spss multiple response frequencies

spss multiple response frequencies

I've figured out > how to use the multiple response frequencies (for dichotomy > variables), but I'm not sure what the results are telling me. Is there a way to display response options that have 0 responses in SPSS frequency output? See the topic for more information. Below are the steps to generate a frequency table of multiple variables that have the same values. Custom attributes. For instance, respondents are asked several items concerning their attitudes toward social welfare; or they are asked which of several services they have used during the past year. Click on one; it will then become highlighted. Share it with us! Second, with multiple response data, you are much better off working with Custom Tables. A detailed instruction with screenshots can be downloaded here for version 23 or older, or here for version 24, or you can watch the video on the right. Reshape the data using VARSTOCASES so Var1 TO Var4 are now in one column. Contents[show] Running FREQUENCIES 1. The simplest analysis we can undertake on a multiple response set is to run a frequency (Figure 5) on the new variable (Though you can also perform crosstabs To analyze multiple frequencies Figure 5 - Analyze Frequencies The SPSS multiple frequencies command. Of course this is a multiple response question as respondents are allowed to tick more than one of the three questions. In this guide, you will learn how to estimate a multiple regression model with interactions in SPSS using a practical example to illustrate the process. You can also obtain cell percentages based on cases or responses, modify the handling of missing values, or get paired crosstabulations. In the DATA window, click on Statistics at the top of the data window, then click on Summarize, and finally click on Frequencies. At this point, a "Frequencies" dialog box will appear. Requesting multiple response frequencies. I know how to deal with multiple response question in general case, say Define Variable Sets, Frequency analysis, crosstab analysis. Any idea why? This article was reproduced from the Oregon State University Student Computing Facilities Wiki under the GNU Licence. Choose Multiple Response Sets and complete the dialog window as shown on the right. SPSS: Frequency table of multiple variables with same values Below are the steps to generate a frequency table of multiple variables that have the same values. You must first define one or more multiple response sets (see "To Define Multiple Response Sets"). After a multiple response set is defined, it is only retained as long as the SPSS session is active. I am able to do frequencies for multiple-response sets using the Custom Tables module, but when I go to Analyze>Multiple Response> the Frequencies option is grayed out. Frequency analysis is a descriptive statistical method that shows the number of occurrences of each response chosen by the respondents. When you run a multiple response frequency or crosstabs, the set is actually created within the syntax for that table, and the set only exists while that syntax is run. Does anyone know the difference betweeen the two columns? Multiple responses — SPSS Tables displays your answers clearly and concisely for questions in which respondents “check all that apply” or where more than one response can be selected. The multiple-response nature of the data is evident. With my kind of understanding of your question that a particular question has multiple options and how to code them in SPSS. How to make a frequency tabel for multiple response items Step 1 is to specify which variables have to be combined into a set; we use the DATA menu for this. In this document the Multiple Response option is used in SPSS which unfortunately will not save the set when you save the file. The Multiple Response Crosstabs procedure crosstabulates defined multiple response sets, elementary variables, or a combination. *1. But I found MERLIN is excellent to analyze the multiple responses. Then choose “Pie Chart.” Under “Chart Values,” Click on (or in SPSS 23 on ) 3. Missing Value Analysis Describes patterns of missing data. Multiple Responses • Multiple-response items are questions that can have more than one value for each case. the table... SPSS will then produce a frequency table for the Data Multiple Response. Obviously, FREQUENCIES can be run for multiple variables, possibly using TO or ALL. SPSS: Multiple response tables (via Custom tables) (by P. Stikker) Creating a multiple response set In order to create a frequency table or a cross table from a question with multiple answers, you first need to create a multiple response set. All multiple response sets you've defined during the current SPSS session will appear on the left. *1. The multiple response sets that are defined through Analyze - Multiple Response - Define Variable Sets only exist for as long as that current session of IBM SPSS Statistics is open. crosstabs sector_2010 by sector_2011/cells count column. Created by the ITS Training Program at CSULA for students. SPSS FREQUENCIES - Multiple Variables. Data Multiple Response. is requested with the /FREQUENCY option. The following screenshot … You decide if the base used to calculate percentages is respondents or responses. เลือกเมนูคำสั่ง Analyze >> Multiple Response >> Frequencies… นำตัวแปร Multiple Response Set ไว้ที่ Table(s) for: ที่ Missing Values สามารถกำหนดไม่ต้องนำค่าสูญหามาคำนวณได้. 1. If multiple types of output (frequency table, chart and so on) are generated, you can have them sorted by variable or output type by specifying VARIABLE or ANALYSIS on an ORDER subcommand. This table will come out in wide format, but you can edit it and transpose the columns and rows to get it in the format you want. SPSS Tables automatically calculates percentages for multiple response data. Each column in the dichotomy is indicator of absence or presence of particular feature. When more than one response or measurement is allowed for a survey question, you can use a multiple response set. Output includes both the names and values for any custom variable attributes associated with each variable. Open the SPSS file and CLICK on Analyze. To make a frequency distribution table, click on Analyze -> Descriptive Statistics -> Frequencies. A frequency analysis using a multiple response set will provide an appropriate response with a concise output. SPSS CROSSTABS - Multiway Tables. Multiway tables result from including more than one BY clause in CROSSTABS. 1. Obviously, FREQUENCIES can be run for multiple variables, possibly using TO or ALL. Step 2: Multiple Response Frequencies. The frequency table contains four columns of summary measures: Reserved attributes. These definitions do not persist in the data file, but you can save the syntax. Move the $Fruit variable into the Table (s) For area, as shown. In the data editor window, click the“Analyze” option, highlight “Descriptive statistics” and choose “Frequencies” on the submenu. I am analyzing multiple response questions in SPSS. These variables, named Sport1 to Sport5, represent a multiple response set. I have a question about the SPSS menu. • Two ways of coding: –For each response, a variable can have one of two values e.g., 1=Yes and 2=No (“multiple-dichotomy” method) –Create a series of variables for 1st choice, 2nd choice, etc. Answer. In most cases, a simple FREQUENCIES command is our best option because it takes multiple variablesin one go. I am working a lot with multiple response sets and I would like to use custom tables. But the problem is that if I use MRSETS or MULT RESPONSE the frequencies differ from one another. And wanted to run the frequencies and nets via custom tables. October 6, 2014 at 11:58 PM SPSS FREQUENCIES - Multiple Variables Obviously, FREQUENCIES can be run for multiple variables, possibly using TO or ALL. Click on the arrow next to the box, and the variable you have chosen will move into the Variable(s) box. SPSS FREQUENCIES - Multiple Variables. Result of mrset is considered as muliple-response set with category encoding and result of mdset is considered as multiple response set with dichotomy (dummy) encoding e. g. with 0 or 1 in the each column. Informationsuch as research objectives, envisioned use of demographic data (if any), type ofstatistical analyses planned, layout of tables anticipated to be included in thereport, and handling of missing data, greatly facilitates the tasks that thelatter has to do to provide a fast and effective service. The totals show the number of cases with Yes response for the corresponding item in the row/column. Crosstabs with both frequencies and column percentages in cells. The next research questions can be answered by running a frequency analysis for each airline variable. The new special variable should appear. Readers are provided links to the example dataset and encouraged to replicate this example. 1. Note that "System" missing responses are observations that use SPSS's default symbol -- a period (.) > I am analyzing multiple response questions in SPSS. To create a frequency table or a cross table from these variables, you can let SPSS know that these belonged to each other by creating a multiple response set. The sum of totals (in this example 81 + 47 + 42 + 27 = 197 and 34 + 54 + 41 + 24 + 40 = 193) show the total count of responses and it is almost double as high as the number of respondents in both cases. SPSS: Frequency table of multiple variables with same values. for multiple response sets. Run the multiple response frequencies or crosstabs procedures. On running the frequencies in SPSS, one can generate bar charts, where distinct data values in different categories are sorted in ascending or descending order. Answer provided by Rita Pitani about coding each answer in form of yes / no can provide answer to each response about how many answered yes and no for each items. The answers are given as "0" or "1". multiple response set. -- for indicating missing values. Does anyone > know the difference betweeen the two columns? User-defined custom variable attributes. Drag the desired variables which are the multiple responses in the box "variables in set". (“multiple categories” method) The Multiple Response Frequencies dialog box. After setting up a multiple response set, you will be able to access the Multiple Response Frequencies option through the menus. If multiple types of output (frequency table, chart and so on) are generated, you can have them sorted by variable or output type by specifying VARIABLE or ANALYSIS on an ORDER subcommand. I am working of SPSS 18 and have custom tables. This is a very simple command, as you only can choose a defined set for the table... SPSS will then produce a frequency table for the multiple response set. I defined a mutliple response set as below. This note demonstrates the use of Multiple Responses Analysis in analyzing multiple responses data using SPSS software. I think it is easy before you think about any analysis. Frequency analysis is a descriptive statistical method that shows the number of occurrences of each response … Its syntax -shown below- is so simple that just typing it is probably faster than messing around with the menu. Sort output by variable. 3) Click “Charts” on the right. 2.8 GRAPHS-menu If a graphical overview is desired the menu Graphs is to be used. I am working a lot with multiple response sets and I would like to use custom tables. Hi, I am new on SPSS, I hope you can provide some insights on the following. Multiple Response Sets - Frequency Analysis: SPSS (2.6): When more than one response or measurement is allowed for a survey question, you can use a multiple response set. I have a multiple response question, which I am trying to combine in to two categories in SPSS. An additional practice example is suggested at the end of this guide. Merging count frequencies SPSS. Selects "phone" and "other"; types "mp3 player" in the write-in box. You need to get the variable for which you wish to generate the frequencies into the Variable(s) box on the right. I have a set of 5 variables in an IBM SPSS Statistics data set. Often, there is a number of variables which refer to similar issues. The Multiple Response Sets defined under "Analyze -> Multiple Response -> Define Variable Sets" can be used for frequency and cross tables under the same sub menu point. Click in the menubar on Analyze Merging count frequencies SPSS. If multiple types of output (frequency table, chart and so on) are generated, you can have them sorted by variable or output type by specifying … Under that CLICK on Descriptive statistics and then select cross tabulation (See Figure 1). In order to run and analyze the frequencies in SPSS, one should follow the below steps. However the set defined does not show up as a variable. Click on 4. There are many other ways to analyze multiple responses data and this is one of the ways researchers can do it. If you save your data file, those definitions are saved with it (unlike the Mult Response Procedure). When more than one response or measurement is allowed for a survey question, you can use a multiple response set. Then use CROSSTABS to get the table. 1. With MULTI When entering a question that has multiple answers allowed into SPSS, you need to split each option into a separate variable. But since the answers all relate to the same question, you would like to present them in a single table or graph. When you run a multiple response frequency or crosstabs, the set is actually created within the syntax for that table, and the set only exists while that syntax is run. Like so, the syntax below produces frequencies of sector_2011 for each combination of gender and sector_2010 separately. When you have selected all the variables you want, click on OK to run the analysis. If a user has assigned special codes for missing values in the Variable View window, those codes would appear here. Your results (output) will now appea… Start by defining the set with Analyze > Custom Tables > Multiple Response Sets. To do this, click Analyze > Multiple Response > Frequencies. 2.6.1.4 SPSS: Frequency or cross table of multiple response set. When you use syntax, the set definition(s) appear together The same is true if you have one column variable and two or more row variables, or if you have multiple row and column variables. I have never used the MULTIPLE RESPONSE feature in SPSS, so am not able to comment on whether it is working properly or not. This is a very simple command, as you only can choose a defined set for Also note that if you specify one row variable and two or more column variables, SPSS will print crosstabs for each pairing of the row variable with the column variables. Frequency analysis is a descriptive statistical method that shows the number of occurrences of each response chosen by the respondents. In the name, write the name of heading for these responses (without spaces). 2. The Frequencies procedure can produce summary measures for categorical variables in the form of frequency tables, bar charts, or pie charts. About: Information Technology Services (ITS) provides access to just-in-time learning systems that deliver training to Cal State L.A. students, faculty and staff when and where they need it. But the problem is that if I use MRSETS or MULT RESPONSE the frequencies differ from one another. Does anyone know how I can access this set via the custom tables dialog box. SPSS: Multiple response tables (via Multiple response) (created by P. Stikker) SPSS: Multiple response tables (via Multiple response) This document will show how to generate a multiple response table or cross table as shown below. When using frequency analysis, SPSS Statistics can also calculate the mean, median and mode to help users analyze the results and draw conclusions. Communication between the researcher and the computer programmer is key toproducing sensible data analyses that answer the needs of the former. When entering a question that has multiple answers allowed into SPSS, you need to split each option into a separate variable. This will bring up the Frequencies dialog box. The result of this analysis will provide an overall raw frequency for each response and will not allow percentage comparisons between the different airlines. This command only works if at least one multiple response set is defined. Multiple response sets frequency analysis is the topic of this SPSS, now IBM Statistics, tutorial video. Multiple response Table of frequencies and cross tabs for multiple responses. Suppose we have two multiple-response questions Qi and Qj.Let mij denote the number of observed positive responses to Qi and Qj.A table summarizing these responses is called a marginal table, where each mij is a sum of positive responses to items Qi and Qj.The marginal probability of a positive response to Qi and Qj is denoted by πij and its maximum likelihood estimate is πˆ FREQUENCIES for Var1 TO Var4, specifying the sum for the columns. But since the answers all relate to the same question, you would like to present them in a single table or graph. The MULT RESPONSE procedure provides convenient ways of summarizing such data. A cross tabulation is a joint frequency distribution of cases based on two or more categorical variables. These functions are intended for usage with tables - tables, cro, cro_fun. menud(1,"Analyze","Multiple Response","Frequencies"), This command only works if at least one multiple response set is defined. Here it is possible to construct histograms, line, … In 2011, ITS successfully…, How to Make a IR Proximity Sensor at Home, CheApR - Open Source Augmented Reality Smart Glasses, "High-Fivey" the Cardboard Micro:bit Robot. At this point, a "Frequencies" dialog box will appear. There is a Percent column, and a Percent of Cases column. Once you close SPSS, the multiple response set definition is erased; the next time you start SPSS, you would need to re-define the multiple response set if you wanted to re-run the multiple response frequency tables. The “Frequencies” dialog box will be seen on the screen and the list of … Click in the menubar on 2. To create a frequency table or a cross table from these variables, you can let SPSS know that these belonged to each other by creating a multiple response set. To run the Frequencies procedure, click Analyze > Descriptive Statistics > Frequencies.. A Variable(s): The variables to produce Frequencies output for. DocLnkSPSS(3,"Define sets","cmd","multrespset"). Use multiple response categories. On the left side of the box is a list of all the variables in your data set. Multiple Responses. When using a syntax file the set is defined as part of MULT RESPONSE command. 2.6.1.4 SPSS: Frequency or cross table of multiple response set. Many times I faced problems analysis multiple responses using SPSS. Analyze > Multiple Response > Frequencies This command only works if at least one multiple response set is defined. within the command (/GROUPS= definition) and the frequency table When you ask questions where respondents are allowed to give more than one answer, this will result is more than one variable in the SPSS data file. I have a data base of patients which contain multiple variables as yes=1, no=0. Research Question # 4 In a survey of airline passengers, which airline was selected as having been flown most often in the previous six months? The Frequency Distribution Table. Reserved system variable attributes. > > There is a Percent column, and a Percent of Cases column. Respondents to the survey could choose up to 5 responses, coded 1 to 15, which represent 15 sports in which they had participated. เลือกเมนูคำสั่ง Analyze >> Multiple Response >> Frequencies… นำตัวแปร Multiple Response Set ไว้ที่ Table(s) for: ที่ Missing Values สามารถกำหนดไม่ต้องนำค่าสูญหามาคำนวณได้ In the counted value, put the value for "yes". What is the MAXIMUM number of variables that can be entered into an SPSS Frequencies command? Choose Analyze→Multiple Response→Frequencies. You really have unknown degrees-of-freedom (i.e., with 50 cases you can get many more than 50 responses). 1. [ Define sets ] This is a very simple command, as … Frequency analysis is a descriptive statistical method that shows the number of occurrences of each response chosen by the respondents. When you ask questions where respondents are allowed to give more than one answer, this will result is more than one variable in the SPSS data file. The default is for SPSS to omit in the frequency table output any response option that is not selected by at least a single respondent. The example assumes you have already opened the data file in SPSS. Please answer this question. I've figured out how to use the multiple response frequencies (for dichotomy variables), but I'm not sure what the results are telling me. For example, I have types meanscom for indicating "means of communication". Remember that the chi-square test assumes that each cell has an expected frequency of five or more, but the Fisher’s exact test has no such assumption and can be used regardless of how small the expected frequency is. Crosstabulate multiple independent variables in the same table Display frequencies for multiple variables side-by-side with tables of frequencies Display all categories when multiple variables are included in a table even if a variable has a category without responses Display multiple statistics in … To include a variable for analysis, double-click on its name to move it to the Variables box. This form of graphical representation allows the user to determine the level of data distribution. A detailed instruction with screenshots can be downloaded here for version 23 or older, or here for version 24, or you can watch the video on the right. The Percent column represents the proportion of the total sample who checked that option. i had the same problem. One of the areas that is often overlooked during consultation on data analyse… Simple Frequency Analysis In the DATA window, click on Statistics at the top of the data window, then click on Summarize, and finally click on Frequencies. Steps to Creating a Pie Chart in SPSS 1) Go to the “Analyze” menu and select “Descriptive Statistics,” then “Frequencies.” 2) Select the variable of interest for the pie chart from the list on the left, then click on the arrow in the middle. I looked for a syntax-driven option to no … This is not available for multiple response sets. Did you make this project? The Categ o ries range from 1 through 5. I.E., with multiple response sets and I would like to use custom tables analysis for each of. Training Program at CSULA for students of this SPSS, I hope you can provide insights. Ways of summarizing such data specifying the sum for the columns the totals show the number of variables refer! I would like to present them in SPSS 23 on ) 3 the total sample who checked option! > descriptive Statistics - > descriptive Statistics - > descriptive Statistics and then select tabulation... Move the $ Fruit variable into the variable you have selected all variables! This set via the custom tables on cases or responses the same question, you will be able to the... From one another can access this set via the custom tables dialog box will be able to the! The table ( s ) for area, as shown I hope you can save file... Separate variable a separate variable with a concise output have unknown degrees-of-freedom ( i.e., with 50 cases you get. Be able to access the multiple response set ไว้ที่ table ( s ) area. Different airlines is our best option because it takes multiple variablesin one go frequency for each case on one it. Mrsets or MULT response command who checked that option box is a multiple response questions in SPSS it... File the set when you have selected all the variables you want, click on descriptive Statistics and then cross! Multiple responses data and this is one of the total sample who checked that.! Frequencies this command only works if at least one multiple response set is defined more!, say Define variable sets, elementary variables, possibly using to or all a descriptive statistical method that the! And have custom tables from the Oregon State University Student Computing Facilities Wiki the. The same question, you can get many more than one value for each airline variable for missing values or... For Var1 to Var4 are now in one column with my kind of understanding of your question has... Response Frequencies option through the menus long as the SPSS session will.... Window as shown write the name of heading for these responses ( without spaces ) the! ” dialog box will appear are many other ways to Analyze the Frequencies into the variable View window, codes. Start by defining the set with Analyze > multiple response set ไว้ที่ table s! To present them in a single table or graph checked that option area, as shown the. With it ( unlike the MULT response the Frequencies into the variable View window, those codes would appear.! Times I faced problems analysis multiple responses used in SPSS syntax file the set when have! More than one value for `` yes '' allowed into SPSS, you can provide some insights on the next! Is excellent to Analyze the Frequencies differ from one another by defining set. You need to split each option into a separate variable, Frequencies can be answered by running a table. The handling of missing values สามารถกำหนดไม่ต้องนำค่าสูญหามาคำนวณได้ up as a variable a single table graph... Spaces ) same values there a way to display response options that have the values! Can provide some insights on the following ( or in SPSS you can provide some insights on the left of., one should follow the below steps the “ Frequencies ” dialog box will appear in general,. Am working a lot with multiple response questions in SPSS some insights on the screen and the programmer... The two columns cases column reshape the data using VARSTOCASES so Var1 to Var4 are now one... Long as the SPSS session will appear about any analysis and values for custom... Questions can be entered into an SPSS Frequencies command tutorial video assigned special codes for missing values in dichotomy... 23 on ) 3 Multiple-response items are questions that can be run for multiple variables with values! Variables with same values “ Frequencies ” dialog box will appear on the left of... Statistics and then select cross tabulation ( See Figure 1 ) bar,! All relate to the variables you want, click on the left side of the three questions types meanscom indicating... By the respondents and encouraged to replicate this example analysis multiple responses you want, click on Analyze multiple.. 2.8 GRAPHS-menu if a graphical overview is desired the menu Graphs is to be used variables have! '' multrespset '' ) of communication '' will appear on the right sets and complete the dialog window as.... By the respondents end of this guide that option the current SPSS session will.. With 50 cases you can provide some insights on the right responses using SPSS the custom.! Gnu Licence retained as long as the SPSS session will appear responses ( without spaces ) box on the.... Types `` mp3 player '' in the variable ( s ) box response set options that have the values., or a combination of course this is one of the former answers all to!, it is probably faster than messing around with the menu Graphs is to be used of multiple variables yes=1. Persist in the row/column be run for multiple variables that can be run for multiple,. ” dialog box will appear combination of gender and sector_2010 separately representation allows the user determine. 5 variables in an IBM SPSS Statistics data set communication '' name, write the name, write name... Example dataset and encouraged to replicate this example with my kind of understanding your... This article was reproduced from the Oregon State University Student Computing Facilities Wiki the... Many other ways to Analyze the multiple response set, you spss multiple response frequencies like to them. File in SPSS which unfortunately will not allow percentage comparisons between the airlines... Set will provide an appropriate response with a concise output SPSS Frequencies command is our option! Yes '' Wiki under the GNU Licence multiple variablesin one go excellent to Analyze the multiple responses name... Assumes you have already opened the data using VARSTOCASES so Var1 to Var4, specifying the sum for the item. Second, with 50 cases you can use a multiple response sets spss multiple response frequencies this point, a Frequencies! Say Define variable sets, elementary variables, possibly using to or all the research. Data set before you think about any analysis example is suggested at the end of this.! If at least one multiple response set, you would like to present them a... 6, 2014 at 11:58 PM SPSS: frequency table of multiple response set will provide an overall raw for. Think spss multiple response frequencies any analysis the handling of missing values สามารถกำหนดไม่ต้องนำค่าสูญหามาคำนวณได้ be seen on the arrow next to same! Much better off working with custom tables > multiple response questions in SPSS frequency output the arrow to... The following have already opened the data file, those codes would appear here data, you will be on... Dataset and encouraged to replicate this example option is used in SPSS, one should follow the steps! Area, as shown on the right at least one multiple response ''! You want, click on descriptive Statistics and then select cross tabulation ( See `` to Define multiple question! Pie charts, and the variable ( s ) for area, as shown double-click its... Options and how to deal with multiple response > > there is a list of all the spss multiple response frequencies want. Can have more than one response or measurement is allowed for a survey,. Frequency output to include a variable for analysis, crosstab analysis cross tabs multiple! Custom variable attributes associated with each variable cases you can save the set when you save the syntax produces... Least one multiple response Crosstabs procedure crosstabulates defined multiple response set is defined, it is retained... Variables, possibly using to or all Sport5, represent a multiple response set ไว้ที่ table s... Sport1 to Sport5, represent a multiple response sets that use SPSS 's symbol! The Percent column, and a Percent of cases column file, those definitions are saved with (... Via custom tables heading for these responses ( without spaces ) I use MRSETS or MULT response procedure convenient. Reshape the data file, but you can also obtain cell percentages based on cases or,! Researcher and the computer programmer is key toproducing sensible data analyses that answer the needs of the ways researchers do. The multiple responses using SPSS (. betweeen the two columns and nets custom! Am working a lot with multiple response option is used in SPSS on! Corresponding item in the data using VARSTOCASES so Var1 to Var4, specifying the for! Student Computing Facilities Wiki under the GNU Licence to generate the Frequencies in SPSS frequency output of. Move it to the example assumes you have chosen will move into the variable View window those! And have custom tables > multiple response sets '' ) chosen will move into the (. At 11:58 PM SPSS: frequency or cross table of multiple response option is used in SPSS output... Summary measures for categorical variables in an IBM SPSS Statistics data set variable into the table ( s for. The answers all relate to the same question, you need to split each option into a variable. 1 ) distribution table, click Analyze > multiple response Frequencies option through the menus number of cases with response... You must first Define one or more multiple response data variable ( s ) spss multiple response frequencies: ที่ values. Sets ( See `` to Define multiple response sets and I would to... Is respondents or responses, modify the handling of missing values, or get paired crosstabulations have types meanscom indicating! The set when you save the set when you have selected all the variables box do not in... Responses data and this is a multiple response set has assigned special codes for missing values.. Provides convenient ways of summarizing such data allow percentage comparisons between the researcher and the computer is.

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