# Frequency Tables. Chapter 500. Introduction. Frequency Tables. Types of Categorical Variables. Data Structure. Missing Values

Save this PDF as:

Size: px
Start display at page:

Download "Frequency Tables. Chapter 500. Introduction. Frequency Tables. Types of Categorical Variables. Data Structure. Missing Values"

## Transcription

1 Chapter 500 Introduction This procedure produces tables of frequency counts and percentages for categorical and continuous variables. This procedure serves as a summary reporting tool and is often used to analyze survey data. This procedure also calculates the multinomial chi-square test. Frequency tables are generally produced on individual variables. For categorical data, the table records the number of observations (the frequency) for each unique value of the variable. For continuous data, you must specify a set of intervals (or bins). The frequency table records the number of observations falling in each interval. Frequency tables are useful for analyzing categorical data and for screening data for data entry errors. Types of Categorical Variables Note that we will refer to two types of categorical variables: Categorical and Grouping or Break. Grouping variables are used to split a database into subgroups. A separate set of reports is generated for each unique set of values of the Grouping variables. The values of a Categorical variable are used to define the rows of the frequency table. Data Structure The data below are a subset of the real estate sales (Resale) dataset provided with the software. This data gives the selling price, the number of bedrooms, the total square footage (finished and unfinished), and the size of the lots for 150 residential properties sold during the last four months in two states. Only the first 8 of the 150 observations are displayed. Resale dataset (subset) State Price Bedrooms TotalSqft LotSize Nev Nev Vir Nev Nev Missing Values Missing values may be ignored or included in the table s counts and percentages

2 Procedure Options This section describes the options available in this procedure. To find out more about using a procedure, turn to the Procedures chapter. Variables Tab This panel specifies the variables or data that will be used in the analysis. Type of Data Input Select the source of the data to analyze. The choices are Column(s) in the Database Data, titles, and labels will be read from the Data Table on the Data Window using the selected variable(s). Specify at least one variable to be used to create the frequency table. The unique values in each variable will form the rows of the tables. If more than one variable is specified, a separate frequency table will be generated for each of the variables. If requested, a combined table will be generated for all variables together. Two types of variables may be specified: Categorical Variables and Numeric Variables. Usually, you will enter categorical variables. 1. Categorical Variables Categorical variables may include text values (e.g. Male, Female ) or index numbers (e.g. 1, 4, 7, 15 to represent 4 states). The numbers or categories may be ordinal (e.g. Low, Medium, High or 1, 2, 3, 4, 5 as in a Likert scale). 2. Numeric Variables Since frequency tables display categorical data, all numeric variables with continuous data must be grouped into categories by the procedure using user-specified rules before the table is created. To enter this type of variable, you must first put a check by Create Other Categorical Variables from Numeric Data to display the numeric variable entry box. You can specify groups by entering the numeric boundaries directly (e.g. Under 21, 21 to 55, and Over 55 ) or by entering the number of intervals to create, the minimum boundary, and/or the interval width. You can only specify a single grouping rule that will be used for all numeric variables. If you have more than one numeric variable, you should group the data directly on the dataset using a Recode Transformation and enter the resulting variables as a categorical variable. Table of Counts Summarized count data, titles, and labels will be read directly from a table on this input window. Frequency Table Variables (Database Input) Categorical Variables Specify one or more categorical variables for use in table columns. Each unique value in each variable will result in a separate column in the table. The data values themselves may be text (e.g. Low, Med, High ) or numeric (e.g. 1, 2, 3 ), but the data as a whole should be categorical. If more than one variable is entered, a separate frequency table will be created for each variable. The data values in each variable will be sorted alpha-numerically before the table columns are created. If you want the values to be displayed in a different order, specify a custom value order for the data variable using the Column Info Table on the Data Window

3 Create Other Categorical Variables from Numeric Data Check this box to create tables with columns from numeric data. When checked, additional options will be displayed to specify how the numeric data will be classified into categorical variables. If you choose to create categorical variables from numeric data, you do not have to enter a categorical variable in the input box above (but you can). If both numeric and categorical variables are entered, a separate table and analysis will be given for each variable. Numeric Variable(s) to Group into Categories Specify one or more variables that have only numeric values to be used in columns of the table. Numeric values from these variables will be combined into a set of categories using the categorization options that follow. If more than one variable is entered, a separate table will be created for each variable. For example, suppose you want to tabulate a variable containing individual income values into four categories: Below 10000, to 40000, to 80000, and Over You could select the income variable here, set Group Numeric Data Using to List of Interval Upper Limits and set the List to Group Numeric Data Using Choose the method by which numeric data will be combined into categories for use in table columns. The choices are: Number of Intervals, Minimum, and/or Width This option allows you to specify the categories by entering any combination of the three parameters: Number of Intervals Minimum Width All three are optional. Number of Intervals This is the number of intervals into which the values of the numeric variables are categorized. If not enough intervals are specified to reach past the maximum data value, more will be added. Range Integer 2 Minimum This value is used in conjunction with the Number of Intervals and Width values to construct a set of intervals into which the numeric variables are categorized. This is the minimum value of the first interval. Range This value must be less than the minimum data value. Width This value is used in conjunction with the Number of Intervals and Minimum values to construct a set of intervals into which the numeric variables are categorized. All intervals will have a width equal to this value. A data value X is in this interval if Lower Limit < X Upper Limit

4 List of Interval Upper Limits This option allows you to specify the categories for the numeric variable by entering a list of interval boundaries directly, separated by blanks or commas. An interval of the form L1 < X L2 is generated for each interval. The actual number of intervals is one more than the number of items specified here. For example, suppose you want to tabulate a variable containing individual income values into four categories: Below 10000, to 40000, to 80000, and Over You would set List of Interval Upper Limits to Note that would be included in the Below interval, but not the to interval. Also, would be included in the to interval, not the Over interval. Frequency (Count) Variable (Database Input) Frequency Variable This optional variable specifies the number of observations that each row represents. When omitted, each row represents a single observation. If your data is the result of previous summarization, you may want certain rows to represent several observations. Note that negative values are treated as a zero weight and are omitted. Fractional values may be used. This option is used when you want to enter previously tabulated data for a multinomial test. Grouping (Break) Variables (Database Input) Number of Grouping Variables Select the number of grouping (break) variables to include for the analysis. All reports and plots will be generated for each unique combination of the values of the grouping variables. You can select up to 8 grouping variables. Grouping Variable Select an optional categorical grouping (or break) variable. All tables, statistical reports, and plots will be generated for each unique value of this variable. If you specify more than one grouping variable, the tables, statistical reports, and plots will generated for each unique combination of the values of the variables chosen. Two-Way Table (Table of Counts Input) Number of Categories (Rows) in the Table Select the number of categories (or rows) in the table. All or Blank When All is entered or this option is left blank, you may enter up to 100 categories in the table. Only rows up to the last row with counts will be analyzed. Number of Variables (Columns) in the Table Select the number of variables (or columns) in the table. A separate frequency table and multinomial test is output for each variable. All variables are combined in the other tables and plots. All or Blank When All is entered or this option is left blank, you may enter up to 100 variables in the table. Only columns up to the last column with counts will be analyzed

5 Table of Counts Enter variable titles, category labels, and counts directly into this table. Enter the titles in the cells on the top row with a faint yellow background. These are bolded automatically. Enter the category labels in the cells in the first column with a faint blue background. These are bolded automatically. Enter counts in the cells with a white background. Cells left empty are treated as zeros. Click the Reset Table button below to reset the table. When resetting the table, the number of categories and variables does not change. Missing Values Tab This panel lets you specify up to five missing values (besides the default of blank). For example, 0, 9, or NA may be missing values in your database. Missing Value Options Missing Value Inclusion Specify whether to include or exclude observations with missing values in the tables and/or reports. Possible selections are: Delete All This option indicates that you want the missing values totally ignored. Include in Counts This option indicates that you want the number of missing values displayed, but you do not want them to influence any of the percentages. All percentages related to missing values are given the value of 0. Include in All This option indicates that you want the missing values treated just like any other category. They will be included in all percentages and counts. Label for Missing Values Specify the label to be used to label missing values in the output. Data Values to be Treated as Missing Missing Value Specify a value to be treated as a missing value by this procedure. This value is treated as a missing value in all active categorical variables. Up to 5 different missing values may be entered

6 Reports Tab These options control which of the available reports and plots are displayed. Select Reports Frequency Table Report Check to display a frequency table for each variable. Multinomial Test Indicate whether to calculate the multinomial test for each variable. Select Reports Expected Values for the Multinomial Test Expected Values The multinomial test is a test of the proportions associated with a frequency table. In order to run the test, you need a set of hypothesized proportions. This box lets you enter these proportions. There are two ways of specifying the hypothesized proportions. First, you can leave it blank to indicate that you want to test whether the proportions in the frequency table are all equal. This is the same as entering 1,1,1,1,1,1 (if the variable has six or fewer categories). Second, you can enter a set of values separated by commas. These values are then rescaled so that they sum to one. For example, the entry 1,1,1,1 would be rescaled to 0.25, 0.25, 0.25, If you enter more numbers than are needed for a particular table, the extras are ignored. If you do not enter enough numbers, the remaining proportions are set to zero. Individual Tables Counts Table Table Percentages Table Specify whether to display this table. Each variable represents a separate column on the table. Combined Table Show Combined Table Specify whether to display a combined table with counts and percentages together. Combined Table Items on Table Counts... Table Percents Specify whether to display these items on the combined table

7 Report Options Tab The following options control the format of the reports. Report Options Variable Names Specify whether to use variable names, variable labels, or both to label output reports. In this discussion, the variables are the columns of the data table. Names Variable names are the column headings that appear on the data table. They may be modified by clicking the Column Info button on the Data window or by clicking the right mouse button while the mouse is pointing to the column heading. Labels This refers to the optional labels that may be specified for each column. Clicking the Column Info button on the Data window allows you to enter them. Both Both the variable names and labels are displayed. Comments 1. Most reports are formatted to receive about 12 characters for variable names. 2. Variable Names cannot contain blanks or math symbols (like + - * /.,), but variable labels can. Value Labels Value Labels are used to make reports more legible by assigning meaningful labels to numbers and codes. The options are Data Values All data are displayed in their original format, regardless of whether a value label has been set or not. Value Labels All values of variables that have a value label variable designated are converted to their corresponding value label when they are output. This does not modify their value during computation. Both Both data value and value label are displayed. Example A variable named GENDER (used as a grouping variable) contains 1 s and 2 s. By specifying a value label for GENDER, the report can display Male instead of 1 and Female instead of 2. This option specifies whether (and how) to use the value labels

8 Table Formatting Column Justification Specify whether data columns in the tables will be left or right justified. Column Widths Specify how the widths of columns in the tables will be determined. The options are Autosize to Minimum Widths Each data column is individually resized to the smallest width required to display the data in the column. This usually results in columns with different widths. This option produces the most compact table possible, displaying the most data per page. Autosize to Equal Minimum Width The smallest width of each data column is calculated and then all columns are resized to the width of the widest column. This results in the most compact table possible where all data columns have the same with. This is the default setting. Custom (User-Specified) Specify the widths (in inches) of the columns directly instead of having the software calculate them for you. Custom Widths (Single Value or List) Enter one or more values for the widths (in inches) of columns in the tables. This option is only displayed if Column Widths is set to Custom (User-Specified). Single Value If you enter a single value, that value will be used as the width for all data columns in the table. List of Values Enter a list of values separated by spaces corresponding to the widths of each column. The first value is used for the width of the first data column, the second for the width of the second data column, and so forth. Extra values will be ignored. If you enter fewer values than the number of columns, the last value in your list will be used for the remaining columns. Type the word Autosize for any column to cause the program to calculate it's width for you. For example, enter 1 Autosize 0.7 to make column 1 be 1 inch wide, column 2 be sized by the program, and column 3 be 0.7 inches wide. Wrap Column Headings onto Two Lines Check this option to make column headings wrap onto two lines. Use this option to condense your table when your data are spaced too far apart because of long column headings

9 Decimal Places Item Decimal Places These decimal options allow the user to specify the number of decimal places for items in the output. Your choice here will not affect calculations; it will only affect the format of the output. Auto If one of the Auto options is selected, the ending zero digits are not shown. For example, if Auto (0 to 7) is chosen, is displayed as is displayed as The output formatting system is not designed to accommodate Auto (0 to 13), and if chosen, this will likely lead to lines that run on to a second line. This option is included, however, for the rare case when a very large number of decimals is needed. Omit Percent Sign after Percentages The program normally adds a percent sign, %, after each percentage. Checking this option will cause this percent sign to be omitted. Plots Tab Select Plots Counts Plot... Table Percentages Plot Check each plot that is to be displayed. Click the plot format button to change the plot settings

10 Example 1 Standard The data for this example are found in the Resale dataset. You may follow along here by making the appropriate entries or load the completed template Example 1 by clicking on Open Example Template from the File menu of the window. 1 Open the Resale dataset. From the File menu of the NCSS Data window, select Open Example Data. Click on the file Resale.NCSS. Click Open. 2 Open the window. Using the Analysis menu or the Procedure Navigator, find and select the procedure. On the menus, select File, then New Template. This will fill the procedure with the default template. 3 Specify the variables. Select the Variables tab. For Type of Data Input select Column(s) in the Database. Double-click in the Categorical Variables text box. This will bring up the variable selection window. Select State and City from the list of variables and then click Ok. State-City will appear in the Categorical Variables box. 4 Specify the report format. Click on the Report Options tab. In Variable Names, select Labels. In Value Labels, select Value Labels. 5 Run the procedure. From the Run menu, select Run Procedure. Alternatively, just click the green Run button. Output Frequency Distribution of State Cumulative Cumulative Graph of State Count Count Percent Percent Percent Nevada % 58.67% Virginia % % Frequency Distribution of City Cumulative Cumulative Graph of Community Count Count Percent Percent Percent Silverville % 18.00% Los Wages % 50.67% Red Gulch % 58.67% Politicville % 76.67% Senate City % 92.67% Congresstown % % This report presents the counts (the frequencies), percentages, and a rough bar graph of the data. Note that the bar graph is constructed so that each is worth 2.5 percentage points

11 Example 2 Multinomial Test Suppose we want to test whether the proportion for Nevada is 50% higher than that for Virginia. The data for this example are found in the Resale dataset. You may follow along here by making the appropriate entries or load the completed template Example 2 by clicking on Open Example Template from the File menu of the Frequency Tables window. 1 Open the Resale dataset. From the File menu of the NCSS Data window, select Open Example Data. Click on the file Resale.NCSS. Click Open. 2 Open the window. Using the Analysis menu or the Procedure Navigator, find and select the procedure. On the menus, select File, then New Template. This will fill the procedure with the default template. 3 Specify the variables. Select the Variables tab. For Type of Data Input select Column(s) in the Database. Double-click in the Categorical Variables text box. This will bring up the variable selection window. Select State from the list of variables and then click Ok. State will appear in the Variables box. 4 Specify the reports. Click on the Reports tab. Check the Frequency Table Report box. Check the Multinomial Test Report box. In the Expected Values for Multinomial Test box, enter 60, Specify the report format. Click on the Report Options tab. In Variable Names, select Labels. In Value Labels, select Value Labels. 6 Run the procedure. From the Run menu, select Run Procedure. Alternatively, just click the green Run button. Output Frequency Distribution of State Cumulative Cumulative Graph of State Count Count Percent Percent Percent Nevada % 58.67% Virginia % % Multinomial Test of State Expected Actual Expected Chi-Square State Count Count Percent Percent Amount Nevada % 60.00% Virginia % 40.00% Chi-Square = with df = 1 Probability Level = The first table is the standard frequency table. The second table presents the results of the multinomial test. Note that in this case, the test is not significant

12 Count The number of observations (rows) in which the variable has the value reported on this line. This is the value of O i. Expected Count The number of observations (rows) that would be obtained if the hypothesized proportions were followed exactly. This is the value of E i. Actual Percent The percent that this category is of the total. Expected Percent The percentage that this category would have if the hypothesized proportions were followed exactly. Chi-Square Amount The amount that this line contributes to the Chi-square statistic. This is equal to CS i = ( O E ) where O i is the actual count and E i is the expected count of the i th category. Chi-Square This is the value of the chi-square test statistic. i E i i 2 ( ) k 2 2 Oi Ei χ k 1 = i= 1 Ei df The degrees of freedom of the above test statistic. This is equal to the number of categories minus one. Probability Level This is the significance level of the multinomial test. If you are testing at an alpha of 0.05, you would reject the null hypothesis that the hypothesized proportions are true if this value is less than

13 Example 3 and Multinomial Tests from Summary Data Using the same variables and data as in Example 2, an alternate way to enter the data for this procedure is to enter the counts for each category directly. This is done by setting Type of Data Input to Table of Counts. You may follow along here by making the appropriate modifications to the current settings or load the completed template Example 3 by clicking on Open Example Template from the File menu of the window. 1 Open the window. Using the Analysis menu or the Procedure Navigator, find and select the procedure. On the menus, select File, then New Template. This will fill the procedure with the default template. 2 Specify the variables. Select the Variables tab. For Type of Data Input select Table of Counts. For Categories (Rows) enter 2. For Variables (Columns) enter 1. In the Table of Counts, enter Nevada and Virginia as the Category Labels, State as the Variable Name, and 88 and 62 as the cell counts. 3 Specify the reports. Click on the Reports tab. Check the Frequency Table Report box. Check the Multinomial Test Report box. In the Expected Values for Multinomial Test box, enter 60, Run the procedure. From the Run menu, select Run Procedure. Alternatively, just click the green Run button. Output Frequency Distribution of State Cumulative Cumulative Graph of State Count Count Percent Percent Percent Nevada % 58.67% Virginia % % Multinomial Test of State Expected Actual Expected Chi-Square State Count Count Percent Percent Amount Nevada % 60.00% Virginia % 40.00% Chi-Square = with df = 1 Probability Level = The output is exactly the same as in Example

14 Example 4 Tables and Plots of Counts and Percentages This example will show how to obtain some of the other table formats that are available from this procedure. The data for this example are found in the Resale dataset. You may follow along here by making the appropriate entries or load the completed template Example 4a by clicking on Open Example Template from the File menu of the window. 1 Open the Resale dataset. From the File menu of the NCSS Data window, select Open Example Data. Click on the file Resale.NCSS. Click Open. 2 Open the window. Using the Analysis menu or the Procedure Navigator, find and select the procedure. On the menus, select File, then New Template. This will fill the procedure with the default template. 3 Specify the variables. Select the Variables tab. For Type of Data Input select Column(s) in the Database. Double-click in the Categorical Variables text box. This will bring up the variable selection window. Select Garage, Fireplace, and Brick from the list of variables and then click Ok. Garage- Fireplace,Brick will appear in the Categorical Variables box. 4 Specify the reports. Click on the Reports tab. Uncheck Frequency Table Report. Check Counts Table. Check Row Percentages Table. Check Column Percentages Table. Check Table Percentages Table. Click on the Plots tab. 5 Specify the plots. Click on the Plots tab. Check Counts Plot. Check Row Percentages Plot. Check Column Percentages Plot. Check Table Percentage Plot. 6 Specify the report format. Click on the Report Options tab. In Variable Names, select Labels. In Value Labels, select Value Labels. 7 Run the procedure. From the Run menu, select Run Procedure. Alternatively, just click the green Run button

15 Output Counts Table Variables Values Garage Brick Size Fireplaces Ratio Total Total Row Percentages Table Variables Values Garage Brick Size Fireplaces Ratio Total 0 7.2% 40.2% 52.6% 100.0% % 0.0% 100.0% 100.0% % 34.2% 22.8% 100.0% % 43.4% 0.0% 100.0% % 0.0% 0.0% 100.0% Total 33.3% 33.3% 33.3% 100.0% Column Percentages Table Variables Values Garage Brick Size Fireplaces Ratio Total 0 4.7% 26.0% 34.0% 21.6% % 0.0% 31.3% 10.4% % 52.0% 34.7% 50.7% % 22.0% 0.0% 16.9% 3 1.3% 0.0% 0.0% 0.4% Total 100.0% 100.0% 100.0% 100.0% Table Percentages Table Variables Values Garage Brick Size Fireplaces Ratio Total 0 1.6% 8.7% 11.3% 21.6% % 0.0% 10.4% 10.4% % 17.3% 11.6% 50.7% 2 9.6% 7.3% 0.0% 16.9% 3 0.4% 0.0% 0.0% 0.4% Total 33.3% 33.3% 33.3% 100.0%

16 Plots Section This report presents tables containing counts and various percentages for all the variables selected. It also provides two-way bar charts of the counts and percentages. An alternate way to enter this summarized data is to set Type of Data Input to Table of Counts. You may follow along here by making the appropriate modifications to the current settings or load the completed template Example 4b by clicking on Open Example Template from the File menu of the window. 8 Modify the Data Input Type. Select the Variables tab. For Type of Data Input, select Table of Counts. For Categories (Rows), enter 5. For Variables (Columns), enter 3. Enter the variable titles, category labels, and counts from the Combined Table in the output into the Table of Counts on the input window. 9 Run the procedure again. From the Run menu, select Run Procedure. Alternatively, just click the green Run button. The output will be exactly the same as that displayed above

17 Example 5 Combined Table This example will show how to obtain a combined table of various counts and percentages. The data for this example are found in the Resale dataset. You may follow along here by making the appropriate entries or load the completed template Example 5a by clicking on Open Example Template from the File menu of the Frequency Tables window. 1 Open the Resale dataset. From the File menu of the NCSS Data window, select Open Example Data. Click on the file Resale.NCSS. Click Open. 2 Open the window. Using the Analysis menu or the Procedure Navigator, find and select the procedure. On the menus, select File, then New Template. This will fill the procedure with the default template. 3 Specify the variables. Select the Variables tab. For Type of Data Input select Column(s) in the Database. Double-click in the Categorical Variables text box. This will bring up the variable selection window. Select Garage, Fireplace, and Brick from the list of variables and then click Ok. Garage- Fireplace,Brick will appear in the Categorical Variables box. 4 Specify the reports. Click on the Reports tab. Uncheck Frequency Table Report. Check Show Combined Table. Check Counts. Check Row Percents. Check Column Percents. Check Table Percents. 5 Specify the report format. Click on the Report Options tab. In Variable Names, select Labels. In Value Labels, select Value Labels. 6 Run the procedure. From the Run menu, select Run Procedure. Alternatively, just click the green Run button

18 Output Combined Table Variables Values Garage Brick Size Fireplaces Ratio Total 0 Count % within Row 7.2% 40.2% 52.6% 100.0% % within Column 4.7% 26.0% 34.0% 21.6% % of Total 1.6% 8.7% 11.3% 21.6% 0.5 Count % within Row 0.0% 0.0% 100.0% 100.0% % within Column 0.0% 0.0% 31.3% 10.4% % of Total 0.0% 0.0% 10.4% 10.4% 1 Count % within Row 43.0% 34.2% 22.8% 100.0% % within Column 65.3% 52.0% 34.7% 50.7% % of Total 21.8% 17.3% 11.6% 50.7% 2 Count % within Row 56.6% 43.4% 0.0% 100.0% % within Column 28.7% 22.0% 0.0% 16.9% % of Total 9.6% 7.3% 0.0% 16.9% 3 Count % within Row 100.0% 0.0% 0.0% 100.0% % within Column 1.3% 0.0% 0.0% 0.4% % of Total 0.4% 0.0% 0.0% 0.4% Total Count % within Row 33.3% 33.3% 33.3% 100.0% % within Column 100.0% 100.0% 100.0% 100.0% % of Total 33.3% 33.3% 33.3% 100.0% This report presents a single table that combines the counts and percentages of all variables selected. An alternate way to enter this summarized data is to set Type of Data Input to Table of Counts. You may follow along here by making the appropriate modifications to the current settings or load the completed template Example 5b by clicking on Open Example Template from the File menu of the window. 7 Modify the Data Input Type. Select the Variables tab. For Type of Data Input, select Table of Counts. For Categories (Rows), enter 5. For Variables (Columns), enter 3. Enter the variable titles, category labels, and counts from the Counts Table in the output into the Table of Counts on the input window. 8 Run the procedure again. From the Run menu, select Run Procedure. Alternatively, just click the green Run button. The output will be exactly the same as that displayed above

### PASS Sample Size Software

Chapter 250 Introduction The Chi-square test is often used to test whether sets of frequencies or proportions follow certain patterns. The two most common instances are tests of goodness of fit using multinomial

### Two Correlated Proportions (McNemar Test)

Chapter 50 Two Correlated Proportions (Mcemar Test) Introduction This procedure computes confidence intervals and hypothesis tests for the comparison of the marginal frequencies of two factors (each with

### Scatter Plots with Error Bars

Chapter 165 Scatter Plots with Error Bars Introduction The procedure extends the capability of the basic scatter plot by allowing you to plot the variability in Y and X corresponding to each point. Each

### Comparables Sales Price

Chapter 486 Comparables Sales Price Introduction Appraisers often estimate the market value (current sales price) of a subject property from a group of comparable properties that have recently sold. Since

### Directions for Frequency Tables, Histograms, and Frequency Bar Charts

Directions for Frequency Tables, Histograms, and Frequency Bar Charts Frequency Distribution Quantitative Ungrouped Data Dataset: Frequency_Distributions_Graphs-Quantitative.sav 1. Open the dataset containing

### Using SPSS, Chapter 2: Descriptive Statistics

1 Using SPSS, Chapter 2: Descriptive Statistics Chapters 2.1 & 2.2 Descriptive Statistics 2 Mean, Standard Deviation, Variance, Range, Minimum, Maximum 2 Mean, Median, Mode, Standard Deviation, Variance,

### Data Management & Analysis Introduction to PASW Statistics

Data Management & Analysis Introduction to PASW Statistics 1 P A S W S T A T I S T I C S V 1 7. 0 ( S P S S F O R W I N D O W S ) 1. Getting Started with SPSS 2 T H E D A T A E D I T O R T H E V A R I

### IBM SPSS Statistics for Beginners for Windows

ISS, NEWCASTLE UNIVERSITY IBM SPSS Statistics for Beginners for Windows A Training Manual for Beginners Dr. S. T. Kometa A Training Manual for Beginners Contents 1 Aims and Objectives... 3 1.1 Learning

### Data Analysis Tools. Tools for Summarizing Data

Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool

### Chi Square Goodness of Fit & Two-way Tables (Create) MATH NSPIRED

Overview In this activity, you will look at a setting that involves categorical data and determine which is the appropriate chi-square test to use. You will input data into a list or matrix and conduct

### Association Between Variables

Contents 11 Association Between Variables 767 11.1 Introduction............................ 767 11.1.1 Measure of Association................. 768 11.1.2 Chapter Summary.................... 769 11.2 Chi

### Modifying Colors and Symbols in ArcMap

Modifying Colors and Symbols in ArcMap Contents Introduction... 1 Displaying Categorical Data... 3 Creating New Categories... 5 Displaying Numeric Data... 6 Graduated Colors... 6 Graduated Symbols... 9

### IBM SPSS Direct Marketing 23

IBM SPSS Direct Marketing 23 Note Before using this information and the product it supports, read the information in Notices on page 25. Product Information This edition applies to version 23, release

### MBA 611 STATISTICS AND QUANTITATIVE METHODS

MBA 611 STATISTICS AND QUANTITATIVE METHODS Part I. Review of Basic Statistics (Chapters 1-11) A. Introduction (Chapter 1) Uncertainty: Decisions are often based on incomplete information from uncertain

### Drawing a histogram using Excel

Drawing a histogram using Excel STEP 1: Examine the data to decide how many class intervals you need and what the class boundaries should be. (In an assignment you may be told what class boundaries to

### IBM SPSS Direct Marketing 22

IBM SPSS Direct Marketing 22 Note Before using this information and the product it supports, read the information in Notices on page 25. Product Information This edition applies to version 22, release

### STEP TWO: Highlight the data set, then select DATA PIVOT TABLE

STEP ONE: Enter the data into a database format, with the first row being the variable names, and each row thereafter being one completed survey. For this tutorial, highlight this table, copy and paste

### SAS Analyst for Windows Tutorial

Updated: August 2012 Table of Contents Section 1: Introduction... 3 1.1 About this Document... 3 1.2 Introduction to Version 8 of SAS... 3 Section 2: An Overview of SAS V.8 for Windows... 3 2.1 Navigating

### SPSS (Statistical Package for the Social Sciences)

SPSS (Statistical Package for the Social Sciences) What is SPSS? SPSS stands for Statistical Package for the Social Sciences The SPSS home-page is: www.spss.com 2 What can you do with SPSS? Run Frequencies

### Appendix 2.1 Tabular and Graphical Methods Using Excel

Appendix 2.1 Tabular and Graphical Methods Using Excel 1 Appendix 2.1 Tabular and Graphical Methods Using Excel The instructions in this section begin by describing the entry of data into an Excel spreadsheet.

### Basic Pivot Tables. To begin your pivot table, choose Data, Pivot Table and Pivot Chart Report. 1 of 18

Basic Pivot Tables Pivot tables summarize data in a quick and easy way. In your job, you could use pivot tables to summarize actual expenses by fund type by object or total amounts. Make sure you do not

### Factorial Analysis of Variance

Chapter 560 Factorial Analysis of Variance Introduction A common task in research is to compare the average response across levels of one or more factor variables. Examples of factor variables are income

### S P S S Statistical Package for the Social Sciences

S P S S Statistical Package for the Social Sciences Data Entry Data Management Basic Descriptive Statistics Jamie Lynn Marincic Leanne Hicks Survey, Statistics, and Psychometrics Core Facility (SSP) July

### NCSS Statistical Software. X-bar and s Charts

Chapter 243 Introduction This procedure generates X-bar and s (standard deviation) control charts for variables. The format of the control charts is fully customizable. The data for the subgroups can be

### SECTION 2-1: OVERVIEW SECTION 2-2: FREQUENCY DISTRIBUTIONS

SECTION 2-1: OVERVIEW Chapter 2 Describing, Exploring and Comparing Data 19 In this chapter, we will use the capabilities of Excel to help us look more carefully at sets of data. We can do this by re-organizing

### The Chi-Square Test. STAT E-50 Introduction to Statistics

STAT -50 Introduction to Statistics The Chi-Square Test The Chi-square test is a nonparametric test that is used to compare experimental results with theoretical models. That is, we will be comparing observed

### Probability Distributions

CHAPTER 5 Probability Distributions CHAPTER OUTLINE 5.1 Probability Distribution of a Discrete Random Variable 5.2 Mean and Standard Deviation of a Probability Distribution 5.3 The Binomial Distribution

### Using Excel for Statistics Tips and Warnings

Using Excel for Statistics Tips and Warnings November 2000 University of Reading Statistical Services Centre Biometrics Advisory and Support Service to DFID Contents 1. Introduction 3 1.1 Data Entry and

### Module 9: Nonparametric Tests. The Applied Research Center

Module 9: Nonparametric Tests The Applied Research Center Module 9 Overview } Nonparametric Tests } Parametric vs. Nonparametric Tests } Restrictions of Nonparametric Tests } One-Sample Chi-Square Test

### Binary Diagnostic Tests Two Independent Samples

Chapter 537 Binary Diagnostic Tests Two Independent Samples Introduction An important task in diagnostic medicine is to measure the accuracy of two diagnostic tests. This can be done by comparing summary

### APPLYING BENFORD'S LAW This PDF contains step-by-step instructions on how to apply Benford's law using Microsoft Excel, which is commonly used by

APPLYING BENFORD'S LAW This PDF contains step-by-step instructions on how to apply Benford's law using Microsoft Excel, which is commonly used by internal auditors around the world in their day-to-day

### Gamma Distribution Fitting

Chapter 552 Gamma Distribution Fitting Introduction This module fits the gamma probability distributions to a complete or censored set of individual or grouped data values. It outputs various statistics

### SPSS Manual for Introductory Applied Statistics: A Variable Approach

SPSS Manual for Introductory Applied Statistics: A Variable Approach John Gabrosek Department of Statistics Grand Valley State University Allendale, MI USA August 2013 2 Copyright 2013 John Gabrosek. All

### Technology Step-by-Step Using StatCrunch

Technology Step-by-Step Using StatCrunch Section 1.3 Simple Random Sampling 1. Select Data, highlight Simulate Data, then highlight Discrete Uniform. 2. Fill in the following window with the appropriate

### Describing, Exploring, and Comparing Data

24 Chapter 2. Describing, Exploring, and Comparing Data Chapter 2. Describing, Exploring, and Comparing Data There are many tools used in Statistics to visualize, summarize, and describe data. This chapter

### Client Marketing: Sets

Client Marketing Client Marketing: Sets Purpose Client Marketing Sets are used for selecting clients from the client records based on certain criteria you designate. Once the clients are selected, you

### Instructions for applying data validation(s) to data fields in Microsoft Excel

1 of 10 Instructions for applying data validation(s) to data fields in Microsoft Excel According to Microsoft Excel, a data validation is used to control the type of data or the values that users enter

### NCSS Statistical Software. K-Means Clustering

Chapter 446 Introduction The k-means algorithm was developed by J.A. Hartigan and M.A. Wong of Yale University as a partitioning technique. It is most useful for forming a small number of clusters from

### Introduction to the TI-Nspire CX

Introduction to the TI-Nspire CX Activity Overview: In this activity, you will become familiar with the layout of the TI-Nspire CX. Step 1: Locate the Touchpad. The Touchpad is used to navigate the cursor

### Creating a Worksheet with Excel

Creating a Worksheet with Excel Introduction Are you spending too much time number-crunching, rewriting financial reports, drawing charts, or searching for your calculator? Throw away your pencil, graph

### In this example, Mrs. Smith is looking to create graphs that represent the ethnic diversity of the 24 students in her 4 th grade class.

Creating a Pie Graph Step-by-step directions In this example, Mrs. Smith is looking to create graphs that represent the ethnic diversity of the 24 students in her 4 th grade class. 1. Enter Data A. Open

### SPSS: Expected frequencies, chi-squared test. In-depth example: Age groups and radio choices. Dealing with small frequencies.

SPSS: Expected frequencies, chi-squared test. In-depth example: Age groups and radio choices. Dealing with small frequencies. Quick Example: Handedness and Careers Last time we tested whether one nominal

### Microsoft Access 2010: Basics & Database Fundamentals

Microsoft Access 2010: Basics & Database Fundamentals This workshop assumes you are comfortable with a computer and have some knowledge of other Microsoft Office programs. Topics include database concepts,

### January 26, 2009 The Faculty Center for Teaching and Learning

THE BASICS OF DATA MANAGEMENT AND ANALYSIS A USER GUIDE January 26, 2009 The Faculty Center for Teaching and Learning THE BASICS OF DATA MANAGEMENT AND ANALYSIS Table of Contents Table of Contents... i

### Data Visualization. Brief Overview of ArcMap

Data Visualization Prepared by Francisco Olivera, Ph.D., P.E., Srikanth Koka and Lauren Walker Department of Civil Engineering September 13, 2006 Contents: Brief Overview of ArcMap Goals of the Exercise

### Multivariate Analysis of Variance (MANOVA)

Chapter 415 Multivariate Analysis of Variance (MANOVA) Introduction Multivariate analysis of variance (MANOVA) is an extension of common analysis of variance (ANOVA). In ANOVA, differences among various

### Class 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1)

Spring 204 Class 9: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the

### Creating Simple Tables and Charts using Microsoft Excel 2013

2015 Bow Valley College 1 Microsoft Excel Vocabulary Creating Simple Tables and Charts using Microsoft Excel 2013 Column: A grouping of information or data organized from top to bottom. In Excel columns

### Chapter 2 Introduction to SPSS

Chapter 2 Introduction to SPSS Abstract This chapter introduces several basic SPSS procedures that are used in the analysis of a data set. The chapter explains the structure of SPSS data files, how to

### Ohio University Computer Services Center August, 2002 Crystal Reports Introduction Quick Reference Guide

Open Crystal Reports From the Windows Start menu choose Programs and then Crystal Reports. Creating a Blank Report Ohio University Computer Services Center August, 2002 Crystal Reports Introduction Quick

### Chapter 5 Analysis of variance SPSS Analysis of variance

Chapter 5 Analysis of variance SPSS Analysis of variance Data file used: gss.sav How to get there: Analyze Compare Means One-way ANOVA To test the null hypothesis that several population means are equal,

### NCSS Statistical Software

Chapter 06 Introduction This procedure provides several reports for the comparison of two distributions, including confidence intervals for the difference in means, two-sample t-tests, the z-test, the

### PURPOSE OF GRAPHS YOU ARE ABOUT TO BUILD. To explore for a relationship between the categories of two discrete variables

3 Stacked Bar Graph PURPOSE OF GRAPHS YOU ARE ABOUT TO BUILD To explore for a relationship between the categories of two discrete variables 3.1 Introduction to the Stacked Bar Graph «As with the simple

### Appendix III: SPSS Preliminary

Appendix III: SPSS Preliminary SPSS is a statistical software package that provides a number of tools needed for the analytical process planning, data collection, data access and management, analysis,

### Data Visualization. Prepared by Francisco Olivera, Ph.D., Srikanth Koka Department of Civil Engineering Texas A&M University February 2004

Data Visualization Prepared by Francisco Olivera, Ph.D., Srikanth Koka Department of Civil Engineering Texas A&M University February 2004 Contents Brief Overview of ArcMap Goals of the Exercise Computer

### Gestation Period as a function of Lifespan

This document will show a number of tricks that can be done in Minitab to make attractive graphs. We work first with the file X:\SOR\24\M\ANIMALS.MTP. This first picture was obtained through Graph Plot.

### Excel Using Pivot Tables

Overview A PivotTable report is an interactive table that allows you to quickly group and summarise information from a data source. You can rearrange (or pivot) the table to display different perspectives

### Trial 9 No Pill Placebo Drug Trial 4. Trial 6.

An essential part of science is communication of research results. In addition to written descriptions and interpretations, the data are presented in a figure that shows, in a visual format, the effect

### Summary of important mathematical operations and formulas (from first tutorial):

EXCEL Intermediate Tutorial Summary of important mathematical operations and formulas (from first tutorial): Operation Key Addition + Subtraction - Multiplication * Division / Exponential ^ To enter a

### Unit 29 Chi-Square Goodness-of-Fit Test

Unit 29 Chi-Square Goodness-of-Fit Test Objectives: To perform the chi-square hypothesis test concerning proportions corresponding to more than two categories of a qualitative variable To perform the Bonferroni

### Factor B: Curriculum New Math Control Curriculum (B (B 1 ) Overall Mean (marginal) Females (A 1 ) Factor A: Gender Males (A 2) X 21

1 Factorial ANOVA The ANOVA designs we have dealt with up to this point, known as simple ANOVA or oneway ANOVA, had only one independent grouping variable or factor. However, oftentimes a researcher has

### Merged Cell. End of Row Marker Cell

Tables in Microsoft Word A table consists of rows and columns of cells that you can fill with text or graphics. When you insert a table, it is displayed as a grid, each section of which is referred to

### An introduction to IBM SPSS Statistics

An introduction to IBM SPSS Statistics Contents 1 Introduction... 1 2 Entering your data... 2 3 Preparing your data for analysis... 10 4 Exploring your data: univariate analysis... 14 5 Generating descriptive

### Regression Clustering

Chapter 449 Introduction This algorithm provides for clustering in the multiple regression setting in which you have a dependent variable Y and one or more independent variables, the X s. The algorithm

### Sample Table. Columns. Column 1 Column 2 Column 3 Row 1 Cell 1 Cell 2 Cell 3 Row 2 Cell 4 Cell 5 Cell 6 Row 3 Cell 7 Cell 8 Cell 9.

Working with Tables in Microsoft Word The purpose of this document is to lead you through the steps of creating, editing and deleting tables and parts of tables. This document follows a tutorial format

### NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )

Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates

### Excel 2007 - Using Pivot Tables

Overview A PivotTable report is an interactive table that allows you to quickly group and summarise information from a data source. You can rearrange (or pivot) the table to display different perspectives

### Years after 2000. US Student to Teacher Ratio 0 16.048 1 15.893 2 15.900 3 15.900 4 15.800 5 15.657 6 15.540

To complete this technology assignment, you should already have created a scatter plot for your data on your calculator and/or in Excel. You could do this with any two columns of data, but for demonstration

### HOW TO COLLECT AND USE DATA IN EXCEL. Brendon Riggs Texas Juvenile Probation Commission Data Coordinators Conference 2008

HOW TO COLLECT AND USE DATA IN EXCEL Brendon Riggs Texas Juvenile Probation Commission Data Coordinators Conference 2008 Goals To be able to gather and organize information in Excel To be able to perform

### Universal Simple Control, USC-1

Universal Simple Control, USC-1 Data and Event Logging with the USB Flash Drive DATA-PAK The USC-1 universal simple voltage regulator control uses a flash drive to store data. Then a propriety Data and

### Data exploration with Microsoft Excel: analysing more than one variable

Data exploration with Microsoft Excel: analysing more than one variable Contents 1 Introduction... 1 2 Comparing different groups or different variables... 2 3 Exploring the association between categorical

### Microsoft Office. Mail Merge in Microsoft Word

Microsoft Office Mail Merge in Microsoft Word TABLE OF CONTENTS Microsoft Office... 1 Mail Merge in Microsoft Word... 1 CREATE THE SMS DATAFILE FOR EXPORT... 3 Add A Label Row To The Excel File... 3 Backup

### EXCEL PIVOT TABLE David Geffen School of Medicine, UCLA Dean s Office Oct 2002

EXCEL PIVOT TABLE David Geffen School of Medicine, UCLA Dean s Office Oct 2002 Table of Contents Part I Creating a Pivot Table Excel Database......3 What is a Pivot Table...... 3 Creating Pivot Tables

### ITS Training Class Charts and PivotTables Using Excel 2007

When you have a large amount of data and you need to get summary information and graph it, the PivotTable and PivotChart tools in Microsoft Excel will be the answer. The data does not need to be in one

### Simulating Chi-Square Test Using Excel

Simulating Chi-Square Test Using Excel Leslie Chandrakantha John Jay College of Criminal Justice of CUNY Mathematics and Computer Science Department 524 West 59 th Street, New York, NY 10019 lchandra@jjay.cuny.edu

### Functions & Data Analysis Tools

Functions & Data Analysis Tools Academic Computing Services www.ku.edu/acs Abstract: This workshop focuses on the functions and data analysis tools of Microsoft Excel. Topics included are the function

### CHAPTER 2 ORGANIZING DATA

CHAPTER 2 ORGANIZING DATA BAR GRAPHS, CIRCLE GRAPHS, AND TIME PLOTS (SECTION 2.1 OF UNDERSTANDABLE STATISTICS) Excel has a Chart Wizard that produces a wide variety of charts. To access the Chart Wizard,

### CD Appendix A3 Excel Troubleshooting and Detailed. Instructions for Office 1997, 2000, XP, and 2003

CD Appendix A3 Excel Troubleshooting and Detailed Instructions for Office 1997, 2000, XP, and 2003 Before using this appendix please read CD Appendixes A1. If problems persist use this appendix to get

### Graphical and Tabular. Summarization of Data OPRE 6301

Graphical and Tabular Summarization of Data OPRE 6301 Introduction and Re-cap... Descriptive statistics involves arranging, summarizing, and presenting a set of data in such a way that useful information

### Chi-Square Test. Contingency Tables. Contingency Tables. Chi-Square Test for Independence. Chi-Square Tests for Goodnessof-Fit

Chi-Square Tests 15 Chapter Chi-Square Test for Independence Chi-Square Tests for Goodness Uniform Goodness- Poisson Goodness- Goodness Test ECDF Tests (Optional) McGraw-Hill/Irwin Copyright 2009 by The

### Data Analysis. Using Excel. Jeffrey L. Rummel. BBA Seminar. Data in Excel. Excel Calculations of Descriptive Statistics. Single Variable Graphs

Using Excel Jeffrey L. Rummel Emory University Goizueta Business School BBA Seminar Jeffrey L. Rummel BBA Seminar 1 / 54 Excel Calculations of Descriptive Statistics Single Variable Graphs Relationships

### Federal Employee Viewpoint Survey Online Reporting and Analysis Tool

Federal Employee Viewpoint Survey Online Reporting and Analysis Tool Tutorial January 2013 NOTE: If you have any questions about the FEVS Online Reporting and Analysis Tool, please contact your OPM point

### Using Mail Merge in Microsoft Word

Using Mail Merge in Microsoft Word Creating the main document On the menu bar, click on Tools. From the pull down menu, select Letters & Mailings, then select Mail Merge... A task pane will appear on the

### Working with Tables: How to use tables in OpenOffice.org Writer

Working with Tables: How to use tables in OpenOffice.org Writer Title: Working with Tables: How to use tables in OpenOffice.org Writer Version: 1.0 First edition: January 2005 First English edition: January

### Step Sheet: Creating a Data Table and Charts

Step Sheet: Creating a Data Table and Charts Using Microsoft Excel Spreadsheets with Data This step sheet will help you build a data table and convert the data into histograms and circle graphs for your

### MICROSOFT ACCESS STEP BY STEP GUIDE

IGCSE ICT SECTION 11 DATA MANIPULATION MICROSOFT ACCESS STEP BY STEP GUIDE Mark Nicholls ICT Lounge P a g e 1 Contents Task 35 details Page 3 Opening a new Database. Page 4 Importing.csv file into the

### Microsoft Access 2010 handout

Microsoft Access 2010 handout Access 2010 is a relational database program you can use to create and manage large quantities of data. You can use Access to manage anything from a home inventory to a giant

### Word 2007 Layout Tools

Word 2007 Layout Tools Contents Section Breaks and Chapters... 1 Section breaks to vary the header or footer... 2 Same header or footer across section boundaries... 2 Page Setup... 3 Change or set page

### Canonical Correlation

Chapter 400 Introduction Canonical correlation analysis is the study of the linear relations between two sets of variables. It is the multivariate extension of correlation analysis. Although we will present

### Excel 2007. Getting Started The Excel Window u v w. Microsoft QUICK Source

Microsoft QUICK Source Excel 2007 Getting Started The Excel Window u v w x y z { u Quick Access Toolbar contains shortcuts for the most commonly used tools. v Microsoft Office Button contains common file

### Microsoft Word 2013 Equations (Level 3)

IT Training Microsoft Word 2013 Equations (Level 3) Contents Introduction 1 Inserting an Equation 1 The Equation Tools Design Tab 2 The Tools Group 2 The Symbols Group 3 The Structures Group 3 Saving Equations

### Introduction Course in SPSS - Evening 1

ETH Zürich Seminar für Statistik Introduction Course in SPSS - Evening 1 Seminar für Statistik, ETH Zürich All data used during the course can be downloaded from the following ftp server: ftp://stat.ethz.ch/u/sfs/spsskurs/

### Creating Advanced Reports with the SAP Query Tool

CHAPTER Creating Advanced Reports with the SAP Query Tool In this chapter An Overview of the SAP Query Tool s Advanced Screens 86 Using the Advanced Screens of the SAP Query Tool 86 86 Chapter Creating

### Microsoft Office Excel 2013

Microsoft Office Excel 2013 Navigating the Excel Interface The Components of the Excel 2013 Interface Component Quick Access Toolbar The ribbon Ribbon tabs Task pane Formula Bar Status bar Description

### Using SPSS 20, Handout 3: Producing graphs:

Research Skills 1: Using SPSS 20: Handout 3, Producing graphs: Page 1: Using SPSS 20, Handout 3: Producing graphs: In this handout I'm going to show you how to use SPSS to produce various types of graph.