Instruction/ maintenance manual of the product FX 1.0 PLUS Casio
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ALGEBRA FX 2.0 PLUS FX 1.0 PLUS User’s Guide 2 ( Additional Functions ) E http://world.casio.com/edu_e/.
CASIO ELECTRONICS CO ., L TD . Unit 6, 1000 North Circular Road, London NW2 7JD, U.K. Important! Please k eep your manual and all inf ormation handy for future ref erence.
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20010101 Contents Chapter 1 Ad vanced Statistics Application 1-1 Adv anced Statistics (ST A T) .............................................................. 1-1-1 1-2 T ests (TEST) .....................................................................
20010101 Adv anced Statistics Application 1-1 Ad vanced Statistics (ST A T) 1-2 T ests (TEST) 1-3 Confidence Interval (INTR) 1-4 Distribution (DIST) 1 Chapter.
20010101 1-1 Adv anced Statistics (ST A T) u u u u u Function Menu The follo wing shows the function menus for the ST A T Mode list input screen. Pressing a function key that corresponds to the added item displays a menu that lets you select one of the functions listed below .
20010101 • Logar ithmic Reg ression ... MSE = Σ 1 n – 2 i =1 n ( y i – ( a + b ln x i )) 2 •E xponential Repression ... MSE = Σ 1 n – 2 i =1 n ( ln y i – ( ln a + bx i )) 2 •P ow er Regression ... MSE = Σ 1 n – 2 i =1 n ( ln y i – ( ln a + b ln x i )) 2 •S in Reg ression .
20010101 4. After you are finished, press i to clear the coordinate values and the pointer from the displa y . · The pointer does not appear if the calculated coordinates are not within the display range. ·T he coordinates do not appear if [Off] is specified for the [Coord] item of the [SETUP] screen.
20010101 u u u u u Common Functions • The symbol “ ■ ” appears in the upper right cor ner of the screen while e xecution 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).
20010101 1-2 T ests (TEST) The Z T est pro vides a var iety of diff erent standardization-based tests. The y mak e it possib le 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.
20010101 The following pages e xplain various statistical calculation methods based on the principles descr ibed abov e . Details concer ning statistical principles and terminology can be found in any standard statistics textbook. On the initial ST A T Mode screen, press 3 (TEST) to display the test men u, which contains the following items.
20010101 Pe rf or m the f ollowing 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 µ ...........
20010101 Calculation Result Output Example µ G 11.4 ........................ direction of test z .................................. z score p .................................. p-value o .................................. mean of sample x σ n -1 ...
20010101 u u u u u 2-Sample Z T est This test is used when the standard deviations f or tw o populations are known to test the h ypothesis . The 2-Sample Z T est is applied to the normal distr ib ution.
20010101 o 1 ................................. mean of sample 1 n 1 ................................. siz e (positive integer) of sample 1 o 2 ........
20010101 u u u u u 1-Prop Z T est This test is used to test for an unknown proportion of successes. The 1-Prop Z T est is applied to the normal distr ibution. Z = n x n p 0 (1– p 0 ) – p 0 p 0 : e xpected sample proportion n : s i z e of sample Pe rf or m the f ollowing key operations from the statistical data list.
20010101 u u u u u 2-Prop Z T est This test is used to compare the propor tion of successes. The 2-Prop Z T est is applied to the nor mal distribution.
20010101 p 1 > p 2 ............................ direction of test z .................................. z score p .................................. p-value ˆ p 1 ................................. estimated propor tion of sample 1 ˆ p 2 ..........
20010101 k k k k k t T ests u u u u u t T est Common Functions Y ou can use the f ollowing graph analysis functions after dr a wing a g r aph. • 1 (T) .
20010101 u u u u u 1-Sample t T est This test uses the hypothesis test for a single unkno wn population mean when the population standard deviation is unkno wn.
20010101 Calculation Result Output Example µ G 11.3 ...................... direction of test t ................................... t score p .................................. p-value o .................................. mean of sample x σ n -1 ....
20010101 u u u u u 2-Sample t T est 2-Sample t T est compares the population means when the population standard deviations are unknown. The 2-Sample t T est is applied to t -distribution.
20010101 The following shows the meaning of each item in the case of list data specification. Data ............................ data type µ 1 ........
20010101 Calculation Result Output Example µ 1 G µ 2 ........................... direction of test t ................................... t score p .................................. p-value df ................................. degrees of freedom o 1 .
20010101 u u u u u LinearReg t T est LinearReg t T est treats paired-v ar iab le data sets as ( x , y ) pairs , and uses the method of least squares to deter mine the most appropriate a , b coefficients of the data for the regression f or mula y = a + bx .
20010101 Calculation Result Output Example β G 0 & ρ G 0 .............. direction of test t ................................... t score p .................................. p-value df ................................. degrees of freedom a ......
20010101 k k k k k χ 2 T est χ 2 T est sets up a n umber of independent groups and tests h ypothesis related to the propor tion of the sample included in each group . The χ 2 T est is applied to dichotomous variab les (var iab le with tw o possible values , such as yes/no).
20010101 After setting all the parameters, align the cursor with [Execute] and then press one of the function k e ys shown below to perf orm the calculation or dr a w the g r aph. • 1 (CALC) ... P erforms the calculation. • 6 (DRA W) ... Draws the g r aph.
20010101 k k k k k 2-Sample F T est 2-Sample F T est tests the h ypothesis for the ratio of sample variances . The F T est is applied to the F distr ibution. F = x 1 n –1 2 σ x 2 n –1 2 σ Pe rf or m the f ollowing key operations from the statistical data list.
20010101 After setting all the parameters, align the cursor with [Execute] and then press one of the function k e ys shown below to perf orm the calculation or dr a w the g r aph. • 1 (CALC) ... P erf or ms the calculation. • 6 (DRA W) ... Draws the g r aph.
20010101 k k k k k ANO V A ANO V A tests the hypothesis that the population means of the samples are equal when there are multiple samples. One-W ay ANO V A is used when there is one independent v ar iable and one dependent variab le . Two - Wa y ANOV A is used when there are tw o independent variab les and one dependent variab le .
20010101 Calculation Result Output Example One-W ay ANO V A Line 1 (A) .................... Factor A df valu e, SS val ue , MS valu e, F value , p-value Line 2 (ERR) ............... Error df va lu e, SS val ue, MS va lue Tw o - W a y ANO V A Line 1 (A) .
20010101 k k k k k ANO V A (T w o-W a y) u u u u u Description The nearby tab le shows measurement results f or a metal product produced by a heat treatment process based on two treatment levels: time (A) and temper ature (B). The e xperiments were repeated twice each under identical conditions .
20010101 u u u u u Input Example u u u u u Results 1-2-25 T ests (TEST).
20010101 1-3 Confidence Interval (INTR) A confidence inter v al is a r ange (interv al) that includes a statistical value, usually the population mean. A confidence inter v al that is too broad makes it difficult to get an idea of where the population value (true value) is located.
20010101 u u u u u General Confidence Interval Precautions Inputting a value in the range of 0 < C-Level < 1 for the C-Le vel setting sets you value y ou input. Inputting a v alue in the r ange of 1 < C-Lev el < 100 sets a value equiv alent to your input divided by 100.
20010101 k k k k k Z Interval u u u u u 1-Sample Z Interval 1-Sample Z Interval calculates the confidence inter val f or an unknown population mean when the population standard deviation is kno wn. The following is the confidence interval. Left = o – Z α 2 σ n Right = o + Z α 2 σ n Ho w e ver , α is the le vel of significance.
20010101 After setting all the parameters, align the cursor with [Execute] and then press the function key shown belo w to perform the calculation. • 1 (CALC) ... P erforms the calculation. Calculation Result Output Example Left ....................
20010101 The following shows the meaning of each item in the case of list data specification. Data ............................ data type C-Le vel ........................ confidence level (0 < C-Lev el < 1) σ 1 ................................
20010101 u u u u u 1-Prop Z Interv al 1-Prop Z Interval uses the n umber of data to calculate the confidence inter val f or an unknown propor tion of successes. The following is the confidence interval. The v alue 100 (1 – α ) % is the confidence le vel.
20010101 u u u u u 2-Prop Z Interval 2-Prop Z Interval uses the n umber of data items to calculate the confidence interval for the defference between the proportion of successes in two populations. The following is the confidence interval. The v alue 100 (1 – α ) % is the confidence le vel.
20010101 Left .............................. inter v al lower limit (left edge) Right ............................ inter v al upper limit (r ight edge) ˆ p 1 ................................. estimated sample propotion for sample 1 ˆ p 2 ...........
20010101 o .................................. mean of sample x σ n -1 ............................. sample standard deviation ( x σ n -1 > 0) n ..
20010101 The following confidence interv al applies when pooling is not in effect. The v alue 100 (1 – α ) % is the confidence le vel. Left = ( o 1 – o 2 )– t df α 2 Right = ( o 1 – o 2 )+ t.
20010101 o 1 ................................. mean of sample 1 x 1 σ n -1 ............................ standard deviation ( x 1 σ n -1 > 0) of sample 1 n 1 ................................. size (positive integer) of sample 1 o 2 ...............
20010101 1-4 Distrib ution (DIST) There is a variety of diff erent types of distr ibution, b ut the most well-known is “normal distr ib ution, ” which is essential f or perfor ming statistical calculations.
20010101 u u u u u Common Distribution Functions After drawing a graph, you can use the P-CAL function to calculate an estimated p-value for a par ticular x va lu e. The following is the general procedure f or using the P-CAL function. 1. After dr awing a graph, press 1 (P-CAL) to display the x value input dialog bo x.
20010101 k k k k k Normal Distribution u u u u u Normal Probability Density Nor mal probability density calculates the probability density of nomal distribution from a specified x value. Nor mal probability density is applied to standard nor mal distribution.
20010101 u u u u u Normal Distribution Pr obability Nor mal distrib ution probability calculates the probability of nor mal distribution data f alling between two specific values. πσ 2 p = 1 e – dx 2 2 σ ( x – µ ) 2 µ a b ∫ a : lo w er boundar y b : upper boundar y Pe rf or m the f ollowing key operations from the statistical data list.
20010101 Calculation Result Output Example p .................................. nor mal distribution probability z:Low ........................... z:Low value (con ver ted to standardize z score for lower value) z:Up .
20010101 After setting all the parameters, align the cursor with [Execute] and then press the function key shown belo w to perform the calculation. • 1 (CALC) ... P erforms the calculation. Calculation Result Output Examples x ......................
20010101 k k k k k Student- t Distribution u u u u u Student- t Pr obability Density Student- t probability density calculates t probability density from a specified x va lu e. f ( x ) = Γ Γ df π – df + 1 2 2 df 2 df + 1 df x 2 1+ Pe rf or m the f ollowing key operations from the statistical data list.
20010101 u u u u u Student- t Distribution Pr obability Student- t distrib ution probability calculates the probability of t distr ib ution data f alling between two specific values.
20010101 Calculation Result Output Example p .................................. Student- t distrib ution probability t:Lo w ...........................
20010101 Calculation Result Output Example p .................................. χ 2 probability density # Current V -Window settings are used f or graph drawing when the SET UP screen's [Stat Wind] setting is [Manual]. The V - Window settings below are set automatically when the [Stat Wind] setting is [A uto].
20010101 u u u u u χ 2 Distrib ution Probability χ 2 distribution probability calculates the probability of χ 2 distribution data falling betw een two specific values. p = Γ 1 2 df df 2 x e dx 2 1 df 2 –1 x 2 – a b ∫ a :l ow er boundar y b : upper boundary Pe rf or m the f ollowing key operations from the statistical data list.
20010101 Calculation Result Output Example p .................................. χ 2 distribution probability k k k k k F Distrib ution u u u u u F Probability Density F probability density calculates the probability density function f or the F distr ib ution at a specified x va lu e.
20010101 Calculation Result Output Example p .................................. F probability density # V-Windo w settings f or graph dr awing are set automatically when the SET UP screen's [Stat Wind] setting is [A uto]. Current V - Window settings are used for graph drawing when the [Stat Wind] setting is [Manual].
20010101 u u u u u F Distribution Pr obability F distribution probability calculates the probability of F distr ib ution data falling between two specific values.
20010101 Calculation Result Output Example p .................................. F distribution probability 1-4-15 Distribution (DIST).
20010101 k k k k k Binomial Distribution u u u u u Binomial Probability Binomial probability calculates a probability at a specified value for the discrete binomial distr ib ution with the specified number of tr ials and probability of success on each trial.
20010101 Calculation Result Output Example p .................................. binomial probability u u u u u Binomial Cumulative Density Binomial cumulative density calculates a cumulative probability at a specified v alue f or the discrete binomial distribution with the specified number of tr ials and probability of success on each tr ial.
20010101 After setting all the parameters, align the cursor with [Execute] and then press the function key shown belo w to perform the calculation. • 1 (CALC) ... P erforms the calculation. Calculation Result Output Example p .......................
20010101 k k k k k Po isson Distribution u u u u u Po isson Probability Po isson probability calculates a probability at a specified value for the discrete P oisson distribution with the specified mean. f ( x ) = x! e – x µ µ ( x = 0, 1, 2, ···) µ :m ean ( µ > 0) Pe rf or m the f ollowing key operations from the statistical data list.
20010101 u u u u u P oisson Cumulative Density Po isson cumulativ e density calculates a cumulativ e probability at specified value for the discrete Poisson distribution with the specified mean. Pe rf or m the f ollowing key operations from the statistical data list.
20010101 k k k k k Geometric Distrib ution u u u u u Geometric Probability Geometr ic probability calculates the probability at a specified v alue, and the number of the trial on which the first success occurs, for the geometr ic distrib ution with a specified probability of success.
20010101 u u u u u Geometric Cumulative Density Geometr ic cumulativ e density calculates a cumulative probability at specified value , the nu mber of the trial on which the first success occurs, f or the discrete geometr ic distr ib ution with the specified probability of success.
An important point after buying a device Casio FX 1.0 PLUS (or even before the purchase) is to read its user manual. We should do this for several simple reasons:
If you have not bought Casio FX 1.0 PLUS yet, this is a good time to familiarize yourself with the basic data on the product. First of all view first pages of the manual, you can find above. You should find there the most important technical data Casio FX 1.0 PLUS - thus you can check whether the hardware meets your expectations. When delving into next pages of the user manual, Casio FX 1.0 PLUS you will learn all the available features of the product, as well as information on its operation. The information that you get Casio FX 1.0 PLUS will certainly help you make a decision on the purchase.
If you already are a holder of Casio FX 1.0 PLUS, but have not read the manual yet, you should do it for the reasons described above. You will learn then if you properly used the available features, and whether you have not made any mistakes, which can shorten the lifetime Casio FX 1.0 PLUS.
However, one of the most important roles played by the user manual is to help in solving problems with Casio FX 1.0 PLUS. Almost always you will find there Troubleshooting, which are the most frequently occurring failures and malfunctions of the device Casio FX 1.0 PLUS along with tips on how to solve them. Even if you fail to solve the problem, the manual will show you a further procedure – contact to the customer service center or the nearest service center
