Statistics 1.0
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Quick Start
You can download the software online from The
Statistics 1.0 Website. Unzip the software and run Statistics. The
features in the main menu are demonstrated by over 100 examples. For any
item in the menu, simply select an appropriate example to see how to input
the statistical samples and parameters. The examples have been carefully
designed to demonstrate all aspects of the software. For details of specific
features, read on.
[Help Topics]
Introduction
Select Introduction  A brief introduction to statistics... from
the main menu. Statistics is concerned with methods of designing and evaluating
statistical experiments to obtain information about practical problems,
for example, inspection of quality of raw material or manufactured products,
the comparision of machines and tools used in production, the varying market
price of stocks and shares, the yield of crop varieties under different
conditions, and so on. For instance, in a production process, the differences
in the quality of products is variation due to numerous factors whose influence
cannot be predicted, so the variation must be regarded as a random variation.
In most cases, the inspection of each item would be too expensive and timeconsuming.
It may even be impossible if it leads to the destruction of the item. Hence
instead of inspecting all the items just a few of them (a sample) are inspected
and from this inspection conclusions can be drawn about the totality (the
population). All these intuitive notions are made precise using probability
theory. A classic example of a statistical experiment called a Galton board,
is shown on the left. As the ball drops, the probabilities that it will
be deflected to the left or right at each triangular obstacle are equal.
The balls are collected in receptacles numbered from left to right. Press
the button 100 Trials to generate a sample. Statistics 1.0 provides
you with all the tools used by professional statisticians to analyze data.
To use the program, select an option from the main menu at the top. For
each menu option, there are several examples that show you how to use that
particular feature of the program.
[Help Topics]
Descriptive Statistics
Select Descriptive Statistics  New sample... from the main menu.
A statistical experiment yeilds a sequence of observations x_{1},
x_{2},
..., x_{n} called a sample. We assume that each sample value
x_{i}
is a real number. The aim is to represent the sample in a suitable tabular
and graphical form. Measures of central tendency and spread are quantities
that often give a very good statistical description of the sample.
Write the Sample in its tabbed box and press the button Descriptive
Statistics. The program will calculate the following:

Frequency Table  sample value, frequency, cumulative frequency, relative
frequency, cumulative relative frequency and percentile

Histogram  class intervals, class frequency, relative class frequency

Measures of Central Tendency  mean, median and modes

Measures of Spread  variance, standard deviation and interquartile range
The program will also generate the graphs of the frequency function and
histogram of the sample. Move the cursor over the graph window to display
the coordinates.
[Help Topics]
Statistical Inference
Select Statistical Inference  New sample... from the main menu.
A statistical experiment yeilds a sequence of observations x_{1},
x_{2},
..., x_{n} called a sample. We assume that each sample value
x_{i}
is a real number drawn randomly from the whole population. The aim is to
find a suitable statistical distribution function that fits the sample
data. This is the statistical distribution function of the whole population
from which the sample was taken. We also determine confidence intervals
for the parameters of the statistical distribution function. Thus, from
the sample, we infer the probability law that governs the whole population.
Write the Sample in its tabbed box and press the button Statistical
Inference. The program will calculate the following:

Hypothesis  an appropriate statistical distribution that fits the sample
data

Estimation of Parameters  using Fisher's method of maximum likelihood

ChiSquare Test  goodness of fit of the statistical distribution and statistical
inference, with 99% confidence

Confidence Intervals  for the parameters of the statistical distribution,
with 95% confidence
The program will also generate the graphs of the probability function of
the statistical distribution and histogram of the sample. Move the cursor
over the graph window to display the coordinates.
[Help Topics]
Quality Control
Select Quality Control  New list of samples... from the main menu.
No production process is so perfect that all the products are completely
alike. There is always a small variation that is caused by uncontrollable
factors and must therefore be regarded as a chance variation. It is important
to ensure that the products have certain required properties. Random samples
of values for a particular required property are taken during the production
run, at regular intervals of time. Each time a sample of the same size
is taken. The aim is to be able to tell, given this list of samples, whether
the production process is running normally, called Quality Control.
Write the List of Samples, the Sample Size, the control
Mean
and Standard Deviation in their respective tabbed boxes and press
the button Quality Control. The program will calculate the following:

Control Limits  for the mean and standard deviation

Control Charts Table  sample values, sample mean, sample standard deviation
and process status
The program will also generate the graphs of the control charts for the
mean and standard deviation. Move the cursor over the graph window to display
the coordinates.
[Help Topics]
Acceptance Sampling
Select Acceptance Sampling  New sampling plan... from the main
menu. Acceptance Sampling is applied in mass production when a producer
is supplying a consumer lots of N items. The decision to accept
or reject a particular lot must be made. This decision is based on the
result of inspecting a sample of size n from the lot and determining
the number of defective items. The producer and consumer agree on a sampling
plan, i.e. an acceptance number c such that if the number of defective
items in a single sample from the lot exceeds c, then the entire
lot is rejected. The producer and consumer may also wish to define the
acceptable quality level AQL and rejectable quality level RQL
(both numbers between 0 and 1) such that the producer's risk (the chance
of rejecting a good lot) and the consumer's risk (the chance of accepting
a bad lot) are mutually agreeable.
Write the Lot Size, the Sample Size, the Acceptance
Number, the Acceptable Quality Level AQL and the Rejectable
Quality Level RQL in their respective tabbed boxes and press the button
Acceptance
Sampling. The program will calculate the following:

Single Sampling Plan Table  fraction defective, operating characteristic
(OC) and average outgoing quality (AOQ)

Producer's Risk

Consumer's Risk

Average Outgoing Quality Limit (AOQL)
The program will also generate the graphs of the operating characteristic
(OC) curve and the average outgoing quality (AOQ) curve. Move the cursor
over the graph window to display the coordinates.
[Help Topics]
Regression and Correlation
Select Regression and Correlation  New sample... from the main
menu. Regression and correlation analysis is used for statistical experiments
in which two quantities are observed simultaneously. One of the variables,
X,
can be regarded as an ordinary variable which can be measured without any
appreciable error. The other variable, Y, is a random variable,
and we are interested in the dependence of Y on X. The experimenter
first selects X values x_{1}, x_{2},
..., x_{n} and then observes Y at those values obtaining
a sample (x_{1}, y_{1}), (x_{2},
y_{2}),
..., (x_{n}, y_{n}). We assume that the mean
of Y is a linear function of X, called the regression line
of Y on X.
Write the sample X values and Y values in their respective
tabbed boxes and press the button Regression and Correlation. The
program will calculate the following:

The Covariance

The Correlation

The Regression Coefficient  maximum likelihood estimate

The Regression line of Y on X

A Confidence Interval for the Regression Coefficient  with 95% confidence
The program will also generate the graphs of the sample points and the
regression line. Move the cursor over the graph window to display the coordinates.
[Help Topics]
Time Series and Trends
Select Time Series and Trends  New time series... from the main
menu. A time series is an ordered sample of observed values for a statistical
experiment, the values being observed at regular intervals of time. The
aim is to understand the underlying patterns and forecast future values
of the time series. We use the method of exponentially smoothed weighted
moving averages ESWMA and trends to make shortterm forecasts.
Write the Time Series, ESWMA Group Size and ESWMA Smoothing
Constant in their respective tabbed boxes and press the button Time
Series and Trends. The program will calculate the following:

The Exponentially Smoothed Weighted Moving Average (ESWMA)

Trends based upon the most recent terms of the time series
The program will also generate the graphs of the time series and the ESWMA.
Move the cursor over the graph window to display the coordinates.
[Help Topics]
Analysis of Variance
Select Analysis of Variance  New list of samples... from the main
menu. The procedure used to test equality of means of several normal populations
is called Analysis of Variance ANOVA. The procedure involves splitting
a total variance into pieces, analyzing it, and then deciding whether to
accept or reject equality of the population means based on the relative
magnitude of these pieces.
Write the List of Samples and Sample Size in their respective
tabbed boxes and press the button Analysis of Variance. The program
will calculate the following:

Analysis of variance table  among populations and residual, calculation
of mean squares

Test of hypothesis  assuming each population is normal with the same variance,
test for the equality of means among all populations

Maximum likelihood estimators  mean and variance
The program will also generate the graphs of the probability and distribution
function of the FDistribution used in testing the hypothesis. Move the
cursor over the graph window to display the coordinates.
[Help Topics]
Probability Distributions
Normal Distribution
Select Probability Distributions  Normal Distribution  New...
from the main menu. Write the parameters mean (real number), standard
deviation (positive real number) and a list of X values (real
numbers) in their respective tabbed boxes and press the button Normal
Distribution. The program will calculate the following:

Range of random variable X

Probability density function f(x)

Distribution function F(x)

Mean and variance

Moment generating function

Statistical table  x values, f(x) values and F(x)
values

Random sample
The program will also generate the graphs of the probability and distribution
functions. Move the cursor over the graph window to display the coordinates.
[Help Topics]
Poisson Distribution
Select Probability Distributions  Poisson Distribution  New...
from the main menu. Write the parameter mean (positive real number)
and a list of X values (nonnegative integers) in their respective
tabbed boxes and press the button Poisson Distribution. The program
will calculate the following:

Range of random variable X

Probability function f(x)

Distribution function F(x)

Mean and variance

Factorial moment generating function

Statistical table  x values, f(x) values and F(x)
values

Random sample
The program will also generate the graphs of the probability and distribution
functions. Move the cursor over the graph window to display the coordinates.
[Help Topics]
Binomial Distribution
Select Probability Distributions  Binomial Distribution  New...
from the main menu. Write the parameters n (positive integer), p
(real number between 0 and 1) and a list of X values (nonnegative
integers) in their respective tabbed boxes and press the button Binomial
Distribution. The program will calculate the following:

Range of random variable X

Probability function f(x)

Distribution function F(x)

Mean and variance

Factorial moment generating function

Statistical table  x values, f(x) values and F(x)
values

Random sample
The program will also generate the graphs of the probability and distribution
functions. Move the cursor over the graph window to display the coordinates.
[Help Topics]
Exponential Distribution
Select Probability Distributions  Exponential Distribution  New...
from the main menu. Write the parameter mean (positive real number)
and a list of X values (positive real numbers) in their respective
tabbed boxes and press the button Exponential Distribution. The
program will calculate the following:

Range of random variable X

Probability density function f(x)

Distribution function F(x)

Mean and variance

Moment generating function

Statistical table  x values, f(x) values and F(x)
values

Random sample
The program will also generate the graphs of the probability and distribution
functions. Move the cursor over the graph window to display the coordinates.
[Help Topics]
Uniform Distribution
Select Probability Distributions  Uniform Distribution  New...
from the main menu. Write the parameters a, b (real numbers
with a less than b) and a list of X values (real numbers
between a and b) in their respective tabbed boxes and press
the button Uniform Distribution. The program will calculate the
following:

Range of random variable X

Probability density function f(x)

Distribution function F(x)

Mean and variance

Moment generating function

Statistical table  x values, f(x) values and F(x)
values

Random sample
The program will also generate the graphs of the probability and distribution
functions. Move the cursor over the graph window to display the coordinates.
[Help Topics]
Hypergeometric Distribution
Select Probability Distributions  Hypergeometric Distribution  New...
from the main menu. Write the parameters N (positive integer), M
(nonnegative integer less than N), n (nonnegative integer
less than N) and a list of X values (nonnegative integers
less than n) in their respective tabbed boxes and press the button
Hypergeometric
Distribution. The program will calculate the following:

Range of random variable X

Probability function f(x)

Distribution function F(x)

Mean and variance

Statistical table  x values, f(x) values and F(x)
values

Random sample
The program will also generate the graphs of the probability and distribution
functions. Move the cursor over the graph window to display the coordinates.
[Help Topics]
Geometric Distribution
Select Probability Distributions  Geometric Distribution  New...
from the main menu. Write the parameter p (real number between 0
and 1) and a list of X values (positive integers) in their respective
tabbed boxes and press the button Geometric Distribution. The program
will calculate the following:

Range of random variable X

Probability function f(x)

Distribution function F(x)

Mean and variance

Factorial moment generating function

Statistical table  x values, f(x) values and F(x)
values

Random sample
The program will also generate the graphs of the probability and distribution
functions. Move the cursor over the graph window to display the coordinates.
[Help Topics]
Beta Distribution
Select Probability Distributions  Beta Distribution  New... from
the main menu. Write the parameters a, b (positive real numbers)
and a list of X values (real numbers between 0 and 1) in their respective
tabbed boxes and press the button Beta Distribution. The program
will calculate the following:

Range of random variable X

Probability density function f(x)

Distribution function F(x)

Mean and variance

Statistical table  x values, f(x) values and F(x)
values
The program will also generate the graphs of the probability and distribution
functions. Move the cursor over the graph window to display the coordinates.
[Help Topics]
Gamma Distribution
Select Probability Distributions  Gamma Distribution  New... from
the main menu. Write the parameters n, l (positive real numbers)
and a list of X values (positive real numbers) in their respective
tabbed boxes and press the button Gamma Distribution. The program
will calculate the following:

Range of random variable X

Probability density function f(x)

Distribution function F(x)

Mean and variance

Moment generating function

Statistical table  x values, f(x) values and F(x)
values
The program will also generate the graphs of the probability and distribution
functions. Move the cursor over the graph window to display the coordinates.
[Help Topics]
Negative Binomial Distribution
Select Probability Distributions  Negative Binomial Distribution 
New... from the main menu. Write the parameters n (positive
integer), p (real number between 0 and 1) and a list of X values
(integers greater than n) in their respective tabbed boxes and press
the button Negative Binomial Distribution. The program will calculate
the following:

Range of random variable X

Probability function f(x)

Distribution function F(x)

Mean and variance

Factorial moment generating function

Statistical table  x values, f(x) values and F(x)
values
The program will also generate the graphs of the probability and distribution
functions. Move the cursor over the graph window to display the coordinates.
[Help Topics]
ChiSquare Distribution
Select Probability Distributions  ChiSquare Distribution  New...
from the main menu. Write the parameter degrees of freedom m (positive
integer) and a list of X values (positive real numbers) in their
respective tabbed boxes and press the button ChiSquare Distribution.
The program will calculate the following:

Range of random variable X

Probability density function f(x)

Distribution function F(x)

Mean and variance

Moment generating function

Statistical table  x values, f(x) values and F(x)
values
The program will also generate the graphs of the probability and distribution
functions. Move the cursor over the graph window to display the coordinates.
[Help Topics]
Student's tDistribution
Select Probability Distributions  Student's tDistribution  New...
from the main menu. Write the parameter degrees of freedom m (positive
integer) and a list of X values (real numbers) in their respective
tabbed boxes and press the button Student's tDistribution. The
program will calculate the following:

Range of random variable X

Probability density function f(x)

Distribution function F(x)

Mean and variance

Statistical table  x values, f(x) values and F(x)
values
The program will also generate the graphs of the probability and distribution
functions. Move the cursor over the graph window to display the coordinates.
[Help Topics]
Fisher's FDistribution
Select Probability Distributions  Fisher's FDistribution  New...
from the main menu. Write the parameter degrees of freedom m (positive
integer) and a list of X values (real numbers) in their respective
tabbed boxes and press the button FDistribution. The program will
calculate the following:

Range of random variable X

Probability density function f(x)

Distribution function F(x)

Mean and variance

Statistical table  x values, f(x) values and F(x)
values
The program will also generate the graphs of the probability and distribution
functions. Move the cursor over the graph window to display the coordinates.
[Help Topics]
Print and Export
Right click on the generated Statistics 1.0 document to select Print and
Export to Microsoft Excel options.
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