### Following are explanations of the most frequently asked about statistics on our reports:

#### Roster of Results Report

Rank

**Rank **is a measure of where a score is positioned relative to all other scores in the group, where a rank of “1” indicates the highest score in the group. In cases where there are multiple instances of the same score, the rank is calculated as the average of the range of ranks covering the duplicate scores. For example, here is a partial list of percent scores and their preliminary and adjusted ranks:

Score (%) |
Rank |
Adj. Rank |

95.4 | 1 | 1 |

92 | 2 | 2.5 |

92 | 3 | 2.5 |

89 | 4 | 4 |

88.5 | 5 | 5 |

Because there are two instances of the score of 92%, the ranks for the two are averaged, and a rank of (2 + 3)/2 = 2.5 is assigned to each.

T-Scores

**T-scores **indicate how many standard deviation units an examinee’s score is above or below the mean. T-Scores always have a mean of 50 and a standard deviation of 10, so any T-Score is directly interpretable. A T-Score of 50 indicates a raw score equal to the mean. A T-Score of 40 indicates a raw score one standard deviation below the mean, while a T-Score of 65 indicates a raw score 1.5 standard deviations above the mean.

Both rank and T-Scores describe test performance in terms of the examinee’s relative position in the distribution of test scores. While rank has the advantage of being easier to understand, it has the serious disadvantage of representing a scale where the percentile units are not equal on all parts of the scale.

A rank difference near the middle of the scale represents a much smaller difference in test performance than the same percentile difference at the ends. T-Scores, on the other hand, provide equal units that can be treated arithmetically. T-Scores from several tests taken during a semester can thus be summed and averaged.

Z-Scores

**Z-Scores** are raw scores expressed in standard deviation units, relative to the mean score. Positive Z-scores indicate a raw score that is above the mean, negative Z-scores indicate a raw score that is below the mean, and a Z-score of zero indicates a raw score that is equal to the mean. In a normally-distributed set of data, the general rule states that 68% of all scores will fall within ±1 SD of the mean; 95% of all scores will fall within ±2 SD, and 99.7% of all scores within ±3 SD. Z-scores between -2.00 and +2.00 are therefore considered relatively ordinary, while values greater than -2.00 and +2.00 are unusual.

#### Test Item Analysis Report

Difficulty Index (DIF Index)

The **Difficulty Index** indicates how many in the entire group answered the question correctly, expressed as a percent.

There is a formula than can be used to calculate or explain this:

c ÷ s = p

Where:

DIF | Difficulty Index |

c | The number of students who answer a question correctly |

s | The total number of students in the class who answered the question |

p | Difficulty level which is then usually turned into a percentage |

The answer will equal a value between 0.0 and 1.0, with harder questions resulting in values closer to 0.0 and easier questions resulting in values closer to 1.0.

Example: Out of the 20 students who answered question five, only thirteen answered correctly.

Therefore: 13 ÷ 20 = 0.65 which also equals 65%

Discrimination Index (DISC Index)

The formula being used for the **Discrimination Index** figure on the Test Item Analysis report is:

DISC = (a – b) / n

Where:

DISC | Discrimination Index |

a | Response frequency of the upper 27% of the scorers |

b | Response frequency of the lower 27% of the scorers |

n | Number of respondents in the upper 27% of the scorers |

The results typically are a range of values (-1 to 1) and the significance of those values may be read as the more positive, the better the item distinguishes between those who have mastered the subject and those who have not. This also means that a negative result for Discrimination Index means that those who scored lower on the exam did better on this question than those who did well on the exam, which an instructor may find interesting.