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Casio CFX-9970G Manual

Casio CFX-9970G Manual

18. statistical graphs and calculations
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Download this manual See also: Programming Manual, Function Manual
Chapter
Statistical Graphs and
Calculations
This chapter describes how to input statistical data into lists, how
to calculate the mean, maximum and other statistical values, how
to perform various statistical tests, how to determine the confi-
dence interval, and how to produce a distribution of statistical
data. It also tells you how to perform regression calculations.
18-1
Before Performing Statistical Calculations
18-2
Paired-Variable Statistical Calculation Examples
18-3
Calculating and Graphing Single-Variable Statistical
Data
18-4
Calculating and Graphing Paired-Variable Statistical
Data
18-5
Performing Statistical Calculations
18-6
Tests
18-7
Confidence Interval
18-8
Distribution
Important!
• This chapter contains a number of graph screen shots. In each case, new
data values were input in order to highlight the particular characteristics of
the graph being drawn. Note that when you try to draw a similar graph, the
unit uses data values that you have input using the List function. Because of
this, the graphs that appears on the screen when you perform a graphing
operation will probably differ somewhat from those shown in this manual.
18

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Summary of Contents for Casio CFX-9970G

  • Page 1 Chapter Statistical Graphs and Calculations This chapter describes how to input statistical data into lists, how to calculate the mean, maximum and other statistical values, how to perform various statistical tests, how to determine the confi- dence interval, and how to produce a distribution of statistical data.

  • Page 2: Before Performing Statistical Calculations

    18-1 Before Performing Statistical Calculations In the Main Menu, select the STAT icon to enter the STAT Mode and display the statistical data lists. Use the statistical data lists to input data and to perform statistical calculations. Use f, c, d and e to move the highlighting around the lists.
  • Page 3 18-2 Paired-Variable Statistical Calculation Examples Once you input data, you can use it to produce a graph and check for tendencies. You can also use a variety of different regression calculations to analyze the data. Example To input the following two data groups and perform statistical calculations 0.5, 1.2, 2.4, 4.0, 5.2 –2.1, 0.3, 1.5, 2.0, 2.4...
  • Page 4 18 - 2 Paired-Variable Statistical Calculation Examples While the statistical data list is on the display, perform the following procedure. !Z2(Man) J(Returns to previous menu.) • It is often difficult to spot the relationship between two sets of data (such as height and shoe size) by simply looking at the numbers.
  • Page 5 18 - 2 Paired-Variable Statistical Calculation Examples • Note that the StatGraph1 setting is for Graph 1 (GPH1 of the graph menu), StatGraph2 is for Graph 2, and StatGraph3 is for Graph 3. 2. Use the cursor keys to move the highlighting to the graph whose status you want to change, and press the applicable function key to change the status.
  • Page 6 18 - 2 Paired-Variable Statistical Calculation Examples u u u u u To display the general graph settings screen [GRPH]-[SET] Pressing 6 (SET) displays the general graph settings screen. • The settings shown here are examples only. The settings on your general graph settings screen may differ.
  • Page 7 18 - 2 Paired-Variable Statistical Calculation Examples u u u u u Graph Color (graph color specification) • {Blue}/{Orng}/{Grn} ... {blue}/{orange}/{green} u u u u u Outliers (outliers specification) • {On}/{Off} ... {display}/{non-display} k k k k k Drawing an Line Graph P.254 Paired data items can be used to plot a scatter diagram.
  • Page 8 18 - 2 Paired-Variable Statistical Calculation Examples k k k k k Displaying Statistical Calculation Results Whenever you perform a regression calculation, the regression formula parameter (such as in the linear regression ) calculation results appear on the display. You can use these to obtain statistical calculation results. Regression parameters are calculated as soon as you press a function key to select a regression type while a graph is on the display.
  • Page 9 18 - 3 Calculating and Graphing Single-Variable Statistical Data 18-3 Calculating and Graphing Single-Variable Statistical Data Single-variable data is data with only a single variable. If you are calculating the average height of the members of a class for example, there is only one variable (height).
  • Page 10 18 - 3 Calculating and Graphing Single-Variable Statistical Data To plot the data that falls outside the box, first specify “MedBox” as the graph type. Then, on the same screen you use to specify the graph type, turn the outliers item “On”, and draw the graph.
  • Page 11 18 - 3 Calculating and Graphing Single-Variable Statistical Data k k k k k Line Graph P.254 A line graph is formed by plotting the data in one list against the frequency of (Graph Type) each data item in another list and connecting the points with straight lines. (Brkn) Calling up the graph menu from the statistical data list, pressing 6 (SET), changing the settings to drawing of a line graph, and then drawing a graph creates...
  • Page 12 18 - 3 Calculating and Graphing Single-Variable Statistical Data minX ....minimum Q1 ....first quartile Med ....median Q3 ....third quartile .... – data mean – population standard deviation .... data mean + population standard deviation maxX ....maximum Mod ....
  • Page 13 18-4 Calculating and Graphing Paired-Variable Statistical Data Under “Plotting a Scatter Diagram,” we displayed a scatter diagram and then performed a logarithmic regression calculation. Let’s use the same procedure to look at the various regression functions. k k k k k Linear Regression Graph P.254 Linear regression plots a straight line that passes close to as many data points as possible, and returns values for the slope and...
  • Page 14 18 - 4 Calculating and Graphing Paired-Variable Statistical Data 6(DRAW) a ..Med-Med graph slope b ..Med-Med graph intercept k k k k k Quadratic/Cubic/Quartic Regression Graph P.254 A quadratic/cubic/quartic regression graph represents connection of the data points of a scatter diagram. It actually is a scattering of so many points that are close enough together to be connected.
  • Page 15 18 - 4 Calculating and Graphing Paired-Variable Statistical Data k k k k k Logarithmic Regression Graph P.254 Logarithmic regression expresses as a logarithmic function of . The standard logarithmic regression formula is , so if we say that X = In , the formula corresponds to linear regression formula 6(g)1(Log)
  • Page 16 18 - 4 Calculating and Graphing Paired-Variable Statistical Data k k k k k Power Regression Graph P.254 Exponential regression expresses as a proportion of the power of . The standard power regression formula is , so if we take the logarithms of both sides we get In = In .
  • Page 17 18 - 4 Calculating and Graphing Paired-Variable Statistical Data 6(DRAW) Gas bills, for example, tend to be higher during the winter when heater use is more frequent. Periodic data, such as gas usage, is suitable for application of sine regression. Example To perform sine regression using the gas usage data shown below...
  • Page 18 18 - 4 Calculating and Graphing Paired-Variable Statistical Data Execute the calculation and produce sine regression analysis results. 1(CALC) Display a sine regression graph based on the analysis results. 6(DRAW) k k k k k Residual Calculation Actual plot points ( -coordinates) and regression model distance can be calcu- lated during regression calculations.
  • Page 19 18 - 4 Calculating and Graphing Paired-Variable Statistical Data • Use c to scroll the list so you can view the items that run off the bottom of the screen...... mean of List data ....sum of List data ....
  • Page 20 18 - 4 Calculating and Graphing Paired-Variable Statistical Data k k k k k Multiple Graphs You can draw more than one graph on the same display by using the procedure P.252 under “Changing Graph Parameters” to set the graph draw (On)/non-draw (Off) status of two or all three of the graphs to draw “On”, and then pressing 6 (DRAW).

  • Page 21: Performing Statistical Calculations

    18-5 Performing Statistical Calculations All of the statistical calculations up to this point were performed after displaying a graph. The following procedures can be used to perform statistical calculations alone. u u u u u To specify statistical calculation data lists You have to input the statistical data for the calculation you want to perform and specify where it is located before you start a calculation.
  • Page 22 18 - 5 Performing Statistical Calculations Now you can use the cursor keys to view the characteristics of the variables. For details on the meanings of these statistical values, see “Displaying Single- P.259 Variable Statistical Results”. k k k k k Paired-Variable Statistical Calculations In the previous examples from “Linear Regression Graph”...
  • Page 23 18 - 5 Performing Statistical Calculations k k k k k Estimated Value Calculation ( , ) After drawing a regression graph with the STAT Mode, you can use the RUN Mode to calculate estimated values for the regression graph's parameters.
  • Page 24 18 - 5 Performing Statistical Calculations k k k k k Probability Distribution Calculation and Graphing You can calculate and graph probability distributions for single-variable statistics. u u u u u Probability distribution calculations Use the RUN Mode to perform probability distribution calculations. Press K in the RUN Mode to display the option number and then press 6 (g) 3 (PROB) 6 (g) to display a function menu, which contains the following items.
  • Page 25 18 - 5 Performing Statistical Calculations 2. Use the STAT Mode to perform the single-variable statistical calculations. 2(CALC)6(SET) c3(List2)J1(1VAR) 3. Press m to display the Main Menu, and then enter the RUN Mode. Next, press K to display the option menu and then 6 (g) 3 (PROB) 6 (g). •...
  • Page 26 18 - 5 Performing Statistical Calculations k k k k k Probability Graphing You can graph a probability distribution with Graph Y = in the Sketch Mode. Example To graph probability P(0.5) Perform the following operation in the RUN Mode. !4(Sketch)1(Cls)w 5(GRPH)1(Y=)K6(g)3(PROB) 6(g)1(P()a.f)w...
  • Page 27 18-6 Tests 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. testing is used for market research and public opinion research that need to be performed repeatedly.
  • Page 28 18 - 6 Tests 2-Sample Test tests the hypothesis that there will be no change in the result for a population when a result of a sample is composed of multiple factors and one or more of the factors is removed. It could be used, for example, to test the carcino- genic effects of multiple suspected factors such as tobacco use, alcohol, vitamin deficiency, high coffee intake, inactivity, poor living habits, etc.

  • Page 29: Table Of Contents

    18 - 6 Tests The following shows the meaning of each item in the case of list data specifica- tion. Data ....data type ..... population mean value test conditions (“G ” specifies two-tail test, “< ” specifies lower one-tail test, “> ”...

  • Page 30: Data

    18 - 6 Tests Perform the following key operation from the statistical result screen. J(To data input screen) cccccc(To Execute line) 6(DRAW) u u u u u 2-Sample Z Test This test is used when the sample standard deviations for two populations are known to test the hypothesis that the population means of the two populations are equal.

  • Page 31: Different From List Data Specification

    18 - 6 Tests The following shows the meaning of parameter data specification items that are different from list data specification..... sample 1 mean ....sample 1 size (positive integer) ....sample 2 mean ....sample 2 size (positive integer) Example To perform a 2-Sample Test when two lists of data are input...

  • Page 32: Sample Size

    18 - 6 Tests u u u u u 1-Prop Z Test This test is used to test whether data that satisfies certain criteria reaches a specific proportion. It tests the hypothesis when sample size and the number of data satisfying the criteria are specified. The 1-Prop Test is applied to standard normal distribution.
  • Page 33 18 - 6 Tests The following key operation can be used to draw a graph. cccc 6(DRAW) u u u u u 2-Prop Z Test This test is used to compare the proportions of two samples that satisfy certain criteria. It tests the hypothesis that the size and the number of data of two samples that satisfy the criteria are as specified.
  • Page 34 18 - 6 Tests 3(>)c ccfw daaw cdaw daaw 1(CALC) > ....direction of test ...... score ..... p-value ˆ p ....estimated proportion of population 1 ˆ p ....estimated proportion of population 2 ˆ p ..... estimated sample proportion ....
  • Page 35 18 - 6 Tests The following shows the meaning of each item in the case of list data specification. Data ....data type ..... population mean value test conditions (“G ” specifies two- tail test, “< ” specifies lower one-tail test, “> ”...
  • Page 36 18 - 6 Tests u u u u u 2-Sample t Test 2-Sample Test uses the sample means, variance, and sample sizes when the sample standard deviations for two populations are unknown to test the hypoth- esis that the two samples were taken from the same population. The 2-Sample Test is applied to standard normal distribution.
  • Page 37 18 - 6 Tests The following shows the meaning of each item in the case of list data specifica- tion. Data ....data type ....sample mean value test conditions (“G ” specifies two-tail test, “< ” specifies one-tail test where sample 1 is smaller than sample 2, “>...
  • Page 38 18 - 6 Tests ....direction of test ...... -value ..... p-value ....degrees of freedom ....sample 1 mean ....sample 2 mean ....sample 1 standard deviation ....sample 2 standard deviation ....sample 1 size ....sample 2 size Perform the following key operation to display a graph.
  • Page 39 18 - 6 Tests The following shows the meaning of each item in the case of list data specifica- tion. & ....p-value test conditions (“G 0” specifies two-tail test, “< 0” specifies lower one-tail test, “> 0” specifies upper one-tail test.) XList ....
  • Page 40 18 - 6 Tests k k k k k Other Tests u u u u u Test Test sets up a number of independent groups and tests hypotheses related to the proportion of the sample included in each group. The Test is applied to dichotomous variables (variable with two possible values, such as yes/no).
  • Page 41 18 - 6 Tests ....value ..... p-value ....degrees of freedom Expected ..expected counts (Result is always stored in MatAns.) The following key operation can be used to display the graph. 6(DRAW) u u u u u 2-Sample F Test 2-Sample Test tests the hypothesis that when a sample result is composed of multiple factors, the population result will be unchanged when one or some of the...
  • Page 42 18 - 6 Tests The following shows the meaning of parameter data specification items that are different from list data specification....sample 1 standard deviation ( > 0) ....sample 1 size (positive integer) ....sample 2 standard deviation ( >...
  • Page 43 18 - 6 Tests u u u u u Analysis of Variance (ANOVA) ANOVA tests the hypothesis that when there are multiple samples, the means of the populations of the samples are all equal. : number of populations : mean of each list : standard deviation of each MS = list...
  • Page 44 18 - 6 Tests 2(3)c 1(List1)c 2(List2)c 3(List3)c 1(CALC) ..... value ..... p-value ....pooled sample standard deviation ....numerator degrees of freedom ....factor sum of squares ....factor mean squares ....denominator degrees of freedom ....error sum of squares ....

  • Page 45: Confidence Interval

    18 - 8 Confidence Interval 18-7 Confidence Interval A confidence interval is a range (interval) that includes the population mean value. 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 possible to obtain reliable results.
  • Page 46 18 - 7 Confidence Interval k k k k k Z Confidence Interval You can use the following menu to select from the different types of confidence interval. • {1-S}/{2-S}/{1-P}/{2-P} ... {1-Sample}/{2-Sample}/{1-Prop}/{2-Prop} Interval u u u u u 1-Sample Z Interval 1-Sample Interval calculates the confidence interval when standard deviation is known.
  • Page 47 18 - 7 Confidence Interval Example To calculate the 1-Sample Interval for one list of data For this example, we will obtain the Interval for the data {11.2, 10.9, 12.5, 11.3, 11.7}, when C-Level = 0.95 (95% confi- dence level) and = 3.
  • Page 48 18 - 7 Confidence Interval ....population standard deviation of sample 1 ( > 0) ....population standard deviation of sample 2 ( > 0) List1 ....list whose contents you want to use as sample 1 data List2 ....list whose contents you want to use as sample 2 data Freq1 ....
  • Page 49 18 - 7 Confidence Interval u u u u u 1-Prop Z Interval 1-Prop Interval uses the number of data to calculate the confidence interval when the proportion is not known. The 1-Prop Interval is applied to standard normal distribution. The following is the confidence interval.
  • Page 50 18 - 7 Confidence Interval u u u u u 2-Prop Z Interval 2-Prop Z Interval calculates the confidence interval when the proportions of two samples are known. The 2-Prop Z Interval is applied to standard normal distribu- tion. The following is the confidence interval. : sample size 1–...
  • Page 51 18 - 7 Confidence Interval ˆ p ....expected p-value 1 ˆ p ....expected p-value 2 ....sample 1 size ....sample 2 size k k k k k t Confidence Interval You can use the following menu to select from two types of confidence interval.
  • Page 52 18 - 7 Confidence Interval Example To calculate the 1-Sample Interval for one list of data For this example, we will obtain the 1-Sample Interval for data = {11.2, 10.9, 12.5, 11.3, 11.7} when C-Level = 0.95. 1(List)c a.jfw 1(List1)c 1(1)c 1(CALC) Left ....
  • Page 53 18 - 7 Confidence Interval Perform the following key operation from the statistical data list. 4(INTR) 2(2-S) 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) List1 ....
  • Page 54 18 - 7 Confidence Interval Example To calculate the 2-Sample Interval when two lists of data are input For this example, we will obtain the 2-Sample Interval for data 1 = {55, 54, 51, 55, 53, 53, 54, 53} and data 2 = {55.5, 52.3, 51.8, 57.2, 56.5} without pooling when C-Level = 0.95.
  • Page 55 18-8 Distribution 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 occur- rences of mean data (highest frequency), with the frequency decreasing as you move away from the center.
  • Page 56 18 - 8 Distribution k k k k k Normal Distribution You can use the following menu to select from the different types of calculation. • {Npd}/{Ncd}/{InvN} ... {normal probability density}/{normal distribution probability}/{inverse cumulative normal distribution} calculation u u u u u Normal probability density Normal probability density calculates the probability that data taken from a normal distribution is less than a specific value.
  • Page 57 18 - 8 Distribution Perform the following key operation to display a graph. 6(DRAW) u u u u u Normal distribution probability Normal distribution probability calculates the probability of normal distribution data falling between two specific values. : lower boundary (x –...
  • Page 58 18 - 8 Distribution • This calculator performs the above calculation using the following: = 1E99, – = –1E99 u u u u 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. f (x)dx = p Specify the probability and use this formula to obtain the integration interval.
  • Page 59 18 - 8 Distribution k k k k k Student-t Distribution You can use the following menu to select from the different types of Student- distribution. • {tpd}/{tcd} ... {Student- probability density}/{Student- distribution probability} calculation u u u u u Student-t probability density Student- probability density calculates whether data taken from a distribution is...
  • Page 60 18 - 8 Distribution Perform the following key operation to display a graph. 6(DRAW) u u u u u Student-t distribution probability Student- distribution probability calculates the probability of distribution data falling between two specific values. : lower boundary df + 1 df +1 –...
  • Page 61 18 - 8 Distribution k k k k k Chi-square Distribution You can use the following menu to select from the different types of chi-square distribution. • {Cpd}/{Ccd} ... { probability density}/{ distribution probability} calculation u u u u u probability density probability density calculates whether data taken from a distribution is less...
  • Page 62 18 - 8 Distribution Perform the following key operation to display a graph. 6(DRAW) u u u u u distribution probability distribution probability calculates the probability of distribution data falling between two specific values. : lower boundary –1 – : upper boundary Perform the following key operation from the statistical data list.
  • Page 63 18 - 8 Distribution k k k k k F Distribution You can use the following menu to select from the different types of distribution. • {Fpd}/{Fcd} ... { probability density}/{ distribution probability} calculation u u u u u F probability density probability density calculates whether data taken from a distribution is less than a specific value.
  • Page 64 18 - 8 Distribution u u u u u F distribution probability distribution probability calculates the probability of distribution data falling between two specific values. : lower boundary n + d n + d : upper boundary – –1 Perform the following key operation from the statistical data list. 5(DIST) 4(F) 2(Fcd)
  • Page 65 18 - 8 Distribution u u u u u Binomial probability Binomial probability calculates whether data taken from a binomial distribution is less than a specific value. n) p = 0, 1, ·······, : success probability n – x f (x) = (1–p) (0 <...
  • Page 66 18 - 8 Distribution u u u u u Binomial cumulative density Binomial cumulative density calculates the probability of binomial distribution data falling between two specific values. Perform the following key operation from the statistical data list. 5(DIST) 5(BINM) 2(Bcd) The following shows the meaning of each item when data is specified using list specification.
  • Page 67 18 - 8 Distribution k k k k k Poisson Distribution You can use the following menu to select from the different types of Poisson distribution. • {Ppd}/{Pcd} ... {Poisson probability}/{Poisson cumulative density} calculation u u u u u Poisson probability Poisson probability calculates whether data taken from a Poisson distribution is less than a specific value.
  • Page 68 18 - 8 Distribution u u u u u Poisson cumulative density Poisson cumulative density calculates the probability of Poisson distribution data falling between two specific values. Perform the following key operation from the statistical data list. 5(DIST) 6(g) 1(POISN) 2(Pcd) The following shows the meaning of each item when data is specified using list specification.
  • Page 69 18 - 8 Distribution u u u u u Geometric probability Geometric probability calculates whether data taken from a geometric distribution is less than a specific value. = 1, 2, 3, ···) x – 1 f (x) = p(1– p) Perform the following key operation from the statistical data list.
  • Page 70 18 - 8 Distribution u u u u u Geometric cumulative density Geometric cumulative density calculates the probability of geometric distribution data falling between two specific values. Perform the following key operation from the statistical data list. 5(DIST) 6(g) 2(GEO) 2(Gcd) The following shows the meaning of each item when data is specified using list specification.

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