Table 8 Scale structure probability curves

Use the "Graphs" pull down menu to obtain these as bit-mapped plots.

 

 

Specify "Graphfile=" to obtain the numbers to plot these yourself.

 

Table 8 includes a line-printer plot of the probability of occurrence for each category. The probability of the extreme categories always approaches 1.0 for corresponding extreme measures.

 

Most scale developers intend this to look like a series of hills, so that each category is in turn the most likely category along the latent variable.

 

Probability Curves

      -3.0       -2.0       -1.0        0.0        1.0        2.0        3.0

       ++----------+----------+----------+----------+----------+----------++

     1 |                                                                   |

       |                                                                   |

       |00                                                               22|

       |  00000                                                     22222  |

       |       000                                               222       |

     P |          000                                         222          |

     r |             00                                     22             |

     o |               00                                 22               |

     b |                 000                           222                 |

     a |                    00        1111111        22                    |

     b |                      0  11111       11111  2                      |

     i |                      1**                 **1                      |

     l |                   111   00             22   111                   |

     i |                 11        00         22        11                 |

     t |              111            00     22            111              |

     y |           111                 00*22                 111           |

       |       1111                    22 00                    1111       |

       |   1111                     222     000                     1111   |

       |111                    22222           00000                    111|

       |               22222222                     00000000               |

     0 |222222222222222                                     000000000000000|

       ++----------+----------+----------+----------+----------+----------++

      -3.0       -2.0       -1.0        0.0        1.0        2.0        3.0

 

The expected score ogive shows the average rating value expected for any measure relative to the item, judge etc. The ogive also indicates the category "zone", e.g., the area between average ratings of 0.5 and 1.5 is marked by 1's plotted on the curve.

 

Expected Score Ogive

      -2.0         -1.0          0.0          1.0          2.0          3.0

       ++------------+------------+------------+------------+------------++

     2 |                                                                  |

       |                                                            222222|

       |                                                     2222222      |

       |                                                22222             |

       |                                           22222                  |

       |                                        122                       |

       |                                    1111                          |

       |                                 111                              |

       |                               11                                 |

       |                            111                                   |

     1 |                         111                                      |

       |                      111                                         |

       |                    11                                            |

       |                 111                                              |

       |             1111                                                 |

       |          001                                                     |

       |     00000                                                        |

       |00000                                                             |

       |                                                                  |

       |                                                                  |

     0 |                                                                  |

       ++------------+------------+------------+------------+------------++

      -2.0         -1.0          0.0          1.0          2.0          3.0

 

Dichotomous plots always look the same:

 

Dichotomous scale structures are always the same:

 

Probability Curves for Dichotomies

     -2.0             -1.0              0.0              1.0              2.0

      ++----------------+----------------+----------------+----------------++

    1 |                                                                     |

      |                                                                     |

      |1                                                                   0|

      | 1111111                                                     0000000 |

      |        11111                                           00000        |

    P |             11111                                 00000             |

    r |                  1111                         0000                  |

    o |                      1111                 0000                      |

    b |                          111           000                          |

    a |                             1111   0000                             |

    b |                                 ***                                 |

    i |                             0000   1111                             |

    l |                          000           111                          |

    i |                      0000                 1111                      |

    t |                  0000                         1111                  |

    y |             00000                                 11111             |

      |        00000                                           11111        |

      | 0000000                                                     1111111 |

      |0                                                                   1|

      |                                                                     |

    0 |                                                                     |

      ++----------------+----------------+----------------+----------------++

     -2.0             -1.0              0.0              1.0              2.0

 

Expected Score Ogive (Model ICC)

     -2.0             -1.0              0.0              1.0              2.0

      ++----------------+----------------+----------------+----------------++

    0 |                                                                     |

      |                                                                     |

      |                                                               000000|

      |                                                        0000000      |

      |                                                  000000             |

      |                                             00000                   |

      |                                         0000                        |

      |                                     0000                            |

      |                                11000                                |

      |                            1111                                     |

      |                        1111                                         |

      |                   11111                                             |

      |             111111                                                  |

      |      1111111                                                        |

      |111111                                                               |

      |                                                                     |

    1 |                                                                     |

      ++----------------+----------------+----------------+----------------++

     -2.0             -1.0              0.0              1.0              2.0


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