rule. |
|
System |
IT/General |
|
Tail
of a Distribution |
The ends of a frequency
distribution where the frequencies are small. |
|
Target
(objective) Cell |
When setting up an LP model for
Solver, this is the cell containing the objective function and is to be
optimised. |
|
t-distribution |
The (theoretical) distribution of
the standardised sample mean (that is, the difference between the sample mean
and the true mean, divided by the standard deviation of the mean), when the
standard deviation is estimated from the sample data. |
|
Test
for Normality |
A test of the hypothesis that the
data observed comes from a Normally distributed variable. |
|
Test
Statistic |
A value calculated from the sample used
to test a hypothesis. |
|
The
Law of total Probability |
The Law of Total Probability gives
a way of dividing up the probability of an outcome by basing it on a
conditioning event. |
|
The
Value Model |
The Value Model provides a means of
transforming decisions and outcomes into monetary values. |
|
The
Value of Information |
The value of information is the
increment that the information brings to a decision. |
|
Time
Series Analysis |
Analysis of time series data, often
with the aim of forecasting future values of the series. The analysis involves finding patterns in
the time series, including trend and seasonality as examples of such
patterns. |
|
Time
Series Data |
A set of values of a variable at
different times, usually regular times (e.g. yearly, monthly, daily, or
hourly). Each time is a case for the
variable. |
|
Time
Series Plot |
A graph of time series data,
usually with time as the horizontal axis variable. |
|
t-multiple |
Same as t-value |
|
TopRank |
TopRank is a part of the Decision
Tools Suite. It is used to cycle
through the input variables to determine the impact of these variables on the
output variables. |
|
Tornado
Graph |
A graph that presents the impact of
the possible range of some of the parameters have on the outcome. The impact is usually sorted from greatest
to least presented from top to bottom of the graph. Hence the name. |
|
Total
Quality Management (TQM) |
A management philosophy based on
the teaching of W Edwards Deming, first developed by the Japanese. The guiding principles for this approach
are found in Demings’ 14 points. |
|
Trade-Off |
|
|
Transient state |
|
|
Transportation
Model |
A specific model that links demand
and supply locations. The objective
is to minimise costs. It often has a
particular structure that allows for the application of a fast solution
algorithm. |
|
Transshipment
Model |
This is very similar to the Transportation
model except that a demand point may also ‘transship’ to another demand point
in order to minimise costs. |
|
Treatment
Group |
A sample group, in an experiment,
that has the same value of the factor of interest (treatment). |
|
Triangular
Distribution |
A probability distribution that
looks like a triangle and is thus determine by 3 points. |
|
t-value |
The test statistic used to test a
null hypothesis about a mean. The standardised sample mean (that is, the difference
between the sample mean and the true mean, divided by the standard deviation
of the mean), when the standard deviation is estimated from the sample data. |
|
Two
Way Sensitivity Analysis |
Much of sensitivity Analysis is
conducted ‘one variable at a time’.
This analysis is done ‘two at a time’ and is presented graphically as
such. |
|
Two-Sided
Confidence Interval |
A
confidence interval with both an upper and a lower limit. The most usual confidence interval form. |
|
Two-tailed |
Refers to both the upper and lower,
tails of a distribution, used in finding two-sided confidence intervals or
carrying out two-sided hypothesis tests.
A hypothesis test where the alternate hypothesis is just that the null
hypothesis is false, which it can be if the test statistic is too big or too
small. |
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Type
I Error |
The error of rejecting the null
hypothesis when it is true. |
|
Type
II Error |
The error of accepting the null
hypothesis when it is false. |
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Unbiased
Estimate |
An sample estimate of a population
characteristic which will get closer to the true value as the sample size
increases. |
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Unboundedness |
The property of a solution that
indicates that the model has no finite solution. |
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Uncertain
Outcome (and its probability) |
An outcome that cannot be predicted
beforehand but which can be associated a probability. |
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Uncertainty |
The state of not knowing the
outcome of an event. |
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Unequal
Variance (heteroscedasticity) |
|
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Uniform
Distribution |
A distribution which has as its
characteristic that all of its X- values have the same probability of
occurring. |
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Uniform
Distribution |
A probability distribution that is
completely flat between two specified points. |
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Unrepresentative
Sample |
A sample which is not
representative of the total population, i.e., does not have all of the
characteristics of the population from which it was drawn. |
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Upper
Control Limit (UCL) |
The upper part of the set of
control limits. |
|
Upper
Specification Limit (USL) |
The upper part of the set of
specification limits. |
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Utility
Function |
A mathematical function to relates
the risk attitude on a scale of 0 to 1 (0=extremely undesirable, 1=extremely
desirable) against monetary value. |
|
Validation
of the Fit |
|
|
Valuing
a European Call Option |
A specific option pricing model for
an option that can be bought or sold on a specific date for a specific price. |
|
Valuing
a More Exotic Call Option |
An option pricing model for a more
complex option where the payoff may be varied. |
|
Variable |
Something which we have values of
for the cases in a set of data. |
|
Variance |
A measure of the spread of data – essentially an
average of the squared deviations of observations about the mean. A powerpoint lesson on basic statistical
summary measures is available in Summary_measures.ppt. |
|
Variance Reduction |
|
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Well-Scaled Model |
This is a model where
the coefficients are approximately of the same order of magnitude. A badly scaled model may be difficult to
solve because of rounding errors. |
|
Western Electric Rules |
A set of rules applied
to control charts to monitor for changes in a process. They include the monitoring of runs of
observations, above and below the target, up and down as well as clumping in
particular parts of the chart. |
|
Winter's Method |
|
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Within Sample Variation |
The variation (variance)
of values of a variable in a particular sample. In Analysis of Variance, designates the variance between units
in the same sample sub-group. |
X. X
|
X-bar,
R Chart |
A control chart typically consists
of two sub charts. The first monitors
for process target, the X-bar, and the second monitors for variability, the
R-chart. X-bar being the average of
the selected sample and R the range of the measurements in that sample. |
|
"X-Y"
Chart |
A two dimensional graph of data on
two variables (X and Y) which shows the relationship between the
variables. Also called a Scatterplot. |
|
Y |
|
|
z-multiple |
Same as z-score |
|
Zone
A Rule |
The Zone A rule specifies how many
observations beyond two standard deviations of the process target constitutes
a ‘signal’ - this is 2 out of 3 consecutive observations on the same side of
the target.. |
|
Zone
B Rule |
The Zone B rule specifies how many
observations beyond one standard deviation of the process target constitutes
a ‘signal’ - this is 4 out of 5 consecutive observations on the same side of
the target. |
|
z-score |
The standardised sample mean, that
is, the difference between the sample mean and the true mean, divided by the
standard deviation of the mean, when the standard deviation is a known value. |