ALGEBRA FX 2.0 PLUS FX 1.0 PLUS

Users Guide

http://world.casio.com/edu_e/
GUIDELINES LAID DOWN BY FCC RULES FOR USE OF THE UNIT IN THE U.S.A. (not applicable to other areas).

NOTICE

This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC Rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference to radio communications. However, there is no guarantee that interference will not occur in a particular installation. If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, the user is encouraged to try to correct the interference by one or more of the following measures: Reorient or relocate the receiving antenna. Increase the separation between the equipment and receiver. Connect the equipment into an outlet on a circuit different from that to which the receiver is connected. Consult the dealer or an experienced radio/TV technician for help.

FCC WARNING

Changes or modifications not expressly approved by the party responsible for compliance could void the users authority to operate the equipment. Proper connectors must be used for connection to host computer and/or peripherals in order to meet FCC emission limits. Connector SB-62 Connector FA-123 Power Graphic Unit to Power Graphic Unit Power Graphic Unit to PC for IBM/Macintosh Machine
Declaration of Conformity
Model Number: Trade Name: Responsible party: Address: Telephone number: ALGEBRA FX 2.0 PLUS / FX 1.0 PLUS CASIO COMPUTER CO., LTD. CASIO, INC. 570 MT. PLEASANT AVENUE, DOVER, NEW JERSEY 07801 973-361-5400
This device complies with Part 15 of the FCC Rules. Operation is subject to the following two conditions: (1) This device may not cause harmful interference, and (2) this device must accept any interference received, including interference that may cause undesired operation.
IBM is a registered trademark of International Business Machines Corporation. Macintosh is a registered trademark of Apple Computer, Inc.
BEFORE USING THE CALCULATOR FOR THE FIRST TIME.
This calculator does not contain any main batteries when you purchase it. Be sure to perform the following procedure to load batteries, reset the calculator, and adjust the contrast before trying to use the calculator for the first time. 1. Making sure that you do not accidently press the o key, slide the case onto the calculator and then turn the calculator over. Remove the back cover from the calculator by pulling with your finger at the point marked 1.
2. Load the four batteries that come with calculator. Make sure that the positive (+) and negative () ends of the batteries are facing correctly.

BACK UP

3. Remove the insulating sheet at the location marked BACK UP by pulling in the direction indicated by the arrow.
4. Replace the back cover, making sure that its tabs enter the holes marked 2 and turn the calculator front side up. The calculator should automatically turn on power and perform the memory reset operation.

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5. Press m. If the Main Menu shown to the right is not on the display, press the P button on the back of the calculator to perform memory reset.

P button

* The above shows the ALGEBRA FX 2.0 PLUS screen.
6. Use the cursor keys (f, c, d, e) to select the SYSTEM icon and press w, then press 2( ) to display the contrast adjustment screen.
7. Adjust the contrast. The e cursor key makes display contrast darker. The d cursor key makes display contrast lighter. 1(INIT) returns display contrast to its initial default. 8. To exit display contrast adjustment, press m.

20010102

Quick-Start
Turning Power On And Off Using Modes Basic Calculations Replay Feature Fraction Calculations Exponents Graph Functions Dual Graph Box Zoom Dynamic Graph Table Function

1 Quick-Start

Welcome to the world of graphing calculators. Quick-Start is not a complete tutorial, but it takes you through many of the most common functions, from turning the power on, and on to graphing complex equations. When youre done, youll have mastered the basic operation of this calculator and will be ready to proceed with the rest of this users guide to learn the entire spectrum of functions available. Each step of the examples in Quick-Start is shown graphically to help you follow along quickly and easily. When you need to enter the number 57, for example, weve indicated it as follows: Press
Whenever necessary, weve included samples of what your screen should look like. If you find that your screen doesnt match the sample, you can restart from the beginning by pressing the All Clear button.

TURNING POWER ON AND OFF

To turn power on, press
o. To turn power off, press !o.
Calculator power turns off automatically if you do not perform any operation within the Auto Power Off trigger time you specify. You can specify either six minutes or 60 minutes as the trigger time.

USING MODES

This calculator makes it easy to perform a wide range of calculations by simply selecting the appropriate mode. Before getting into actual calculations and operation examples, lets take a look at how to navigate around the modes.

To select the RUN MAT Mode

1. Press

m to display the Main Menu.

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2 Quick-Start

2. Use

defc to highlight RUN and then press w.
This is the initial screen of the RUN MAT Mode, where you can perform manual calculations, matrix calculations, and run programs.

BASIC CALCULATIONS

With manual calculations, you input formulas from left to right, just as they are written on paper. With formulas that include mixed arithmetic operators and parentheses, the calculator automatically applies true algebraic logic to calculate the result.

Example: + 61

1. Press 2. Press
o to clear the calculator. bf*d+gbw.

Parentheses Calculations

Example: 15 (3 + 61)

bf*(d +gb)w.

Built-In Functions
This calculator includes a number of built-in scientific functions, including trigonometric and logarithmic functions.
Example: 25 sin 45 Important! Be sure that you specify Deg (degrees) as the angle unit before you try this example.

3 Quick-Start

SET UP
u3 to display the SET UP screen.

2. Press

cccc1 (Deg) to specify i to clear the menu. o to clear the unit. cf*sefw.
degrees as the angle unit. 3. Press 4. Press 5. Press

REPLAY FEATURE

With the replay feature, simply press or to recall the last calculation that was performed so you can make changes or re-execute it as it is.
Example: To change the calculation in the last example from (25 sin 45) to (25 sin 55)
1. Press 2. Press 3. Press 4. Press 5. Press
d to display the last calculation. d twice to move the cursor (t) to 4. D to delete 4. f. w to execute the calculation again.

REPLAY

4 Quick-Start

FRACTION CALCULATIONS

You can use the key to input fractions into calculations. The symbol { is used to separate the various parts of a fraction.

Example: 1 15/16 + 37/9

o. b$bf$ bg+dh$ jw.

Indicates 6 7/ 144

Converting a Mixed Fraction to an Improper Fraction
While a mixed fraction is shown on the display, press improper fraction.

!$to convert it to an

!$again to convert back to a mixed fraction.
Converting a Fraction to Its Decimal Equivalent
While a fraction is shown on the display, press equivalent. Press
$ to convert it to its decimal
$ again to convert back to a fraction.

5 Quick-Start

EXPONENTS

Example: 1250 2.065

o. bcfa*c.ag. M and the ^ indicator appears on the display. f. The ^5 on the display indicates that 5 is an exponent. w.

6 Quick-Start

GRAPH FUNCTIONS
The graphing capabilities of this calculator makes it possible to draw complex graphs using either rectangular coordinates (horizontal axis: x ; vertical axis: y) or polar coordinates (angle: ; distance from origin: r). All of the following graphing examples are performed starting from the calculator setup in effect immediately following a reset operation.
Example 1: To graph Y = X(X + 1)(X 2)

1. Press 2. Use

defc to highlight GRPH TBL, and then press w.

3. Input the formula.

v (v+b) (v -c)w

4. Press

5(DRAW) or w to draw the graph.
Example 2: To determine the roots of Y = X(X + 1)(X 2)
4(G-SLV) to display the pull-up menu.

7 Quick-Start

b(Root). Press e for other roots.
Example 3: Determine the area bounded by the origin and the X = 1 root obtained for Y = X(X + 1)(X 2)

i4(G-SLV)c.

i(dx).

3. Use

d to move the pointer to the location where X = 1, and then press w. Next, use e to
move the pointer to the location where X = 0, and then press
w to input the integration range,
which becomes shaded on the display.

8 Quick-Start

DUAL GRAPH
With this function you can split the display between two areas and display two graphs on the same screen.
Example: To draw the following two graphs and determine the points of intersection
Y1 = X(X + 1)(X 2) Y2 = X + 1.2
1. Press (G+G) to specify G+G for the Dual Screen setting.

u3ccc2

i, and then input the two functions. v(v+b) (v-c)w v+b.cw 5(DRAW) or w to draw the graphs.

3. Press

BOX ZOOM
Use the Box Zoom function to specify areas of a graph for enlargement. 1. Press

2(ZOOM) b(Box).

to move the pointer 2. Use to one corner of the area you want to specify and. then press

defc w

9 Quick-Start
3. Use to move the pointer again. As you do, a box appears on the display. Move the pointer so the box encloses the area you want to enlarge.
4. Press , and the enlarged area appears in the inactive (right side) screen.

DYNAMIC GRAPH

Dynamic Graph lets you see how the shape of a graph is affected as the value assigned to one of the coefficients of its function changes.
Example: To draw graphs as the value of coefficient A in the following function changes from 1 to 3

Y = AX2

and then press
d e f c to highlight DYNA, w.

10 Quick-Start

4. Press (VAR) of 1 to coefficient A.
bw to assign an initial value

5. Press

2(RANG) bwdwb
to specify the range and increment of change in coefficient A.

6. Press

(DYNA) to start Dynamic Graph drawing. 7. Press The graphs are drawn 10 times.

11 Quick-Start

TABLE FUNCTION
The Table Function makes it possible to generate a table of solutions as different values are assigned to the variables of a function.
Example: To create a number table for the following function

Y = X (X+1) (X2)

v(v+b) (v-c)w

4. Press table.

6(g)5(TABL) to generate the number
To learn all about the many powerful features of this calculator, read on and explore!

Handling Precautions

Your calculator is made up of precision components. Never try to take it apart. Avoid dropping your calculator and subjecting it to strong impact. Do not store the calculator or leave it in areas exposed to high temperatures or humidity, or large amounts of dust. When exposed to low temperatures, the calculator may require more time to display results and may even fail to operate. Correct operation will resume once the calculator is brought back to normal temperature. The display will go blank and keys will not operate during calculations. When you are operating the keyboard, be sure to watch the display to make sure that all your key operations are being performed correctly. Replace the main batteries once every 2 years regardless of how much the calculator is used during that period. Never leave dead batteries in the battery compartment. They can leak and damage the unit. Keep batteries out of the reach of small children. If swallowed, consult a physician immediately. Avoid using volatile liquids such as thinner or benzine to clean the unit. Wipe it with a soft, dry cloth, or with a cloth that has been moistened with a solution of water and a neutral detergent and wrung out. Always be gentle when wiping dust off the display to avoid scratching it. In no event will the manufacturer and its suppliers be liable to you or any other person for any damages, expenses, lost profits, lost savings or any other damages arising out of loss of data and/or formulas arising out of malfunction, repairs, or battery replacement. It is up to you to prepare physical records of data to protect against such data loss. Never dispose of batteries, the liquid crystal panel, or other components by burning them. When the Low Main Batteries! message or the Low Backup Battery! message appears on the display, replace the main power supply batteries or the back up battery as soon as possible. Be sure that the power switch is set to OFF when replacing batteries. If the calculator is exposed to a strong electrostatic charge, its memory contents may be damaged or the keys may stop working. In such a case, perform the Reset operation to clear the memory and restore normal key operation. If the calculator stops operating correctly for some reason, use a thin, pointed object to press the P button on the back of the calculator. Note, however, that this clears all the data in calculator memory. Note that strong vibration or impact during program execution can cause execution to stop or can damage the calculators memory contents. Using the calculator near a television or radio can cause interference with TV or radio reception. Before assuming malfunction of the unit, be sure to carefully reread this users guide and ensure that the problem is not due to insufficient battery power, programming or operational errors.

Be sure to keep physical records of all important data!
Low battery power or incorrect replacement of the batteries that power the unit can cause the data stored in memory to be corrupted or even lost entirely. Stored data can also be affected by strong electrostatic charge or strong impact. It is up to you to keep back up copies of data to protect against its loss. In no event shall CASIO Computer Co., Ltd. be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials. Moreover, CASIO Computer Co., Ltd. shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party. The contents of this users guide are subject to change without notice. No part of this users guide may be reproduced in any form without the express written consent of the manufacturer. The options described in Chapter 10 of this users guide may not be available in certain geographic areas. For full details on availability in your area, contact your nearest CASIO dealer or distributor.

1 Contents

Contents
Getting Acquainted Read This First! Chapter 1 Basic Operation
1-1 1-2 1-3 1-4 1-5 1-6 1-7 1-8 Keys.... 1-1-1 Display.... 1-2-1 Inputting and Editing Calculations.. 1-3-1 Option (OPTN) Menu... 1-4-1 Variable Data (VARS) Menu... 1-5-1 Program (PRGM) Menu.. 1-6-1 Using the Set Up Screen... 1-7-1 When you keep having problems.. 1-8-1
Chapter 2 Manual Calculations
2-1 2-2 2-3 2-4 2-5 2-6 2-7 2-8 Basic Calculations... 2-1-1 Special Functions.... 2-2-1 Specifying the Angle Unit and Display Format.. 2-3-1 Function Calculations... 2-4-1 Numerical Calculations... 2-5-1 Complex Number Calculations.. 2-6-1 Binary, Octal, Decimal, and Hexadecimal Calculations with Integers... 2-7-1 Matrix Calculations... 2-8-1

Chapter 3 List Function

3-1 3-2 3-3 3-4 Inputting and Editing a List... 3-1-1 Manipulating List Data... 3-2-1 Arithmetic Calculations Using Lists.. 3-3-1 Switching Between List Files.. 3-4-1
Chapter 4 Equation Calculations
4-1 4-2 4-3 4-4 Simultaneous Linear Equations... 4-1-1 Higher Degree Equations... 4-2-1 Solve Calculations... 4-3-1 What to Do When an Error Occurs... 4-4-1

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2 Contents

Chapter 5 Graphing

5-1 5-2 5-3 5-4 5-5 5-6 5-7 5-8 5-9 5-10 5-11 Sample Graphs... 5-1-1 Controlling What Appears on a Graph Screen.. 5-2-1 Drawing a Graph... 5-3-1 Storing a Graph in Picture Memory.. 5-4-1 Drawing Two Graphs on the Same Screen.. 5-5-1 Manual Graphing... 5-6-1 Using Tables... 5-7-1 Dynamic Graphing... 5-8-1 Graphing a Recursion Formula... 5-9-1 Changing the Appearance of a Graph.. 5-10-1 Function Analysis... 5-11-1

Chapter 6 Statistical Graphs and Calculations
6-1 6-2 6-3 6-4 Before Performing Statistical Calculations.. 6-1-1 Calculating and Graphing Single-Variable Statistical Data.. 6-2-1 Calculating and Graphing Paired-Variable Statistical Data. 6-3-1 Performing Statistical Calculations... 6-4-1
Chapter 7 Computer Algebra System and Tutorial Modes (ALGEBRA FX 2.0 PLUS only)
7-1 7-2 7-3 7-4 Using the CAS (Computer Algebra System) Mode. 7-1-1 Algebra Mode... 7-2-1 Tutorial Mode... 7-3-1 Algebra System Precautions.. 7-4-1

Chapter 8 Programming

8-1 8-2 8-3 8-4 8-5 8-6 8-7 8-8 Basic Programming Steps... 8-1-1 Program Mode Function Keys... 8-2-1 Editing Program Contents... 8-3-1 File Management... 8-4-1 Command Reference... 8-5-1 Using Calculator Functions in Programs.. 8-6-1 Program Mode Command List.. 8-7-1 Program Library... 8-8-1
Chapter 9 System Settings Menu
9-1 9-2 9-3 9-4 9-5 Using the System Settings Menu... 9-1-1 Memory Operations... 9-2-1 System Settings... 9-3-1 Reset... 9-4-1 Tutorial Lock (ALGEBRA FX 2.0 PLUS only).. 9-5-1

3 Contents

Chapter 10
10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8

Data Communications

Connecting Two Units... 10-1-1 Connecting the Unit with a CASIO Label Printer. 10-2-1 Connecting the Unit to a Personal Computer. 10-3-1 Performing a Data Communication Operation.. 10-4-1 Data Communications Precautions... 10-5-1 Sending a Screen Shot... 10-6-1 Add-ins.... 10-7-1 MEMORY Mode... 10-8-1

Appendix

7 Error Message Table... -1-1 Input Ranges.... -2-1 Specifications.... -3-1 Index.... -4-1 Key Index... -5-1 P Button (In case of hang up)... -6-1 Power Supply.... -7-1

Getting Acquainted

Read This First!

About this Users Guide

u! x( )
The above indicates you should press ! and then x, which will input a symbol. All multiple-key input operations are indicated like this. Key cap markings are shown, followed by the input character or command in parentheses.

uFunction Keys and Menus

Many of the operations performed by this calculator can be executed by pressing function keys 1 through 6. The operation assigned to each function key changes according to the mode the calculator is in, and current operation assignments are indicated by function menus that appear at the bottom of the display. This users guide shows the current operation assigned to a function key in parentheses following the key cap for that key. 1(Comp), for example, indicates that pressing 1 selects {Comp}, which is also indicated in the function menu. When (g) is indicated in the function menu for key 6, it means that pressing 6 displays the next page or previous page of menu options.

u Menu Titles

Menu titles in this users guide include the key operation required to display the menu being explained. The key operation for a menu that is displayed by pressing K and then {MAT} would be shown as: [OPTN]-[MAT]. 6(g) key operations to change to another menu page are not shown in menu title key operations.

0-1-1 Getting Acquainted

uGraphs
As a general rule, graph operations are shown on facing pages, with actual graph examples on the right hand page. You can produce the same graph on your calculator by performing the steps under the Procedure above the graph. Look for the type of graph you want on the right hand page, and then go to the page indicated for that graph. The steps under Procedure always use initial RESET settings.

5-1-1 Sample Graphs

5-1 Sample Graphs
k How to draw a simple graph (1)

Description

To draw a graph, simply input the applicable function. Example

5-1-2 Sample Graphs

To graph y = 3x2

Procedure

1 m GRPH-TBL 2 dvxw 3 5(DRAW) (or w)

Set Up

1. From the Main Menu, enter the GRPH TBL Mode.

Result Screen

Execution
2. Input the function you want to graph. Here you would use the V-Window to specify the range and other parameters of the graph. See 5-3-1. 3. Draw the graph.
The step numbers in the SET UP and Execution sections on the left hand page correspond to the Procedure step numbers on the right hand page. Example: Left hand page 3. Draw the graph. Right hand page 3 5(DRAW)(or w)

u Command List

The Program Mode Command List (page 8-7) provides a graphic flowchart of the various function key menus and shows how to maneuver to the menu of commands you need. Example: The following operation displays Xfct: [VARS]-[FACT]-[Xfct]

u Page Contents

Three-part page numbers are centered at the top of each page. The page number 1-2-3, for example, indicates Chapter 1, Section 2, page 3.

Icon RUN STATistics

1-2-2 Display
The following explains the meaning of each icon. Mode Name Description Use this mode for arithmetic calculations and function calculations, and for calculations involving binary, octal, decimal, and hexadecimal values and matrices. Use this mode to perform single-variable (standard deviation) and paired-variable (regression) statistical calculations, to perform tests, to analyze data and to draw statistical graphs. Use this mode to store functions, to generate a numeric table of different solutions as the values assigned to variables in a function change, and to draw graphs. Use this mode to store graph functions and to draw multiple versions of a graph by changing the values assigned to the variables in a function. Use this mode to store recursion formulas, to generate a numeric table of different solutions as the values assigned to variables in a function change, and to draw graphs. Use this mode to draw graphs of implicit functions. Use this mode to solve linear equations with two through six unknowns, quadratic equations, and cubic equations. Use this mode to store programs in th program area and to run programs.

1-2-3 Display

k About the Function Menu
Use the function keys (1 to 6) to access the menus and commands in the menu bar along the bottom of the display screen. You can tell whether a menu bar item is a menu or a command by its appearance. Command (Example: Pull-up Menu (Example: ) )
Pressing a function key that corresponds to a menu bar command executes the command. Pressing a function key that corresponds to a pull-up menu opens the menu. You can use either of the following two methods to select a command from a pull-up menu.

GRaPH-TaBLe

DYNAmic graph

RECURsion

CONICS EQUAtion PRoGraM
Input the key to the left of the command on the pull-up menu. Use the f and c cursor keys to move the highlighting to the command you want, and then press w. The symbol ' to the right of a command indicates that executing the command displays a submenu. To cancel the pull-up menu without inputting the command, press i.

k About Display Screens

This calculator uses two types of display screens: a text screen and a graphic screen. The text screen can show 21 columns and 8 lines of characters, with the bottom line used for the function key menu. The graph screen uses an area that measures 127 (W) 63 (H) dots.
Computer Algebra Use this mode to perform algebraic calculations. Syetem ALGEBRA TUTORial LINK MEMORY SYSTEM Use this mode for step-by-step solution of expressions. Use this mode to determine the expression type and solve mode, and for interactive equation solutions. Use this mode for step-by-step solution of expressions. Use this mode to manage data stored in memory. Use this mode to initialize memory, adjust contrast, and to make other system settings.

Text Screen

Graph Screen
The contents of each type of screen are stored in independent memory areas. The contents of each type of screen are stored in independent memory areas.
#The contents of each type of screen are stored in independent memory areas.
#The contents of each type of screen are stored in independent memory
u Supplementary Information

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Supplementary information is shown at the bottom of each page in a

(Notes) block.

indicates a note about a term that appears in the * indicates a note that provides general informationsame page as the note.the same section # about topic covered in as the note.

u Regression Formula Copy Function from a Regression Calculation Result Screen
In addition to the normal regression formula copy function that lets you copy the regression calculation result screen after drawing a statistical graph (such as Scatter Plot), the STAT Mode also has a function that lets you copy the regression formula obtained as the result of a regression calculation. To copy a resulting regression formula, press 6(COPY).
k Tests, Confidence Interval, and Distribution Calculations
The STAT Mode includes functions for performing tests, and confidence interval and distribution calculations. You can find explanations of each of these functions in the following sections: 1-2 Tests, 1-3 Confidence Interval, and 1-4 Distribution.

u Parameter Settings

The following describes the two methods you can use to make parameter settings for test, confidence interval, and distribution calculations. Selection With this method, you press the function key that corresponds to the setting you want to select from the function menu. Value Input With this method, you directly input the parameter value you want to input. In this case, nothing appears in the function menu. Pressing i returns to the list input screen, with the cursor in the same position it was at before you started the parameter setting procedure. Pressing ! i(QUIT) returns to the top of list input screen. Pressing w without pressing 1(CALC) under Execute item advances to calculation execution. To return to the parameter setting screen, press i, A, or w.
1-1-4 Advanced Statistics (STAT)

u Common Functions

The symbol appears in the upper right corner of the screen while execution of a calculation is being performed and while a graph is being drawn. Pressing A during this time terminates the ongoing calculation or draw operation (AC Break). Pressing i or w while a calculation result or graph is on the display returns to the parameter setting screen. Pressing ! i(QUIT) returns to the top of list input screen. Pressing A while a calculation result is on the display returns to the parameter setting screen. Pressing u 5(GT) after drawing a graph switches to the parameter setting screen (GT function). Pressing u 5(GT) again returns to the graph screen. The GT function is disabled whenever you change a setting on the parameter setting screen, or when you perform a u 3(SET UP) or ! K(V-Window) operation. You can perform the PICT menu's screen save or recall functions after drawing a graph. The ZOOM function and SKETCH function are disabled. The TRACE function is disabled, except for the graph display of two-way ANOVA. The graph screen cannot be scrolled. After drawing a graph, you can use a Save Result feature to save calculation results to a specific list. Basically, all items are saved as they are displayed, except for the first line title. Each time you execute Save Result, any existing data in the list is replaced by the new results.

1-2-1 Tests (TEST)

1-2 Tests (TEST)
The Z Test provides a variety of different standardization-based tests. They make it possible to test whether or not a sample accurately represents the population when the standard deviation of a population (such as the entire population of a country) is known from previous tests. Z testing is used for market research and public opinion research, that need to be performed repeatedly. 1-Sample Z Test tests for the unknown population mean when the population standard deviation is known. 2-Sample Z Test tests the equality of the means of two populations based on independent samples when both population standard deviations are known. 1-Prop Z Test tests for an unknown proportion of successes. 2-Prop Z Test tests to compare the proportion of successes from two populations. The t Test tests the hypothesis when the population standard deviation is unknown. The hypothesis that is the opposite of the hypothesis being proven is called the null hypothesis, while the hypothesis being proved is called the alternative hypothesis. The t-test is normally applied to test the null hypothesis. Then a determination is made whether the null hypothesis or alternative hypothesis will be adopted. 1-Sample t Test tests the hypothesis for a single unknown population mean when the population standard deviation is unknown. 2-Sample t Test compares the population means when the population standard deviations are unknown. LinearReg t Test calculates the strength of the linear association of paired data.
2 Test tests hypothesis concerning the proportion of samples included in each of a number
of independent groups. Mainly, it generates cross-tabulation of two categorical variables (such as yes, no) and evaluates the independence of these variables. It could be used, for example, to evaluate the relationship between whether or not a driver has ever been involved in a traffic accident and that persons knowledge of traffic regulations. 2-Sample F Test tests the hypothesis for the ratio of sample variances. It could be used, for example, to test the carcinogenic effects of multiple suspected factors such as tobacco use, alcohol, vitamin deficiency, high coffee intake, inactivity, poor living habits, etc. ANOVA tests the hypothesis that the population means of the samples are equal when there are multiple samples. It could be used, for example, to test whether or not different combinations of materials have an effect on the quality and life of a final product. One-Way ANOVA is used when there is one independent variable and one dependent variable. Two-Way ANOVA is used when there are two independent variables and one dependent variable.

1-2-2 Tests (TEST)

The following pages explain various statistical calculation methods based on the principles described above. Details concerning statistical principles and terminology can be found in any standard statistics textbook. On the initial STAT Mode screen, press 3(TEST) to display the test menu, which contains the following items. 3(TEST)b(Z). Z Tests (p. 1-2-2) c(T). t Tests (p. 1-2-10) d(2 ). 2 Test (p. 1-2-18) e(F). 2-Sample F Test (p. 1-2-20) f(ANOVA). ANOVA (p. 1-2-22)

k Z Tests

u Z Test Common Functions
You can use the following graph analysis functions after drawing a graph. 1(Z). Displays z score. Pressing 1 (Z) displays the z score at the bottom of the display, and displays the pointer at the corresponding location in the graph (unless the location is off the graph screen). Two points are displayed in the case of a two-tail test. Use d and e to move the pointer. Press i to clear the z score. 2(P). Displays p-value. Pressing 2 (P) displays the p-value at the bottom of the display without displaying the pointer. Press i to clear the p-value.

u 1-Sample Z Test

This test is used when the population standard deviation is known to test the hypothesis. The 1-Sample Z Test is applied to the normal distribution.

o : mean of sample

o : assumed population mean : population standard deviation n : size of sample
# Executing an analysis function automatically stores the z and p values in alpha variables Z and P, respectively.
# The following V-Window settings are used for drawing the graph. Xmin = 3.2, Xmax = 3.2, Xscale = 1, Ymin = 0.1, Ymax = 0.45, Yscale = 0.1

1-2-3 Tests (TEST)

Perform the following key operations from the statistical data list. 3(TEST) b(Z) b(1-Smpl)
The following shows the meaning of each item in the case of list data specification. Data.. data type
.. population mean value test conditions (G 0 specifies two-tail test, < 0 specifies lower one-tail test, > 0 specifies upper one-tail test.) 0.. assumed population mean .. population standard deviation ( > 0)
List.. list whose contents you want to use as data (List 1 to 20) Freq.. frequency (1 or List 1 to 20) Save Res. list for storage of calculation results (None or List 1 to 20) Execute.. executes a calculation or draws a graph The following shows the meaning of parameter data specification items that are different from list data specification.

t.. p.. o.. xn-1.. n..

t score
p-value mean of sample sample standard deviation size of sample

1-2-13 Tests (TEST)

u 2-Sample t Test
2-Sample t Test compares the population means when the population standard deviations are unknown. The 2-Sample t Test is applied to t-distribution. The following applies when pooling is in effect.

o1 o1 xp n12 n + n 2 1

x1n-1 : standard deviation of

sample 1

xp n1 =
(n11)x1 n12 +(n21)x2 n12 n1 + n 2 2
x2n-1 : standard deviation of

sample 2

n1 : size of sample 1 n2 : size of sample 2 xpn -1 : pooled sample standard

deviation

df = n1 + n2 2

df : degrees of freedom

The following applies when pooling is not in effect.
o1 o2 x1 n12 x2n12 n1 + n2

1 C 2 (1C )2 + n11 n21

x1 n12 n1 x1 n12 x2n12 n1 + n2
n1 : size of sample 1 n2 : size of sample 2 df : degrees of freedom
Perform the following key operations from the statistical data list. 3(TEST) c(T) c(2-Smpl)

1-2-14 Tests (TEST)

1.. sample mean value test conditions (G 2 specifies two-tail test, < 2 specifies one-tail test where sample 1 is smaller than sample 2, > 2 specifies one-tail test where sample 1 is greater than sample 2.)
List(1). list whose contents you want to use as data of sample 1 (List 1 to 20) List(2). list whose contents you want to use as data of sample 2 (List 1 to 20) Freq(1). frequency of sample 1 (1 or List 1 to 20) Freq(2). frequency of sample 2 (1 or List 1 to 20) Pooled.. pooling On (in effect) or Off (not in effect) Save Res. list for storage of calculation results (None or List 1 to 20) Execute.. executes a calculation or draws a graph The following shows the meaning of parameter data specification items that are different from list data specification.
o1.. mean of sample 1 x1n-1.. standard deviation (x1n-1 > 0) of sample 1 n1.. size (positive integer) of sample 1 o2.. mean of sample 2 x2n-1.. standard deviation ( x2n-1 > 0) of sample 2 n2.. size (positive integer) of sample 2

1-2-15 Tests (TEST)

t.. t score p.. p-value df.. degrees of freedom o1.. mean of sample 1 o2.. mean of sample 2 x1n-1.. standard deviation of sample 1 x2n-1.. standard deviation of sample 2 xpn-1.. pooled sample standard deviation (Displayed only when Pooled:

# The matrix must be at least two lines by two columns. An error occurs if the matrix has only one line or one column.
# Pressing 2 ('MAT) while setting parameters enters the MATRIX editor, which you can use to edit and view the contents of matrices.

1-2-19 Tests (TEST)

2.. 2 value
p.. p-value df.. degrees of freedom
You can use the following graph analysis functions after drawing a graph. 1(CHI). Displays 2 value. Pressing 1 (CHI) displays the 2 value at the bottom of the display, and displays the pointer at the corresponding location in the graph (unless the location is off the graph screen). Press i to clear the 2 value. 2(P). Displays p-value. Pressing 2 (P) displays the p-value at the bottom of the display without displaying the pointer. Press i to clear the p-value.
# Pressing 6('MAT) while a calculation result is displayed enters the MATRIX editor, which you can use to edit and view the contents of matrices. # The following V-Window settings are used for drawing the graph. Xmin = 0, Xmax = 11.5, Xscale = 2, Ymin = 0.1, Ymax = 0.5, Yscale = 0.1
# Executing an analysis function automatically stores the 2 and p values in alpha variables C and P, respectively.

1-2-20 Tests (TEST)

k 2-Sample F Test
2-Sample F Test tests the hypothesis for the ratio of sample variances. The F Test is applied to the F distribution.

x1n12 x2n12

Perform the following key operations from the statistical data list. 3(TEST) e(F)
The following is the meaning of each item in the case of list data specification. Data.. data type
1.. population standard deviation test conditions (G 2 specifies two-tail test, < 2 specifies one-tail test where sample 1 is smaller than sample 2, > 2 specifies one-tail test where sample 1 is greater than sample 2.)
List(1). list whose contents you want to use as data of sample 1 (List 1 to 20) List(2). list whose contents you want to use as data of sample 2 (List 1 to 20) Freq(1). frequency of sample 1 (1 or List 1 to 20) Freq(2). frequency of sample 2 (1 or List 1 to 20) Save Res. list for storage of calculation results (None or List 1 to 20) Execute.. executes a calculation or draws a graph The following shows the meaning of parameter data specification items that are different from list data specification.
x1n-1.. standard deviation (x1n-1 > 0) of sample 1 n1.. size (positive integer) of sample 1 x2n-1.. standard deviation (x2n-1 > 0) of sample 2 n2.. size (positive integer) of sample 2

1-2-21 Tests (TEST)

1G2. direction of test
F.. F value p.. p-value o1.. mean of sample 1 (Displayed only for Data: List setting.) o2.. mean of sample 2 (Displayed only for Data: List setting.) x1n-1.. standard deviation of sample 1 x2n-1.. standard deviation of sample 2 n1.. size of sample 1 n2.. size of sample 2

1-2-23 Tests (TEST)

One-Way ANOVA Line 1 (A).. Factor A df value, SS value, MS value, F value, p-value Line 2 (ERR).. Error df value, SS value, MS value Two-Way ANOVA Line 1 (A).. Factor A df value, SS value, MS value, F value, p-value Line 2 (B).. Factor B df value, SS value, MS value, F value, p-value Line 3 (AB). Factor A Factor B df value, SS value, MS value, F value, p-value *Line 3 does not appear when there is only one observation in each cell. Line 4 (ERR).. Error df value, SS value, MS value
F.. F value p.. p-value df.. degrees of freedom SS.. sum of squares MS. mean squares
With Two-Way ANOVA, you can draw Interaction Plot graphs. The number of graphs depends on Factor B, while the number of X-axis data depends on the Factor A. The Y-axis is the average value of each category. You can use the following graph analysis function after drawing a graph. 1(TRACE). Trace function Pressing d or e moves the pointer on the graph in the corresponding direction. When there are multiple graphs, you can move between graphs by pressing f and c. Press i to clear the pointer from the display.
# Graphing is available with Two-Way ANOVA only. V-Window settings are performed automatically, regardless of SET UP screen settings.
# Using the TRACE function automatically stores the number of conditions to alpha variable A and the mean value to variable M, respectively.

1-2-24 Tests (TEST)

k ANOVA (Two-Way)

u Description

The nearby table shows measurement results for a metal product produced by a heat treatment process based on two treatment levels: time (A) and temperature (B). The experiments were repeated twice each under identical conditions.
B (Heat Treatment Temperature) A (Time) A1 A2 B, 133 , B139 , , 132 122
Perform analysis of variance on the following null hypothesis, using a significance level of 5%. Ho : No change in strength due to time Ho : No change in strength due to heat treatment temperature Ho : No change in strength due to interaction of time and heat treatment temperature

u Solution

Use two-way ANOVA to test the above hypothesis. Input the above data as shown below. List1={1,1,1,1,2,2,2,2} List2={1,1,2,2,1,1,2,2} List3={113,116,139,132,133,131,126,122 } Define List 3 (the data for each group) as Dependent. Define List 1 and List 2 (the factor numbers for each data item in List 3) as Factor A and Factor B respectively. Executing the test produces the following results. Time differential (A) level of significance P = 0.2458019517 The level of significance (p = 0.2458019517) is greater than the significance level (0.05), so the hypothesis is not rejected. Temperature differential (B) level of significance P = 0.04222398836 The level of significance (p = 0.04222398836) is less than the significance level (0.05), so the hypothesis is rejected. Interaction (A B) level of significance P = 2.78169946e-3 The level of significance (p = 2.78169946e-3) is less than the significance level (0.05), so the hypothesis is rejected. The above test indicates that the time differential is not significant, the temperature differential is significant, and interaction is highly significant.

1-2-25 Tests (TEST)

u Input Example

u Results

1-3-1 Confidence Interval (INTR)
1-3 Confidence Interval (INTR)
A confidence interval is a range (interval) that includes a statistical value, usually the population mean. A confidence interval that is too broad makes it difficult to get an idea of where the population value (true value) is located. A narrow confidence interval, on the other hand, limits the population value and makes it difficult to obtain reliable results. The most commonly used confidence levels are 95% and 99%. Raising the confidence level broadens the confidence interval, while lowering the confidence level narrows the confidence level, but it also increases the chance of accidently overlooking the population value. With a 95% confidence interval, for example, the population value is not included within the resulting intervals 5% of the time. When you plan to conduct a survey and then t test and Z test the data, you must also consider the sample size, confidence interval width, and confidence level. The confidence level changes in accordance with the application. 1-Sample Z Interval calculates the confidence interval for an unknown population mean when the population standard deviation is known. 2-Sample Z Interval calculates the confidence interval for the difference between two population means when the population standard deviations of two samples are known. 1-Prop Z Interval calculates the confidence interval for an unknown proportion of successes. 2-Prop Z Interval calculates the confidence interval for the difference between the propotion of successes in two populations. 1-Sample t Interval calculates the confidence interval for an unknown population mean when the population standard deviation is unknown. 2-Sample t Interval calculates the confidence interval for the difference between two population means when both population standard deviations are unknown. On the initial STAT Mode screen, press 4 (INTR) to display the confidence interval menu, which contains the following items. 4(INTR)b(Z). Z intervals (p. 1-3-3) c(T). t intervals (p. 1-3-8)

# There is no graphing for confidence interval functions.
1-3-2 Confidence Interval (INTR)
u General Confidence Interval Precautions
Inputting a value in the range of 0 < C-Level < 1 for the C-Level setting sets you value you input. Inputting a value in the range of 1 < C-Level < 100 sets a value equivalent to your input divided by 100.
# Inputting a value of 100 or greater, or a negative value causes an error (Ma ERROR).
1-3-3 Confidence Interval (INTR)

k Z Interval

u 1-Sample Z Interval
1-Sample Z Interval calculates the confidence interval for an unknown population mean when the population standard deviation is known. The following is the confidence interval.
Left = o Z 2 n Right = o + Z 2 n
However, is the level of significance. The value 100 (1 ) % is the confidence level. When the confidence level is 95%, for example, inputting 0.95 produces 1 0.95 = 0.05 =. Perform the following key operations from the statistical data list. 4(INTR) b(Z) b(1-Smpl)
The following shows the meaning of each item in the case of list data specification. Data.. data type C-Level. confidence level (0 < C-Level < 1)
.. population standard deviation ( > 0)
List.. list whose contents you want to use as sample data (List 1 to 20) Freq.. sample frequency (1 or List 1 to 20) Save Res. list for storage of calculation results (None or List 1 to 20) Execute.. executes a calculation The following shows the meaning of parameter data specification items that are different from list data specification.
1-3-4 Confidence Interval (INTR)
After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation. 1(CALC). Performs the calculation. Calculation Result Output Example
Left.. interval lower limit (left edge) Right.. interval upper limit (right edge)
o.. mean of sample xn-1.. sample standard deviation

u 2-Sample Z Interval

2-Sample Z Interval calculates the confidence interval for the difference between two population means when the population standard deviations of two samples are known. The following is the confidence interval. The value 100 (1 ) % is the confidence level.

1-3-8 Confidence Interval (INTR)
1.. estimated sample propotion for sample 1 p 2.. estimated sample propotion for sample 2 p n1.. size of sample 1 n2.. size of sample 2

k t Interval

u 1-Sample t Interval
1-Sample t Interval calculates the confidence interval for an unknown population mean when the population standard deviation is unknown. The following is the confidence interval. The value 100 (1 ) % is the confidence level.

Left = o tn 1

xn1 Right = o+ tn n
Perform the following key operations from the statistical data list. 4(INTR) c(T) b(1-Smpl)
The following shows the meaning of each item in the case of list data specification. Data.. data type C-Level. confidence level (0 < C-Level < 1) List.. list whose contents you want to use as sample data (List 1 to 20) Freq.. sample frequency (1 or List 1 to 20) Save Res. list for storage of calculation results (None or List 1 to 20) Execute.. executes a calculation The following shows the meaning of parameter data specification items that are different from list data specification.
1-3-9 Confidence Interval (INTR)
o.. mean of sample xn-1.. sample standard deviation n.. size of sample

u 2-Sample t Interval

2-Sample t Interval calculates the confidence interval for the difference between two population means when both population standard deviations are unknown. The t interval is applied to t distribution. The following confidence interval applies when pooling is in effect. The value 100 (1 ) % is the confidence level.

Left = (o1 o2) tn +n

xp n12 n + n xp n12 n + n 2 1

Right = (o1 o2)+ tn +n

1-3-10 Confidence Interval (INTR)
The following confidence interval applies when pooling is not in effect. The value 100 (1 ) % is the confidence level.

Left = (o1 o2) tdf

x1 n12 x2 n12 + n nx1 n12 x2 n12 + n n1 2

Right = (o1 o2)+ tdf 2

C 2 + (1C) n11 n21
x1 n12 n1 C= x1 n12 x2 n12 n1 + n2
Perform the following key operations from the statistical data list. 4(INTR) c(T) c(2-Smpl)
The following shows the meaning of each item in the case of list data specification. Data.. data type C-Level. confidence level (0 < C-Level < 1) List(1). list whose contents you want to use as data of sample 1 (List 1 to 20) List(2). list whose contents you want to use as data of sample 2 (List 1 to 20) Freq(1). frequency of sample 1 (1 or List 1 to 20) Freq(2). frequency of sample 2 (1 or List 1 to 20) Pooled.. pooling On (in effect) or Off (not in effect) Save Res. list for storage of calculation results (None or List 1 to 20) Execute.. executes a calculation The following shows the meaning of parameter data specification items that are different from list data specification.

1-3-11 Confidence Interval (INTR)
o1.. mean of sample 1 x1n-1.. standard deviation (x1n-1 > 0) of sample 1 n1.. size (positive integer) of sample 1 o2.. mean of sample 2 x2n-1.. standard deviation (x2n-1 > 0) of sample 2 n2.. size (positive integer) of sample 2
df.. degrees of freedom o1.. mean of sample 1 o2.. mean of sample 2 x1n-1.. standard deviation of sample 1 x2n-1.. standard deviation of sample 2 xpn-1.. pooled sample standard deviation
(Displayed only when Pooled: On setting.)
1-4-1 Distribution (DIST)

1-4 Distribution (DIST)

There is a variety of different types of distribution, but the most well-known is normal distribution, which is essential for performing statistical calculations. Normal distribution is a symmetrical distribution centered on the greatest occurrences of mean data (highest frequency), with the frequency decreasing as you move away from the center. Poisson distribution, geometric distribution, and various other distribution shapes are also used, depending on the data type. Certain trends can be determined once the distribution shape is determined. You can calculate the probability of data taken from a distribution being less than a specific value. For example, distribution can be used to calculate the yield rate when manufacturing some product. Once a value is established as the criteria, you can calculate normal probability when estimating what percent of the products meet the criteria. Conversely, a success rate target (80% for example) is set up as the hypothesis, and normal distribution is used to estimate the proportion of the products will reach this value. Normal probability density calculates the probability density of normal distribution from a specified x value. Normal distribution probability calculates the probability of normal distribution data falling between two specific values. Inverse cumulative normal distribution calculates a value that represents the location within a normal distribution for a specific cumulative probability. Student- t probability density calculates t probability density from a specified x value. Student- t distribution probability calculates the probability of t distribution data falling between two specific values. Like t distribution, distribution probability can also be calculated for 2, F, Binomial, Poisson, and Geometric distributions. On the initial STAT Mode screen, press 5 (DIST) to display the distribution menu, which contains the following items. 5(DIST)b(Norm). Normal distribution (p. 1-4-3) c(T). Student-t distribution (p. 1-4-7) d(2). 2 distribution (p. 1-4-9) e(F). F distribution (p. 1-4-12) f(Binmal). Binomial distribution (p. 1-4-16) g(Poissn). Poisson distribution (p. 1-4-19) h(Geo). Geometric distribution (p. 1-4-21)

# There is no graphing for normal distribution probability.
1-4-5 Distribution (DIST)
p.. normal distribution probability z:Low.. z:Low value (converted to standardize z score for lower value) z:Up.. z:Up value (converted to standardize z score for upper value)
u Inverse Cumulative Normal Distribution
Inverse cumulative normal distribution calculates a value that represents the location within a normal distribution for a specific cumulative probability.
Tail: Left upper boundary of integration interval =?

f (x)dx = p

Tail: Right lower boundary of integration interval =?
Tail: Central upper and lower boundaries of integration interval =? =?
Specify the probability and use this formula to obtain the integration interval. Perform the following key operations from the statistical data list. 5(DIST) b(Norm) d(Invrse)
Data is specified using parameter specification. The following shows the meaning of each item. Tail. probability value tail specification (Left, Right, Central) Area.. probability value (0 < Area < 1)
Save Res. list for storage of calculation results (None or List 1 to 20) Execute.. executes a calculation
1-4-6 Distribution (DIST)
After setting all the parameters, align the cursor with [Execute] and then press the function key shown below to perform the calculation. 1(CALC). Performs the calculation.
Calculation Result Output Examples
x.. inverse cumulative normal distribution (Tail:Left upper boundary of integration interval) (Tail:Right lower boundary of integration interval) (Tail:Central upper and lower boundaries of integration interval)
# There is no graphing for inverse cumulative normal distribution.
1-4-7 Distribution (DIST)

k Student-t Distribution

u Student-t Probability Density
Student- t probability density calculates t probability density from a specified x value.

df+1 2

x2 df + 1 1+ 2 df f (x) = df df 2

5(DIST) c(T) b(P.D)

Data is specified using parameter specification. The following shows the meaning of each item.
x.. data df.. degrees of freedom (df > 0)

p.. Student-t probability density
# Current V-Window settings are used for graph drawing when the SET UP screen's [Stat Wind] setting is [Manual]. The VWindow settings below are set automatically
when the [Stat Wind] setting is [Auto]. Xmin = 3.2, Xmax = 3.2, Xscale = 1, Ymin = 0.1, Ymax = 0.45, Yscale = 0.1
1-4-8 Distribution (DIST)
u Student-t Distribution Probability
Student- t distribution probability calculates the probability of t distribution data falling between two specific values.

df + p= df 2 df

x2 1+ df
Perform the following key operations from the statistical data list. 5(DIST) c(T) c(C.D)
df.. degrees of freedom (df > 0)
# There is no graphing for Student-t distribution probability.
1-4-9 Distribution (DIST)
p.. Student- t distribution probability t:Low.. t:Low value (input lower value) t:Up.. t:Up value (input upper value)

k 2 Distribution

u 2 Probability Density
2 probability density calculates the probability density function for the 2 distribution at a specified x value.

1 df 2

Perform the following key operations from the statistical data list. 5(DIST) d(2) b(P.D)
x.. data df.. degrees of freedom (positive integer)
Save Res. list for storage of calculation results (None or List 1 to 20) Execute.. executes a calculation or draws a graph After setting all the parameters, align the cursor with [Execute] and then press one of the function keys shown below to perform the calculation or draw the graph. 1(CALC). Performs the calculation. 6(DRAW). Draws the graph.
1-4-10 Distribution (DIST)
p.. 2 probability density
when the [Stat Wind] setting is [Auto]. Xmin = 0, Xmax = 11.5, Xscale = 2, Ymin = -0.1, Ymax = 0.5, Yscale = 0.1
1-4-11 Distribution (DIST)
u 2 Distribution Probability
2 distribution probability calculates the probability of 2 distribution data falling between two specific values.

p= 1 df 2

Perform the following key operations from the statistical data list. 5(DIST) d(2) c(C.D)
df.. degrees of freedom (positive integer)
# There is no graphing for 2 distribution probability.
1-4-12 Distribution (DIST)
p.. 2 distribution probability

k F Distribution

u F Probability Density F probability density calculates the probability density function for the F distribution at a specified x value.