Wright Map

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The Wright Map is an aggregate map of all students' current proficiency levels versus all the item difficulties, oriented on the same logit scale. One map is produced for each dimension in the model. In addition, maps of item step parameters are produced for each dimension if the Display Step Map option is set to Yes.

  1. Select Reports – Item Reports - Wright Map. You will be presented with a dialog window with the display options described in Table 1 and shown in Figure 1.
  2. Table 1. Display options for Wright Maps.
    Option Description
    Title The title you provide will appear at the top of the report. By default, this value is “Wright Map.”
    File Name Use the Browse... button to select the folder you want and then enter the filename you want the map to be stored in. ConstructMap will automatically store the report as a text file, so you do not need to add the .txt to your filename. ConstructMap will automatically store the Thurstonian threshold data in tt_filename.txt in the same directory.
    Item Set Browse... to the Item Set that you want to be included in the Wright Map. If you want to see all of the items, select the “base” Item Set.
    Display Raw Scores Select Yes if you want to see Raw Scores on the Wright Map, otherwise select No.
    Display Item Names Select Yes if you want to see item names in the report; select No if you want to see item numbers.
    Show Estimate Type Select Yes if you want to see the estimate type (e.g., EAP, MLE, etc.); select No if you do not want the estimate type shown in the report heading.
    Display Step Map ConstructMap will produce a map of Thurstonian threshold values by default. Select Yes here if you also want to see a map of item parameter values. The Step Map is usually not needed for dichotomous tests.
    Step Labels Select either raw responses (e.g. item1.a), category numbers (e.g., item1.3) or short labels for the step indicators (e.g., item1.COR). Short labels can be defined within each Criterion Zone.
    Max. Defined Range Set the maximum logit value to display. This option allows you to reduce or expand the visible area of the Wright Map to be different from the logit range defined in the Estimation Options (it does not change the way proficiency estimates are computed).
    Min. Defined Range Set the minimum logit value to display.
    Rows/Interval First, select Rows or Interval. Then, select the number of rows to be displayed per page, or the logit interval per row.



    This example uses the SEPUP Demo sample project.

  3. To obtain Wright Maps similar to those displayed here, use the default values as shown in Figure 1 and a file name of wmSEPUP_1. Click on OK to continue.
  4. A Wright Map shows the distribution of student proficiencies against item difficulties. One map is produced for each dimension in the model. In addition, maps of item step parameters are produced for each dimension if the Display Step Map option is set to Yes.

    Figure 1. Display options window for a Wright Map in ConstructMap.

    As shown in Figure 2, the top part of the report provides heading information about the report: 85 cases were used to generate the report and no filters were active; the item set is “1-12” and the title of the report is Wright Map. The proficiency estimation type is maximum likelihood (MLE) and the report shows items and proficiency estimates for the DCI variable.

    Figure 2. Wright Map displaying Thurstonian Thresholds for Item Set "1-12" on the DCI variable.

    The first column of data (starting from the left edge) shows the units for a continuous scale of logits, in this case from -6 to 6 (only the range 0 to 6 is displayed in the figure). The second column (not displayed in this EAP example), is labeled “raw” and appears only if Display Raw Scores has been set to Yes. The raw score is only displayed on a row when all cases at that proficiency level attained the same raw score; however, students may have attained those scores from completing different items. The raw score is the sum of the responses on items the respondent attempted. The next column, labeled “students”, shows a histogram of student proficiencies in which each X represents one or more students’ locations along the logit scale. Students with locations higher on the scale are more proficient than students lower on the scale.

    The last column, labeled “Thurstonian Thresholds”, shows the Thurstonian thresholds for each non-zero score of each item. Items are identified by their names (e.g.,DCI-AID, DCI-OD, ...) rather than their numbers (e.g., 1, 2, 3...) because the display option Display Item Names was set to Yes. Thurstonian thresholds are the locations at which students have a 50% probability of achieving that score or higher. For example, the Thurstonian threshold of 2.0 for step 3 of item “DCI-AID (which means a score of 3, or a response in category 4) shown in Figure 2 implies that respondents with a proficiency of 2.0 logits are as likely to achieve a score of 0, 1 or 2 as they are of achieving a score of 3 or higher on the item. Item scores with locations higher on the scale are more difficult to achieve than item scores lower on the scale.


    Figure 3 shows similar data, except that instead of Thurstonian thresholds, item step difficulty estimates are displayed. This optional map is displayed when Display Step Map is set to Yes in the Wright Map options dialog window. These item locations are interpreted differently from Thurstonian thresholds. Here, the location of item-step DCI-AID.3 on this map (i.e., at a logit score of 2.0) shows the difficulty of achieving a 3 rather than a 2 on item "DCI-AID". When computing response probabilities, the probability of obtaining a score of 3 on the item is the product of the probabilities of achieving a score of 1 rather than 0, of achieving a score of 2 rather than 1 and of achieving a score of 3 rather than 2, or P(x=1) * P(x=2) * P(x=3).

    Figure 3. Wright Map of Item parameters for the DCI variable of the SEPUP project.

    In another excerpt from this map, shown in Figure 4, we see that achieving a score of 3 rather than 2 on item “DCI-OD” requires far more additional ability than moving from a score of 1 to a score of 2. Because this is a rating scale model, in which the tau parameters are constant across all the items within a dimension, we will see the same item step difficulty patterns for all of the items. This would not generally be the case for a partial credit model.

    Figure 4. Continuation of Wright Map of item parameters for the DCI variable of the SEPUP project.

    By using all of the information the Wright map produces, teachers can gain insights about student performance relative to item content and the knowledge and skills that are necessary to move from one score level to another. Assessment designers can also use this information to analyze the quality of individual items and the contribution each item makes toward measuring a particular range on the ability scale.

  5. Note that these maps can be quite large, so scroll bars may appear at the side of the map. Drag the scroll bar down to see more of the report.
  6. Since this report produces text file output as well as an output screen, you can print this report using Word or Notepad. The file will be located in the folder you specified on the Wright Map Display Options window (note the filename in the upper left-hand corner of the heading area).
  7. Close the map display by clicking on the close box, CloseX.jpg, in the upper right-hand corner.

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