 	         	STATSPACK V1.1
		        --------------
              
		Statistical Software for the HP 48G/GX
                      graphics calculators

                       by Stuart Sidders

                     Watford Maths Centre


                         
Contents:

1.0	Introduction
2.0	System Requirements
3.0	Disclaimer	
4.0	Registration
5.0	Installation
6.0	Library Menu
7.0	General Functions and Features
8.0	Program Details
8.01    STATSPACK: Module 1: Binomial probability function
8.02		   	     Menu Keys
8.03		             Graphical Display
8.10    STATSPACK: Module 2: Poisson probability distribution
8.11		             Menu Keys
8.12		             Graphical Display
8.20    STATSPACK: Module 3: Normal probability distribution
8.21		             Menu Keys
8.22		             PICT menu key
8.30    STATSPACK: Module 4: Percentage points on the Normal distribution
8.31		             Menu Keys
9.0	About
10.0	Uninstall
11.0	Acknowledgments
12.0	World Wide Web (WWW)
	











1.0	Introduction
--------------------

STATSPACK is a suite of program modules that have been written to cover a variety of common statistical functions.

The full version contains the following modules:
 
 Module 1) The Binomial probability distribution
 Module 2) The Poisson probability distribution
 Module 3) The Normal probability distribution
 Module 4) (z) Percentage points for the standardised Normal distribution


The program that is presented here is:

 a demo of module 1, the Binomial Probability Distribution from STATSPACK.
 ------------------------------------------------------------------------

As a teacher of mathematics and statistics, I wrote the program primarily for my students. It has been tried and tested over many months and is written for the HP 48G/GX calculators. ( Please note that the full version can only run on an HP48GX )

Various symbols are used in the documentation but cannot be reproduced exactly as seen on the calculator due to the limitations of this text editor.

	Symbol 		Meaning

	u		mean  (mu)
	o^2		variance  (sigma squared)
	

There is a facility on the HP48GX to calculate Normal probabilities but I have often found this cumbersome to use and so I developed the Normal distribution program to enhance this existing command.


2.0	System Requirements
---------------------------

Module		Description		Calculator	Memory (nearest K)
------		-----------		----------	------

  1		Bin. Dist.		HP48G/GX	21K
  2		Pois. Dist.		HP48G/GX	17K
  3		Norm. Dist.		HP48G/GX	20K
  4		z % points		HP48G/GX	11K

(all)		STATSPACK		HP48GX		60K
         



3.0	Disclaimer
------------------
Although every effort has been made to eliminate errors in the software, I take no responsibility for any loss of memory or damage these programs cause to your calculator.

I would advise that a calculator is fully backed up before loading this library.



4.0	Registration
--------------------

All demo modules are presented as SHAREWARE. To obtain the full version please register for the program in one of the following ways.

The current cost of which is $12(US) for a single module or 25$ for the complete version.

  1) On Compuserve - GO SWREG and look for the appropriate reg id. as listed      below

	Module		Description		Reg ID	  
	------		-----------		------

	  1		Bin. Dist.		13665
  	  2		Pois. Dist.		13676
	  3		Norm. Dist.		13679
	  4		z % points		13681

	(all)		STATSPACK		13682


  2) or you can obtain a copy direct from
			
                      	Stuart Sidders
			Watford Maths Centre
			40 Rickmansworth Road,
			Watford,
			Hertfordshire,
			WD1 7HT
			ENGLAND. 

	  Please make cheques payable to WATFORD MATHS CENTRE

	     Cost 7 for any single module.
                      or
	     20 for STATSPACK (the complete version)

	     Price includes disc, postage and packing.
		

	As a registered user, you are entitled to full support.


5.0	Installation
--------------------

     All modules come in the form of a library.
     To install a library to port 0: ( similar for port 1 )
        1) Check that a previous version of STATSPACK if installed is 	   	   removed. ( See section 10.0 to uninstall the program )
        2) Dowload the library file to the HP 
        3) Recall the library to the stack
        4) 0 STO if storing in port 0 or 1 STO if in port 1
        5) Execute OFF-ON keys or ON-C
        6) (Optional) Delete the variable created by the download procedure
           from its directory.

    

6.0	Library Menu
--------------------

STATSPACK Modules are accessed via the STPK menu key in the library.
The menu will then change to display the available program module(s).

(Please note that menu keys will only reflect loaded modules)
	
	BINO	Binomial probability distribution

	POISS	Poisson probability distribution
	
	NORM	Normal distribution

	z	Percentage points for the Normal distribution
                (not available on this demo)	
	

7.0   General functions and features
------------------------------------

The following functions apply to all program modules

 *  Movement between fields:
       Use the cursor arrow keys to move between fields or the ENTER key.

 *  Use the ENTER function key to submit a value to a field

 *  Algebraic entry is available

 *  Any value can be edited using the EDIT function key

 *  Radians or degree modes are available




8.0 Program details
-------------------


8.01	STATSPACK: Module 1:  Binomial Probability Distribution

Menu Key: BINO


This module evaluates probabilities for any random variable X which
follows a binomial model.

The notation used is X~B(n,p) where n is the number of trials and p
the probability of success.

The program allows calculation of P(X=a), P(X<a), P(a<X<b) etc

A menu key APRX is available to automatically approximate the distribution to the Poisson or Normal distributions depending on the size of the parameters if required. Use of this key can speed up calculations at the expense of accuracy. Answers are generally correct to about 3 decimal places.
When the APRX menu key is selected, the approximations are made if the conditions below are met.

 * The Poisson approximation is automatically used when n>50 and p<0.1
 * The Normal approximation is automatically used when np<5 and n(1-p)<5

Notification of an approximation will be made by a message appearing in the top right of the display.

           * N APRX   Normal approximation being used
           * P APRX   Poisson approximation being used


A facility is given to compare the actual probability to that of the Normal or Poisson approximations via the NORM or POISS menu keys.

Any distribution can be graphically displayed and probabilities traced.
Axes are set automatically.        



Limitation: Maximum of 2000 trials


The demo version has restrictions placed on the range of trials n that
are available.

          These are  n<=5,  50<=n<=60 and n>=200.

The registered version allows all values of n in the range 1-2000.



8.02	Menu Keys

The menu keys are dynamic, i.e. will appear when circumstances allow.

 The following keys allow calculation of various probabilities

  Menu Key     Row	Function 

   X= 		1 	Calculates P(X=a)	
   X<		1	Calculates P(X<a)
   X>		1	Calculates P(X>a)
   X<=		1	Calculates P(X<=a)
   X>=		1	Calculates P(X>=a)
   <X<		2	Calculates P(a<X<b)
   <=X<=    	2	Calculates P(a<=X<=b)



  HOLD         1/2	This key toggles the calculation of any probability 			on/off
         		( Useful when changing several fields )

  NORM	 	2	Normal approximation to the underlying Binomial 			distribution. This function is dynamic and only 			appears when a probability has been calculated.
 
  POISS	 	2	Poisson approximation to the underlying Binomial 			distribution. This function is dynamic and only 			appears when a probability has been calculated. 
                  	   
  STK^ 		2	Dumps the Distribution and the current probability to 			the stack. This function is dynamic and only appears 			when a probability has been calculated.
                	
  PLOT		3	Displays graphically the distribution. This function 			is dynamic and only appears when n and p are given.
	          
                  
  APRX		3	Sets the approximation mode on. Approximates 				probabilities automatically to the Poisson or Normal 			distributions. ( See notes in 7.1 )



8.03	Graphical Display: PLOT menu functions

When any graph is displayed via the PLOT menu key, the menu will change and the user is presented with the following.

  Menu Key     Row	Function 

   P() 		1 	This function will trace across the graph displaying
              		probabilities. A small tick mark moves under the x 			axis to highlight the current probability in the 			distribution.

   Exit		1	Exit to main program


The cancel key can be hit at any time to terminate a lengthy plot. The trace feature will still work, despite the incomplete graph. Useful if you want to trace a graph only and do not wish to view the distribution.

Axes are automatically set to cover a suitable domain.




8.10	STATSPACK: Module 2:  Poisson Probability Distribution

Menu Key: POISS


This program evaluates probabilities for any random variable X which
follows a Poisson model.


The notation used is X~P(u) where u is the mean.

The program allows calculation of P(X=a), P(X<a), P(a<X<b) etc

A menu key APRX is available to automatically approximate the distribution to the Normal distribution depending on the size of the parameters, if required. Use of this key can speed up calculations at the expense of accuracy. Answers are generally correct to about 3 decimal places.
When the APRX menu key is selected, the approximations are made if the conditions below are met.

 * The Normal approximation is automatically used when the mean >20

Notification of an approximation will be made by a message appearing in the top right of the display.

           * N APRX   Normal approximation being used

A facility is given to compare the actual probability to that of the Normal  approximation via the NORM menu key.

Any distribution can be graphically displayed and probabilities traced.
Axes are set automatically.        


The demo version has restrictions placed on the mean, u.
          These are  u<=5,  20<=u<=30 and u>=100.

The registered version allows the mean to be any value >0.  


8.11	Menu Keys

The menu keys are dynamic, i.e. will appear when circumstances allow.

 The following keys allow calculation of various probabilities

  Menu Key     Row	Function 

   X= 		1 	Calculates P(X=a)	
   X<		1	Calculates P(X<a)
   X>		1	Calculates P(X>a)
   X<=		1	Calculates P(X<=a)
   X>=		1	Calculates P(X>=a)
   <X<		2	Calculates P(a<X<b)
   <=X<=    	2	Calculates P(a<=X<=b)



  HOLD         1/2	This key toggles the calculation of any probability 			on/off
         		( Useful when changing several fields )

  NORM	 	2	Normal approximation to the underlying Binomial 			distribution. This function is dynamic and only 			appears when a probability has been calculated.
               	   
  STK^ 		2	Dumps the Distribution and the current probability to 			the stack. This function is dynamic and only appears 			when a probability has been calculated.
                	
  PLOT		3	Displays graphically the distribution. This function 			is dynamic and only appears when the mean is given.
	                            
  APRX		3	Sets the approximation mode on. Approximates 				probabilities automatically to the Normal 				distribution. ( See notes in 7.11 )



8.12 Graphical Display: PLOT menu functions

When any graph is displayed via the PLOT menu key, the menu will change and the user is presented with the following.

  Menu Key     Row	Function 

   P() 		1 	This function will trace across the graph displaying
              		probabilities. A small tick mark moves under the x 			axis to highlight the current probability in the 			distribution.

   Exit		1	Exit to main program


The cancel key can be hit at any time to terminate a lengthy plot. The trace feature will still work, despite the incomplete graph. Useful if you want to trace a graph only and do not wish to view the distribution.

Axes are automatically set to cover a suitable domain.


 

8.20	STATSPACK: Module 3: Normal Probability Distribution

Menu Key: NORM


This module evaluates probabilities for any random variable X which
follows a Normal (Gaussian) distribution.

The notation used is X~N(u,o^2) where u is the mean and o^2 the variance.

The program allows calculation of P(X<a), P(X>a) and P(a<X<b)

8.21	Menu Keys

  Menu Key     Row	Function 

   X<		1	Calculates P(X<a)
   X>		1	Calculates P(X>a)
   <X<		1	Calculates P(a<X<b)


  HOLD          1	This key toggles the calculation of any probability 			on/off
         		( Useful when changing several fields )
   
  PICT		1	Displays standardised z values corresponding to the 			observed values in a graphical way. ( see 				section 7.23 below for more details ). This menu key 			is dynamic and will be displayed when a probability 			has been calculated.

  STK^ 		1	Dumps the Distribution and the current probability to 			the stack. This menu key is dynamic and will be 			displayed when a probability has been calculated.



8.22	PICT menu key

This key provides the user with a graphical display of a Normal curve and the standardised curve. The curves are not drawn to scale but do provide a visual display of the mapping between an observed value and its equivalent z value.
When this screen is displayed a new menu will appear.
	
  Menu Key     Row	Function	

    VALUE	1	Displays the value of any highlighted field
    STK^	1	Dumps the highlighted field to the stack
    EXIT	1	Returns to main program

When the VALUE key is selected the current menu will disappear and the full value of the highlighted field will be shown. The user can navigate all fields by using the cursor arrow keys. To return the menu, just hit any menu key. 
 

The demo version has restrictions placed on the mean, u.
The allowed range is:-

            u<=5, u>=100.

The registered version has no restrictions placed on the mean.


8.30	STATSPACK: Module 4:  Percentage Points on the Normal Distribution

Menu Key: z  (zDEM on demo version only)

This program will evaluate the percentage points for a standardised Normal distribution. The user is shown a standardised Normal distribution graph
   ie Z~N(0,1)

Probabilities can be entered either as a percentage or as a value from 0-1.
Percentages are the default method of entry.
These values can be either the upper or lower tails.

As soon as the upper or lower tail value is entered, the corresponding z value will be evaluated and displayed. The displayed graph will then be shaded to reflect the selected percentage probability.

Values can be dumped to the stack.

The demo version has restrictions placed on the upper or lower tails p and q respectively.

The allowed range is:-

            p<=10% (lower tail) and  q<=10% (upper tail)

Any value in the range 0-100% or 0-1 is allowed in the registered version.


8.31	Menu Keys

  Menu Key     Row	Function 

   %		1	Toggles percentage mode ON/OFF


  STK^ 		1	Dumps the calculated z value to the stack. This menu 			key is dynamic and will be displayed when a z value 			has been calculated.


 



9.0	ABOUT:  Information pages

   Several pages providing information about STATSPACK

   MENUKEYS: 

(Please note: Some or all of these menus will be available depending on the  modules that have been selected from STATSPACK)

       	ABOUT 			Title page - version 

       	WWW 			General information

       	REG 	Demo only	Details on how to register for the full 				version of STATSPACK

	BINO	Demo only	Restrictions on binomial distribution demo

	POISS	Demo only	Restrictions on Poisson distribution demo

	NORM	Demo only	Restrictions on Normal distribution demo

	z	Demo only	Restrictions on z percentage points demo
	
 
   To exit from this menu display hit the cancel key.

   
10.0	Uninstall
-----------------
To remove this a program module from the library, do the following:

	1) Select the HOME directory
	2) Enter the library number identifier to the stack. Library number            identifiers are listed in the table below.
           
		Library Number Identifier

		1026    STATSPACK modules (registered versions)
		1027	Module 1 Demo
		1028	Module 2 Demo
		1029	Module 3 Demo
		1030	Module 4 Demo
           
        3) Select 'left shift', 'library' 'DETAC' (this will detach the 	   library from the HOME directory)
	4) Enter the library identifier in the form
	   :0:'Library Number' if stored in port 0 or
	   :1:'Library Number' if stored in port 1

	   example :0:1026  

	5) Now enter 'left shift', 'Purge'
           example.
           To remove a version of STATSPACK you should see :0:1026 PURGE or 	   :1:1026 PURGE for example 
	6) Press ENTER and the library should now be removed.
		


11.0	Acknowledgments
-----------------------

There were a number of occasions in the writing of this program that I ran into programming difficulties. Many thanks go to Lee Buck for the time he spent answering my queries.



12.0	World Wide Web (WWW)
----------------------------
 
For further details of STATSPACK and latest information on 		forthcoming modules, upgrades etc.

visit:

        http://ourworld.compuserve.com/homepages/WMC_CalcSoft
   
If you have any comments good or bad or any suggestions for future 	modules, please contact me at:-

     E-Mail: 101565,2240    (Compuserve)

     Internet: 101565.2240@compuserve.com

