Iteman. User Manual WE MAKE ASSESSMENTS SMARTER, FASTER, AND FAIRER. Classical Item and Test Analysis

Transcription

1 Iteman WE MAKE ASSESSMENTS SMARTER, FASTER, AND FAIRER User Manual Classical Item and Test Analysis Version 4.4 April 2017

2 Contact Information Assessment Systems Corporation 125 Main Street SE Minneapolis, MN License Unless you have purchased multiple licenses for Iteman 4.4, your license is a singleuser license. Technical Assistance and support If you need technical assistance using Iteman 4.4, please contact support@assess.com., Please provide us with the invoice number for your license purchase when you request technical assistance. Citation Assessment Systems Corporation (2017). User Manual for Iteman 4.4. Minneapolis, MN: Author. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means electronic, mechanical, photocopying, recording, or otherwise without the prior written consent of the publisher. Copyright 2017 by Assessment Systems Corporation All Rights Reserved Iteman is the trademark of Assessment Systems Corporation

3 Table of Contents 1. Introduction... 1 Your Iteman 4 License and Unlocking Your Copy Input Files and File Menu... 4 The Data Matrix File... 4 Data Matrix File: Delimited... 4 Data Matrix File: Fixed-Width... 5 Data Matrix File: Iteman 3 Data Format... 5 The Item Control File... 6 File Menu Running the Program... 9 The Files Tab... 9 The Input Format Tab Differential Item Functioning (DIF) The Scoring Options Tab The Output Options Tab Using Multiple Runs Files Creating a Multiple Runs File Opening a Multiple Runs File A Sample MRF File Getting Started: Running the sample files What s in the Report? Output: Introduction Section Test-Level Output: Summary Statistics Test-Level Output: Reliability Analysis Test-Level Output: Graphics Test-Level Output: Conditional Standard Error of Measurement Item-Level Output How do I interpret the output? Item Difficulty The P value (Multiple Choice) The Item Mean (Polytomous) Item Discrimination Multiple Choice Items Polytomous Items... 31

4 DIF Statistics Option statistics Scores Output File Collusion Index (Bellezza & Bellezza, 1989) References Appendix A: The Iteman 3 Header The Control Line The Keyed Responses The Number of Alternatives The Scale Inclusion Codes Appendix B: Troubleshooting Please check the data file format specifications Please check the number of items or number of ID columns specified in the Iteman 3 Header Please select an input file with an Iteman 3 Header Valid item responses of 0 were identified. The Iteman 3 Header does not support item responses that begin at At least one valid item response of 0 was identified At least one unidentified response character was identified and will be scored as incorrect Check the data matrix file, examinee XXX did not respond to all XXX items Appendix C: Formulas Conditional Standard Error of Measurement Formulas Livingston Classification Consistency Index Differential Item Functioning Item Collusion Index Appendix D: Program Defaults File... 46

5 1. Introduction Iteman is a Windows application designed to provide detailed item and test analysis reports using classical test theory (CTT). The purpose of these reports is to help testing programs evaluate and improve the quality of test items by examining their psychometric characteristics. Iteman has a friendly graphical user interface (GUI) that makes it easy to run the program, even if you are not familiar with psychometrics. The GUI is organized into five tabs: Settings, Files, Input Format, Scoring Options, and Output Options. These are discussed in detail in Chapter 3: Running the Program. Iteman 4.4 offers several substantial advantages over Iteman 3, which was available approximately : 1. The most important advantage is the addition of graphics. It is now possible to produce an item quantile plot for each item. Moreover, you control the number of points in the plot. Additional graphics are also produced. 2. Iteman 4 is able to handle pretest (trial or unscored) items items that are not included in the final score but for which statistics are still desired. 3. More statistics are calculated, including the alpha (KR-20) reliability coefficient with each item deleted, several split-half reliability coefficients (both with and without Spearman-Brown correction), conditional standard error of measurement, and subgroup P (proportion correct) statistics for up to seven ordered groups. 4. Instead of simple ASCII text files, the output is now automatically assembled as a formal report document, which saves the menial copy-and-paste typically done to draft a report. Results are also in a comma-separated value (CSV) format that is able to be manipulated (sorted, highlighted, etc.) in spreadsheet software. It additionally produces a CSV file of examinee scores. 5. Scaled scores and subscores can calculated. 6. Scores can be classified into two groups at a specified cut score, and the two groups can use your labels, such as Pass and Fail. 7. Items can be analyzed relative to an external score rather than the total score on a test. 8. The maximum number of items that can be analyzed has been increased to 10, A batch type of capability, using a Multiple Runs File has, been added to allow you to run multiple data sets without having to use the graphic user interface for 1

6 each run. Multiple Runs files can be created outside Iteman in a text editor or interactively within Iteman. Your Iteman 4 License and Unlocking Your Copy Unless you have purchased a network or multiple-computer license, your license for Iteman 4 is a single-user license. If you would like to use Iteman 4 on a network or by more than one user, please contact us to arrange for the appropriate number of additional licenses. Iteman 4 is downloadable as a demonstration version. It is limited to no more than 100 items and 100 examinees, but has no expiration date. We can permanently convert your demo copy to the fully functioning software by , phone, or fax once you have completed the license purchase. To purchase, visit the To unlock Iteman 4, please activations@assess.com with: 1. Your name and address. 2. Your organization or affiliation. 3. Your invoice number (in the top right corner of your invoice). You should make a record of your invoice number since you might be asked for it if you request technical support. 4. The App ID. You can copy it from the screen below or click the Request a License Key button to automatically open an message. Click CLOSE to proceed using the demo version. 2

7 Figure 1.1: Screen Visible When Iteman 4 is Locked When we receive the App ID from you and confirm your payment, we will respond with a License Key that you will need to enter into this same. Once you enter the code(s) that we send you, your copy will be unlocked and fully functional. 3

8 2. Input Files and File Menu Iteman 4 requires two input files: the Data Matrix File and an Item Control File. The formats for these files are described in the following sections. The approach is inspired by statistical analysis software, which often has a Variables tab and a Data tab. The Data Matrix File The Data Matrix File is the file that contains examinee identification (ID) or name, and the responses to each item. Responses can be alphabetical (A,B,C,D or a,b,c,d ) or numerical (1,2,3,4 ), where A = a = 1, etc. It follows the standard approach of rows being people and columns being items or observations. Iteman accepts 3 formats: delimited, fixed-width, and Iteman 3. Data Matrix File: Delimited Iteman 4 permits the use of a data matrix file that is delimited by either a comma or a tab. The comma separated value (.csv) approach is often the easiest to work with because you can edit the files in standard spreadsheet software. As shown in Figure 2.1, this now permits the inclusion of variable length examinee IDs. Chapter 3: Running the Program describes how to specify a delimited input file. Figure 2.1: Example of a Comma-Delimited Data Matrix File Person9,4,2,1,3,3,2,3,4,1,2 Person10,1,2,1,3,3,2,3,4,1,0 Person11,3,3,2,3,1,2,3,4,1,3 Person12,1,2,2,3,3,2,3,4,1,4 Person13,2,2,1,4,3,2,3,4,1,1 If a differential item functioning (DIF) analysis was requested the DIF group membership code should follow the examinee ID as shown by Figure 2.2. It is important to note that the DIF membership codes (M and F) will not be recognized if they are included as part of the examinee ID (e.g., Person9M). Figure 2.2: Example of a Comma-Delimited Data Matrix with DIF Codes Person9,M,4,2,1,3,3,2,3,4,1,2 Person10,F,1,2,1,3,3,2,3,4,1,0 Person11,M,3,3,2,3,1,2,3,4,1,3 Person12,F,1,2,2,3,3,2,3,4,1,4 Person13,F,2,2,1,4,3,2,3,4,1,1 4

9 Data Matrix File: Fixed-Width The Fixed-Width approach is a text file where all columns must be aligned exactly. This hearkens back to the days of DOS. It still has the advantage of being able to store data far more efficiently than a CSV file or Microsoft Excel spreadsheet. An example of this is shown in Figure 2.3 for 10 items and 5 examinees. In this file, there are 9 columns of ID (the last two are blank) and 10 columns of responses. Figure 2.3: Example of an Input Data File (No Ignored Columns) Person Person Person Person Person Additional columns can be ignored, so it is not necessary to delete any data if your data file has information other than ID and responses. For example, your file might contain exam dates, locations, education level, or sensitive personal data that you do not want included in the output. An example of this is shown in Figure 2.4; you might want to include examinee ID numbers (the first six columns) in your output but not names. Chapter 3: Running the Program describes how to skip these columns. Figure 2.4: Example of an Input Data File (Columns to Ignore) John Doe M Jane Doe F Jack Hall M Jim Hill M Jen Smith F Data Matrix File: Iteman 3 Data Format Iteman 4 permits the analysis of a Data Matrix File in the format used with Iteman 3 (and other programs in the 1990s Item and Test Analysis package), which includes four header lines of control information in the data file rather than in a separate control file. If the Iteman 3 header is included in the Data Matrix File, then the user should specify this with the checkbox on the Files tab of Iteman 4. This approach has the advantage of using only one input file, but the disadvantage that it does not include Item IDs or domains. See Appendix A for a description of the Iteman 3 header. 5

10 The Item Control File The previous version of Iteman required that the specifications for the test be provided on the first four lines of the data file, with all the data itself moved down to line 5. Iteman 4 provides the specifications as a separate Item Control File. This makes it easier to produce, as well as allows for the handling of a greater amount of information. This file is tabdelimited or comma-delimited, which means that you can construct it in a spreadsheet program and then Save As a tab-delimited text file or CSV. There are six columns of information in the control file for each item. Begin each item on a new line. 1. Item ID: cannot contain a tab character, but length can vary across items. 2. Key(s): Correct answer(s) as A,B,C,D or 1,2,3,4 for standard multiple choice questions. Multiple correct answers should be entered without a comma. Example: AB 1 if items are scored dichotomous. For polytomous items: + if positively scored or if negatively or reverse scored. 3. Number of alternatives (maximum is 15). For multiple-choice data that are already scored (converted to 0 or 1), the number of options is 2. However, we recommend recoding so that 1=correct and 2=incorrect, as starting at 0 is typically reserved for partial credit items. 4. Domain or content area (unique domain label, maximum is 50). 5. Inclusion status: Y = Yes (included in the analysis) N = No (not included) P = Pretest 6. Item type: M = Multiple-choice items with responses that begin at 1 or A. For scored multiple-choice data (0/1), see P below. R = Rating scale items: polytomous items with responses that begin at 1 or A). P = Partial credit items with numeric responses that begin at 0 (e.g., 0, 1, 2, 3). This includes multiple-category partial credit items, and dichotomously scored multiple-choice items (scored 0 or 1). An example of the control file is shown in Figure 2.5. There are ten items, with nine multiple choice items and one partial credit item. The first five are in Domain 1, while the latter five are in Domain 2. The first four items in each domain are scored, while the fifth 6

11 item in each is a pretest item. The keyed answers are either 1, 2, 3, or 4 for each multiple choice item since each item has 4 alternatives. Keys can be alphabetical or numeric. Item 7 has two keyed responses, 3 and 1. For Item 7, item responses will be scored as correct if the examinee answers either 3 or 1. If an item is polytomously scored, the key should be + if positively scored and - if negatively (reverse) scored. Item 10 is a positively scored (+) partial credit item with item responses that begin at 0. For item 10, the item responses will be 0, 1, 2, 3, and 4, since the item has five options. The control file should have as many lines as there are items in the test. The program counts the lines of information in the control file, and that serves as the total number of items in the test. There is a maximum of 10,000 items (lines) in Iteman 4. Figure 2.5: Example of an Item Control File Item Science Y M Item Science Y M Item Science Y M Item Science Y M Item Science P M Item Reading Y M Item Reading Y M Item Reading Y M Item Reading Y M Item Reading P P File Menu The File Menu contains commands for program defaults, options, and multiple runs. 7

12 Create/Run Multiple Runs File If you would like to interactively create a Multiple Runs File (MRF) you can do so by clicking opening the File menu and selecting Create a Multiple Runs File. In addition, you can run a previously saved MRF by clicking Run a Saved Multiple Runs File. Open an Options Files This open allows you to open a previously saved Options File. The selected Options File will automatically override the current program defaults when opened. The Options File is equivalent to a Program Defaults file, and contains the options requested in the user interface. Save an Options File To save the current GUI settings to an external file of your choice, you can do so by selecting that option on the Files menu. The Options File is necessary for a Multiple Runs File where the program settings are read in from an external file and not selected using the GUI. Save the Program Defaults This will overwrite the existing program defaults with the changes made during the current run of the program. These changes will appear the next time the program is loaded. For more information on the Program Defaults File see Appendix D. 8

13 3. Running the Program Iteman s interface is divided into four tabs. The Files tab specifies the files to be used: Data Matrix, Item Control, Output, and an optional external score file. The Input Format tab tells Iteman what to expect in your input. For fixed-width, it specifies the columns of the Data Matrix File for IDs and item responses and permits you to specify the character code used in the Data Matrix to indicate omitted/skipped and not administered items. In addition, this tab is where you can request and set up a DIF analysis. The Scoring Options tab enables you to perform scaled scoring and to perform dichotomous classification. The Output Options tab specifies options for the output. The Files Tab To specify the files on the Files tab (Figure 3.1), click on the speed button for each file. This will activate a standard dialog window to specify the path and name of each file. If the Data Matrix File has an Iteman 3 (ITAP) header, be sure to check this box: The Item Control file box will be disabled when the Iteman 3 Header box is checked, as will the options on the Input Format tab. Name your output file in the third box. The output file must have a.docx extension. The fourth box allows you to name your Run. This will appear on the title page of the report output. The final box is used if you have a file containing examinee scores that have been produced by some method other than number-correct that you wish to use as the basis for your statistics (for example, a scaled score reported by your testing vendor). The scores in this file, one line per examinee, must be in the same order as those in the examinee data file. 9

14 Figure 3.1: The Files Tab The Input Format Tab The Input Format tab (Figure 3.2) tells Iteman what to expect in your data file. First, select your approach: Fixed Width or Delimited. If you are using the fixed width approach, specify the number of columns devoted to examinee ID information that you want to capture for your score output, then specify the column in which the IDs begin. Next, specify the column in which item responses begin. This column number can be increased to skip unwanted columns. 10

15 Figure 3.2: The Input Format Tab If the Data Matrix File is delimited, specify so by clicking on the Data matrix is delimited by a: checkbox. Next specify whether the data file is delimited by a tab character or a comma. Selecting that the data matrix file is delimited will disable the Data matrix file includes an Iteman 3 Header box and the three fixed width column boxes. If the delimited response matrix does not include examinee ID in the first column, make sure that the Response matrix includes examinee ID box is not checked. If you have a special character in your data representing omitted/skipped responses or not-administered items, these are specified next. These responses will be treated separately, with frequencies provided in the output. If all items were answered by all examinees, you can leave these characters as the default value, and of course no examinees will be noted as having such characters. Empty cells are treated as omits by default. 11

16 If your Data Matrix File includes an Iteman 3 header, the options on this tab will be deactivated and the following message will be displayed: Differential Item Functioning (DIF) DIF is an analysis of bias, for example if the item is easier for an ethnic majority, using the Mantel-Haenszel approach. To request a DIF analysis for each scored dichotomous item select the checkbox next to that option. If you are performing a DIF analysis you must specify which column the group code appears in. This option is not valid for delimited input and will remain deactivated; Iteman assumes the second column is group code. The create X ability levels for the DIF test option specifies the number of ability levels created for purposes of the Mantel-Haenszel DIF test. Specify the characters used to identify the reference and focal groups. These characters are not case sensitive. Specify the labels for the reference and focal groups. The labels provided will be used in the output when the DIF test is significant. The Scoring Options Tab The Scoring Options tab (Figure 3.3) provides the options to perform scaled scoring and/or dichotomous classification. If your testing program reports scaled scores based on raw number-correct scores, these can be calculated directly. Scaled scores are computed using the scaling function (detailed below) for the total number correct scores and/or the domain number-correct scores. Scaled scoring is often used to mask details about the test, such as exact number of items or raw cutoff score, or to express scores on a different scale than number correct. Most large-scale tests use a form of scaled scoring. o Linear scaling: The raw scores are first multiplied by the slope coefficient then the intercept is added to the product. For example, if you want the scores to be reported on a scale of 100 to 200 for a test of 50 items, the scaled score could be specified as SCALE = RAW o Standardized scaling: The raw scores are converted to have a mean of X and a standard deviation of Y. This form of scaling is useful if you desire to center the 12

17 mean of the test around a constant value for use in a report. For example, the classic IQ scale with mean=100 and SD=15. Figure 3.3: The Scoring Options Tab If you want to perform dichotomous classification of examinees, such as pass/fail, click the box next to that statement. It is possible to classify based on either total number-correct or the scaled total number-correct scores. o Cutscore: The cutscore, aka passing score or cutpoint, is the value at which scores are classified as in the high group. Scores below the cutscore are classified as being in the low group. o Low group label: Label used in the Scores output file for those in the low group. o High group label: Label used in the Scores output file for those in the high group. 13

18 The Output Options Tab The Output Options tab (Figure 3.4) provides the ability to tailor the output report to your specific needs. Figure 3.4: The Output Options Tab Item statistic flagging allows you to specify an acceptable range for a statistic. For example, if you want to identify all items that have a P (proportion correct) outside 0.40 and 0.98, it can be specified here, and then the output will label items with low P as LP and high P as HP. The acceptable item mean range is used to flag the item means of polytomous items to identify outlier items. Flags are further explained in Chapter 4. 14

19 Selecting the Exclude omits from option statistics box will prevent omits from having the full complement of option statistics computed for them. The default of scoring omits as incorrect affects the reliability coefficients, and provides the full complement of option statistics for omits. For polytomous items, omits are automatically excluded from the option statistics. If you want to have the point-biserial and biserial correlations corrected for spuriousness, click the check box next to that statement. Spuriousness refers to the fact that an item s scores are included in the total score, so correlating an item with the total score implies that it is being correlated with itself to some extent. This effect is negligible if there are a large number of items on the test (e.g., more than 30), but Iteman 4 provides the option to correct for this issue, which should be utilized for tests of 30 items or less. Produce quantile plots for each item is one of the most important options in the interface. Checking this will produce a graphical plot of the specified number of subgroups (up to 7) for each item; interpretation of these plots is discussed in Chapter 4: Interpretation of the Output. The quantile plot will be produced for only the first 9 alternatives for an item. Click the check box for this option if you wish to produce quantile plots for each item, with every page of the output containing the plot and the statistics table for a given item. Produce the quantile plot data table will provide a table for each item that contains the proportions in each subgroup that are shown graphically in the quantile plot. The quantile plot data table will present the subgroup proportions for up to 15 alternatives plus the omit and not administered codes. Create X groups for the quantile plots allows you to increase or decrease the number X of examinee groups used for constructing the quantile plots. This number can range from 2 to 7. Larger numbers of points are recommended only for large sample sizes of at least 1,000 examinees. Produce collusion index matrix (multiple-choice item only) will provide a data forensics (cheating) analysis using the response similarity approach of Bellezza and Bellezza (1989). The full matrix is saved in a separate BBO-matrix.csv file. The analysis involves comparisons between all possible pairs of examinees to see if their responses might be similar. Pairs of responses are considered as suspect i.e., flagged, if the index value is below the threshold you specify on the right. This should be very low, such as , as this approach can easily produce false positives, especially without a correction like Bonferroni. Iteman produces the response similarity analysis only for scored multiplechoice items. If you need to convert multiple-choice (ABCD) data into dichotomously-scored (0/1) data, Iteman 4 provides an option for this. 15

20 Save item control file (if Iteman 3 input) will create a Control File for you in the Iteman 4 format. The control file will also be saved with the same name as the output file, but with Control.txt appended to the end of the filename. Include omit codes in the data matrix and Include not administered codes in the data matrix determines whether omit/not administered codes are kept in the scored matrix or scored as incorrect (0). Omit/not administered codes are automatically left in the data matrix for polytomous items. The Flags panel on the right allows you to specify the text you want to use for key flag, low and high flags for P-value, point-biserial correlation, item mean, and DIF flag. For example, you might want to change LP (low P) to LowDiff. Using Multiple Runs Files Creating a Multiple Runs File If you would like to perform multiple item analyses with a single run of the program, then you should create a Multiple Runs File (MRF). For example, if you work with school assessments and at the end of the year you are presented with 80 different tests to analyze but they are all formatted similarly, you can run Iteman once rather than 80 times. To interactively create an MRF, select the Create a multiple runs file button on the Settings tab. This will open the window shown in Figure 3.5 that allows the interactive setup of the multiple runs file. Note that the options are grayed out because no path has been selected. This interactive window contains the MRF text editor window which shows the files/options selected for the multiple runs file. To create an MRF: 1. Select the folder where the files used for the analysis are stored. Click Add Path to add the Path to the MRF. (You must complete steps 2, 3, and 4 to perform an analysis.) 2. Select the Options File: a. If you saved the program options to an external file, open this file and select Add Options. The Options file will be added to the MRF. b. If you wish to use the program defaults, select Use Defaults. The Keyword DEFAULTS will appear in the MRF text editor next to OPTS. 3. Select the item control file (the data file(s) must follow the item control keyword): 16

21 a. If you are using an Item Control File, use the file open icon to select the then select Add Control. The name of the control file will appear in the MRF box next to CTRL. b. If the data matrix includes an Iteman 3 Header then select the Skip Control box. A blank space will appear next to the CTRL statement in the MRF box. 4. Select the data file(s) and click Add Data. Figure 3.5: The Multiple Runs File Window Note that if you enter a file name that does not exist in the selected folder, and select Add, the program will not add the file to the MRF. It is important to note that the options*, control**, and data files for a specific analysis all must reside within the same folder. *Unless the defaults are used **Unless an Iteman 3 Header is used 17

22 You may delete entries in the MRF text editor by clicking on the line and hitting Delete or Backspace. However the following file sequence must be observed for the MRF to work correctly: 1. The first PATH keyword must be followed by the OPTS, CTRL, and DATA lines 2. If you wish to use a different OPTS file, that file must appear after the PATH statement. 3. The CTRL statement must be followed by the DATA line(s). To Save the text in the MRF editor box to an external file, select the Save MRF button. This will allow you to save the MRF to a folder of your choosing. An example of a completed MRF file is shown below. To Run the MRF select the RUN MRF box. Note that the text in the MRF editor box will automatically be saved to an external file when you run the MRF. The saved MRF text file will have the word MRF appended to the end of the filename of the last selected data file. The following output files will be generated for each DATA file in the MRF 1. DATA.rtf The main rich text output file that includes the graphics and tables 2. DATA.csv The comma-separated values output file 3. DATA Scores.csv The scores saved as a comma-separated values file The following output files are optional and will be generated for each DATA file in the MRF if requested in the Options File: 4. DATA Matrix.txt The scored data matrix file 5. DATA Control.txt The item control file if the original data matrix file used an Iteman 3 Header and a scored data matrix was requested Opening a Multiple Runs File A previously saved multiple runs file can be opened using the File menu. To do so select the file and click Open. Iteman 4 will automatically run the opened multiple runs file. The file can be one saved from the interactive window described above or one created in a text editor. The format of the MRF file is as follows: 1. Keyword PATH separated by a tab followed by the Windows path 2. Keyword OPTS separated by a tab followed by the options file name (if an external options file is used) or DEFAULTS if the program defaults are to be used 3. Keyword CTRL separated by a tab followed by the item control file name (if an item control file is used) or Iteman 3 if the data matrix includes an Iteman 3 Header. 4. Keyword DATA separated by a tab followed by the data file name. 18

23 MRFs may also be created or edited in a test editor. They must, however, be saved as pure text (not word professing) files. A Sample MRF File Figure 3.6 displays a sample Multiple Runs File: PATH C:\Sample Files\ OPTS Sample.options CTRL Control.txt DATA Exam1.txt DATA Exam2.txt DATA Exam3.txt CTRL ITEMAN 3 DATA Exam4.txt Figure 3.6: A Sample Multiple Runs File The data files Exam1.txt, Exam2.txt, and Exam3.txt all make use of the control file Control.txt. The data file Exam4.txt uses an Iteman 3 Header, so the CTRL line with ITEMAN 3 precedes the DATA line. The new CTRL line overrides the previous CTRL file Control.txt and the keyword ITEMAN 3 deactivates the input of the control file. A new PATH statement at the end of this file would change the folder location of any following OPTS, CTRL and DATA files to be analyzed. An MRF file can have any number of lines. Getting Started: Running the sample files For a new user, the best way to start is by running the sample files that come with the software. This will provide experience with the necessary steps to run the program after the input files have been successfully made. Version 4.4 of Iteman 4 is installed with three sets of sample files: multiple choice (MC) only, polytomous rating scale (RS) only, and a mixed test. The mixed test is intended to simulate an educational exam where there are a large number of multiple-choice items (40 in this case) and a few constructed response items (2 in this case). To run the sample files, follow these steps, one step for each tab. 1. Specify your files. You can name your output file whatever you like. Figure 3.9 shows what the Files tab should now look like. 2. The sample data file has 6 columns of ID information, beginning in column 1, while item responses begin in column 7. These are determined by counting columns in the data 19

24 file (advanced text editors can count this for you, such as Notepad++). Specify these numbers on the Input Format Tab. There is no missing data in the sample file, so you do not have to be concerned with the Omit or Not Administered characters. 3. Specify any Scoring Options and Output Options you wish. The program will run successfully if you do not make any changes on the third and fourth tabs. Once the program has successfully run, you will be shown a message to tell you that the run is complete, and where to find the output file. Clicking Yes will open the relevant directory. 20

25 4. What s in the Report? Iteman 4 provides three default output files: (1) a DOCX report, (2) a CSV file of item statistics and (3) a CSV file of examinee scores. In addition, there is the optional output of scored item responses. The CSV file of test and item statistics includes the same statistics as are in the DOCX report, but in CSV form so you can manipulate the data in a spreadsheet or easily upload it into item banking software such as FastTest. Output: Introduction Section The primary output, the DOCX report, is presented as a formal report that can be provided to test developers or subject matter experts (SMEs). It begins with a title page which is followed by summary information of the input specifications. This is important for historical purposes; if the report is read a few years from now, it will be evident how Iteman 4 was set up to produce the report. If more than 250 items are analyzed, the itemlevel report will be divided into separate files. The test-level output and the item-level output for the first 250 items will be saved in the first file. The second file will be comprised of the item-level output for items Additional item-level files will be created for all k items with each file containing the output for up to 250 items. Test-Level Output: Summary Statistics Next, the report provides test-level summary statistics based on raw number-correct scores (or external scores if utilized). This is done for the total score (all items) as well as the actual score (scored items only), pretest items only, and all domains or content areas. The following are definitions of the columns in this table. Label Explanation Score which portion of the test that the row is describing Items number of items in that portion of the test Mean average number correct SD standard deviation, a measure of dispersion (a range of ± two SDs from the mean includes approximately 95% of the examinees, if their number-correct scores are normally distributed) Min score the minimum number of items an examinee answered correctly Max score the maximum number of items an examinee answered correctly 21

26 Mean P Item Mean Mean R average item difficulty statistic for that portion; also the average proportion-correct score if there are no omitted responses (not reported if there are no multiple choice items) average of the item means for polytomous items (not reported if there are no polytomous items) average item-total correlation for that portion of the test The test-level summary table (Table 4.1) allows you to make important comparisons between these various parts of the test. For example, are the new pretest items of comparable difficulty to the current scored items? Are items in Domain 2 more difficult than Domain 1? Were the mean and standard deviation (SD) of the raw scores what should be expected? Table 4.1: Example Summary Statistics Score Items Mean SD Min Score Max Score Mean P Mean Rpbis All items Scored Items Pretest items Domain Domain Domain Test-Level Output: Reliability Analysis The reliability analysis provides a table that summarizes the reliability statistics computed by Iteman 4. Coefficient α (alpha) and the SEM (based on α) are computed for all items, scored items only, pretest items only, and for each domain separately. Three forms of split-half reliability are computed. First the test is randomly divided into two halves and the Pearson product-moment correlation is computed between the total score for the two halves. Also provided is the split-half correlation between the total scores for the first half and the second half of the test, and the odd- and even-numbered items on the test. Since these correlations are computed using half the total number of items, the Spearman- Brown corrected correlations are also provided. If a dichotomous classification was performed, and all the scored items are multiple choice, the Livingston decision consistency index is computed at the cut-score (expressed as number-correct scores). The equation for the Livingston index is provided in Appendix C. Table 4.2: Example Reliability Analysis 22

27 Score Alpha SEM Split-Half (Random) Split-Half (First-Last) Split-Half (Odd-Even) S-B Random S-B First- Last S-B Odd- All items Scored items Pretest items Domain Domain Domain Even Test-Level Output: Graphics After the test-level statistical table, a grouped frequency distribution figure is presented, showing the distribution of number-correct scores for the scored items, as seen in Figure 4.1. Similar graphs are produced for each domain, if you have more than one domain. Figure 4.1: Example Score Distribution After the histograms for the scored items, histograms for the item statistics are provided, each followed by a table of numerical values corresponding to the histograms. If there were scored multiple-choice items, the histogram for the item P values and Rpbis correlations are provided. If there were scored polytomous items then the histogram for the item means and the Pearson r correlations are provided. 23

28 Next, scatterplots are provided of the P value by Rpbis if there are scored multiple-choice items, and of the item mean by Pearson s r if there are scored polytomous items. Test-Level Output: Conditional Standard Error of Measurement The classical CSEM function is plotted for observed number-correct scores between 0 and the total number of scored items. The CSEM plot is provided only if there are no scored polytomous items. The plot is computed using Lord s (1984) Formula IV. CSEM Formula IV makes the explicit assumption that all items are scored (0/1), so it cannot be computed for total score when there are polytomous scored items. A sample CSEM plot is shown in Figure 4.2. A low value means that we expect that examinee to get a similar score upon a retake. Figure 4.2: Example CSEM Function If dichotomous classification was performed, then the CSEM is reported at the cutscore (expressed as number correct). If you used a scaled cutscore, this scaled cutscore is converted to the raw number-correct scale for reporting. Item-Level Output After the test-level statistics, a detailed table of the statistics for each item is provided, one item to a page. If the quantile plots option is selected, that is also provided on the same page, as shown in Figure 4.3 for a dichotomously scored item and Figure 4.4 for a polytomous item. The quantile plot, as seen in Figure 4.3, is arguably the best way to graphically depict the performance of an item with classical test theory. It is constructed by dividing the sample 24

29 into X groups based on overall number-correct score, or an external score if used, and then calculating the proportion of each group that selected each option. For a four-option multiple-choice item with three score groups as in the example, there are 12 data points. The 3 points for a given option are connected by a colored line. A good item will typically have a positive slope on the line for the correct/keyed answer, while the slope for the incorrect options should be negative. 25

30 Figure 4.3: Example Item-Level Output for a Multiple-Choice Item 26

31 Figure 4.4: Example Item-Level Output for a Polytomous Item 27

32 The item information table in Figures 4.3 and 4.4 provides the item sequence number, item ID, keyed response, number of options, and the domain the item is in. The item statistics table provides item-level statistics and is described separately for multiple-choice and polytomous items. Label N P Domain Rpbis* Domain Rbis* Total Rpbis Total Rbis Alpha w/o Flags Label N Mean Domain r* Domain Eta* + Total r Total Eta + Alpha w/o Flags Multiple-Choice Items Explanation Number of examinees that responded to the item Proportion correct Point-biserial correlation of keyed response with domain score Biserial correlation of keyed response with domain score Point-biserial correlation of keyed response with total score Biserial correlation of keyed response with total score The coefficient alpha of the test if the item was removed Any flags, given the bounds provided; LP = Low P, HP = High P, LR = Low rpbis, HR = High rpbis, K = Key error (rpbis for a distractor is higher than rpbis for key), DIF for any item with a significant DIF test result Polytomous Items Explanation Number of examinees that responded to the item Average score for the item Correlation of item (Pearson s r) with domain score Coefficient eta from an ANOVA using item and domain scores Correlation of item (Pearson s r ) with total score Coefficient eta from an ANOVA using item and total scores The coefficient alpha of the test if the item was removed Any flags, given the bounds provided; same as dichotomous except that mean score instead of P *Output provided if there are 2+ domains. + Eta is reported if the item has 3+ categories, otherwise the biserial correlation will be reported. If requested, the DIF test results also appear in the classical statistics table and are defined below. 28

33 Label M-H p Bias Against Explanation The Mantel-Haenszel DIF statistic p-value associated with M-H test statistic If p is less than 0.05, the group the item is biased against The following table provides explanations for option-level information in the third table seen in Figures 4.3 and 4.4, Option statistics. Label Option Weight N Prop. Rpbis Rbis Mean Color (key) Explanation Letter/Number of the option Scoring weight for polytomous items Number of examinees that selected the option Proportion of examinees that selected the option Point-biserial correlation (rpbis) of option with total score Biserial correlation of option with total score Average score of examinees that selected the option Color of the option on the quantile plot The keyed answer will be denoted by **KEY** for multiple choice items The final table in Figures 4.3 and 4.4 presents the calculations for the quantile plots. The number of columns in this table will match the number of score groups you specified on the Output Options tab. Iteman 4 was designed to produce DOCX output instead of PDF output to allow you to make additions/modifications to the report. A very useful addition would be to paste item text and comments below the plot/table for each item (Figures 4.3 and 4.4). The report can then be delivered to content experts with an easy-to-read plot, detailed tables, and the item text neatly arranged on each page, one page for each item. 29

34 5. How do I interpret the output? At a higher level, the use of Iteman 4 output has two steps: first, to identify which items perform poorly, and secondly to diagnose the problems present in those items. The following are some definitions of, and considerations for, item statistics. Item Difficulty The P value (Multiple Choice) The P value is the proportion of examinees that answered an item correctly (or in the keyed direction). It ranges from 0.0 to 1.0. A high value means that the item is easy, and a low value means that the item is difficult. The minimum P value bound represents what you consider the cut point for an item being too difficult. For a relatively easy test, you might specify 0.50 as a minimum, which means that 50% of the examinees have answered the item correctly. For a test where we expect examinees to do poorly, the minimum might be lowered to 0.4 or even 0.3. The minimum should take into account the possibility of guessing; if the item is multiple-choice with four options, there is a 25% chance of randomly guessing the answer, so the minimum should probably not be The maximum P value represents the cut point for what you consider to be an item that is too easy. The primary consideration here is that if an item is so easy that nearly everyone gets it correct, it is not providing much information about the examinees. In fact, items with a P of 0.95 or higher typically have very poor point-biserial correlations. The Item Mean (Polytomous) The item mean is the average of the item responses converted to numeric values across all examinees. The range of the item mean is dependent on the number of categories and whether the item responses begin at 0. The interpretation of the item mean depends on the type of item (rating scale or partial credit). A good rating scale item will have an item mean close to ½ of the maximum, as this means that on average, examinees are not endorsing categories near the extremes of the continuum. The minimum item mean bound represents what you consider the cut point for the item mean being too low. The maximum item mean bound represents what you consider the cut point for the item mean being too high. The number of categories for the items must be considered when 30

35 setting the bounds of the minimum/maximum values. This is important as all items of a certain type (e.g., 3-category) might be flagged. Item Discrimination Multiple Choice Items The item point-biserial (r-pbis) correlation. The Pearson point-biserial correlation (r-pbis) is a measure of the discrimination, or differentiating strength, of the item. It ranges from.0 to 1.0. A good item is able to differentiate between examinees of high and low ability, and will have a higher point-biserial, but rarely above A negative point-biserial is indicative of a very poor item, because then the high-ability examinees are answering incorrectly, while the low examinees are answering it correctly. A point-biserial of 0.0 provides no differentiation between low-scoring and high-scoring examinees, essentially random noise. The minimum item-total correlation bound represents the lowest discrimination you are willing to accept. This is typically a small positive number, like 0.10 or If your sample size is small, it could possibly be reduced. The maximum item-total correlation bound is almost always 1.0, because it is typically desired that the r-pbis be as high as possible. The item biserial (r-bis) correlation. The biserial correlation is also a measure of the discrimination, or differentiating strength, of the item. It ranges from 1.0 to 1.0. The biserial correlation is computed between the item and total score as if the item was a continuous measure of the trait. Since the biserial is an estimate of Pearson s r it will be larger in absolute magnitude than the corresponding point-biserial. The biserial makes the stricter assumption that the score distribution is normal. The biserial correlation is not recommended for traits where the score distribution is known to be non-normal (e.g., pathology). Polytomous Items Pearson s r correlation. The Pearson s r correlation is the product-moment correlation between the item responses (as numeric values) and total score. It ranges from 1.0 to 1.0. The r correlation indexes the linear relationship between item score and total score and assumes that the item responses for an item form a continuous variable. The r correlation and the r-pbis are equivalent for a 2-category item. 31

36 The minimum item-total correlation bound represents the lowest discrimination you are willing to accept. Since the typical r correlation (0.5) will be larger than the typical rpbis (0.3) correlation, you may wish to set the lower bound higher for a test with polytomous items (0.2 to 0.3). If your sample size is small, it could possibly be reduced. The maximum item-total correlation bound is almost always 1.0, because it is typically desired that the r-pbis be as high as possible. Eta coefficient. The eta coefficient is computed using an analysis of variance with the item response as the independent variable and total score as the dependent variable. The eta coefficient is the ratio of the between groups sum of squares to the total sum of squares and has a range of 0 to 1. The eta coefficient does not assume that the item responses are continuous and also does not assume a linear relationship between the item response and total score. As a result, the eta coefficient will always be equal or greater than Pearson s r. Note that the biserial correlation will be reported if the item has only 2 categories. DIF Statistics Differential item functioning (DIF) occurs when the performance of an item differs across groups of examinees. These groups are typically called the reference (usually majority) and focal (usually minority) groups. The goal of this analysis is to flag items that are potentially biased against one group. There are a number of ways to evaluate DIF. The current version of Iteman utilizes the Mantel-Haenszel statistic, where each group is split into several ability levels, and the probability of a correct response compared between the focal and reference groups for each level. See Appendix C for the equations. Results of this analysis are added into both the CSV and RTF output files. Mantel-Haenszel The Mantel-Haenszel (M-H) coefficient is reported for each item as an odds ratio. The coefficient is a weighted average of the odds ratios for each θ level. If the odds ratio is less than 1.0, then the item is more likely to be correctly endorsed by the reference group than the focal group. Likewise, odds ratios greater than 1.0 indicate that the focal group was more likely to correctly endorse the item than the focal group. The RTF file contains the overall M-H coefficient for an item; the CSV output file also includes the odds ratios for each θ level. These ratios can be used to determine if the DIF present was constant for all abilities (uniform DIF) or varied conditional on θ (crossing DIF). The M-H coefficient is not sensitive to crossing DIF, so null results should be checked to confirm that there wasn t crossing DIF present. 32

37 z-test Statistic The negative of the natural logarithm of the M-H odds ratio was divided by its standard error to obtain the z-test statistic used to test the significance of the M-H against a null of zero DIF (odds ratio of 1.0). This test statistic is provided in the CSV output file. p The two tailed p value associated with the z test for DIF. Items with p values less than.05 will be flagged as having significant DIF. Bias Against The group the item is biased against when the p value is less than.05. In the context of the M-H test for DIF, the group that the item is biased against has a lower probability of a correct response than the other group, controlling for ability level. Option statistics Each option has a P value and an r-pbis. The values for the keyed response serve as the statistics for the item as a whole, but it is the values for the incorrect options (the distractors) that provide the opportunity to diagnose issues with the item. A high P for a distractor means that many examinees are choosing that distractor; a high positive r-pbis means that many high-ability examinees are choosing that distractor. Such a situation identifies a distractor that is too attractive, and could possibly be argued as correct. Scores Output File The CSV score output file provides the scores for each examinee, separated by item type. Figure 4.5 displays the scores for 10 examinees. The columns in this file are as follows: 1. Sequence The row number of the examinee in the data file. 2. ID Examinee ID from the data file. 3. Scored items The total number-correct (raw) score for all scored items across all domains. 4. All items The total number-correct score for all scored items across all domains plus all of the pretest items included in the test. 5. Pretest items Provides the number-correct scores for the pretest items only. 6. Scored Proportion Correct The proportion of scored items correct across all domains. This value is only output if there are no scored polytomous items. 7. Rank The rank of the examinee s score, from 1 to N, which is calculated as the number of examinees with total scores for the scored items (column 1) greater than or equal to the given examinee. Examinees that are tied with the same score receive the lowest 33

38 rank available (e.g., Examinees 4 and 8 have ranks of 4,167). Examinee(s) with the highest score will receive a rank of Percentile The percentage of examinees whose total score falls below the given score. 9. Group The score group an examinee is classified into is based on total score for all the scored items. The number of score groups is determined by the value set in the Create X score groups for the quantile plots / summary table box on the Output Options tab. 10. Domain X The final column(s) in the scores output file contain the domain scores separately for each domain. If more than one domain was specified in the Item Control File, then the total number-correct scores calculated separately for each domain would be found after the Group column. If the test has only one domain, this will not be included, as it will be the same as the Scored items column. 12. Scaled Total Score If scaled scores were computed for total score these will appear. 12. Scaled Domain Score X If scaled scores were requested for each domain and there is more than one domain these will be provided. 13. Classification If dichotomous classification was performed the results of the classification will be provided. Classification can be performed with the raw total number-correct scores or the scaled total number correct score. 14. CSEM III The conditional standard error of measurement Formula III from Lord (1984) if there are no scored polytomous items. 15. CSEM IV The conditional standard error of measurement formula IV from Lord (1984) if there are no scored polytomous items. Across all observed scores, this formula is most comparable to the classical SEM found in Table 4.2. Figure 4.5: Sample Examinee Scores Output 34