# Quiz statistics report

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One of 4 Quiz reports

This report gives a statistical (psychometric) analysis of the quiz, and the questions within it. The front page of this report gives a summary of the whole test. There are then links to drill down into a detailed analysis of a particular question.

The full report (overview, and detailed analysis of all questions) can be downloaded in a variety of formats, as can the quiz structure analysis table.

For a general introduction to psychometrics, this 45-minute seminar gives a very good an approachable introduction.

### Overall quiz statistics

This is the first page of the report.

#### Quiz information

This table gives some basic information about the test as a whole, including some statistics for the total score:

• Quiz name
• Name of the course it is part of
• Open and close dates (if applicable)
• Total number of first/add attempts
• Average grade for first/all attempts
• Skewness and Kurtosis of the grade distribution
• Coefficient of internal consistency (sometimes called Cronbach Alpha) - This is a measure of whether all the items in the quiz are testing basically the same thing. Thus it measures the consistency of the text, which is a lower bound for the validity. Higher numbers here are better.
• Error ratio - the variation in the grades comes from two sources. First some students are better than others at what is being tested, and second there is some random variation. We hope that the quiz grades will largely be determined by the student's ability, and that random variation will be minimised. The error ratio estimates how much of the variation is random, and so lower is better.
• Standard error - this is derived from the error ratio, and is a measure of how much random variation there is in each test grade. So, if the Standard error is 10%, and a student scored 60%, then their real ability probably lies somewhere between 50% and 70%.

#### Quiz structure analysis

This lists all the questions in the quiz with various statistics:

• Q# - shows the question number, question type icon, and preview and edit icons
• Question name - the name is a link to the detailed analysis of this question.
• Attempts - how many attempts included this question
• Facility Index - a fancy name for the average score as a percentage. Higher score means easier question.
• Standard Deviation - how much variation there was in the scores for this question
• Random guess score - the score the student would get by guessing randomly
• Intended/Effective weight - Intended weight is simply what you set up when editing the quiz. If question 1 is worth 3 marks out of a total of 10 for the quiz, the the intended weight is 30%. The effective weight is an attempt to estimate, from the results, how much of the actual variation was due to this question. So, ideally the effective weights should be close to the intended weights.
• Discrimination index - this is the correlation between the score for this question and the score for the whole quiz. That is, for a good question, you hope that the students who score highly on this question are the same students who score highly on the whole quiz. Higher numbers are better.
• Discriminative efficiency - another measure that is similar to Discrimination index

Where random questions are used, there is one row in the table for the random question, followed by further rows, one for each real question that was selected in place of this random question.

Quiz statistics calculations gives further details on all these quantities.

### Quiz question statistics

You get to this page by clicking on the name of a question in the Quiz structure analysis.

#### Question information

Some basic information about the question.

#### Question statistics

This repeats the information from the table row from the Quiz structure analysis that relates to this question.

#### Analysis of responses

This gives a frequency analysis of the different responses that were given to each part of the question. The details of the analysis depends on the question type, and not all question types support this. For example, essay question responses cannot be analysed.

### Report options

You can choose whether to run the report on all attempts, or just the first attempt by each student. Some of the calculations used in the report are based on assumptions that may not apply to quizzes that allow more than one attempt.

Also, because computing the statistics takes some time, the report will store the computed values and re-use them for up to 15 minutes. Therefore, there is a display of how recently the statistics were calculated, with a button to recalculate them immediately.