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Creating Effective Classroom Tests
by Christine Coombe and Nancy Hubley
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VIII. Statistics

Statistics simply mean mathematical forms of exam results. Unfortunately, the term statistics often has negative connotations for language teachers. Yet teachers can easily learn how to use statistics to get information about their students' performance on a test and to check the test's reliability. Basic statistics provide information on individual students, the class as a whole, the course content and how it has been taught. Every teacher can benefit from this feedback. The most important statistics are simple arithmetic concepts which are easy to compute with a hand calculator.


Basic Statistics for Classroom Testing
Computing Basic Statistics for Classroom Use

Basic Statistics for Classroom Testing

The most useful statistics for classroom teachers are known as descriptive statistics. They "describe" the population of students taking the test. The mean, mode, median, standard deviation, and range are common descriptive statistics. Of these, the mean is the most important for classroom teachers.
Other descriptive statistics are important for large-scale, high stakes testing and can easily be obtained with computer applications such as Excel. See the annotated bibliography for suggestions on testing books that cover the use of other statistics.

The Mean: Once a test has been administered to a group of students, the first step for any classroom teacher should be to compute the mean score or arithmetic average. The mean is the sum of all the scores divided by the number of scores.

Mean scores can be computed for the test as a whole or for each section (i.e. listening, reading, writing etc.) of a test. Computing a mean score can give you information as to the reliability of the test. In general, mean scores that fall within the 70th percentile (i.e. from 70 to 79) are said to be valid indicators of test reliability. For shorter or mastery quizzes, however, teachers can expect higher means.

Pass/Fail Rate: Another useful statistic to compute is the pass or failure rate for a given test or quiz. This is most simply done by a grade breakdown. The first step in this process is to count the number of A's, B's, C's, and D's received on the test. This number represents the pass rate for a given test. Divide this number by the total number of students who took the test and you have the pass rate. To compute the failure rate, count the number of F's or failing grades and divide this number by the total number of students who took the exam.

Histograms: Histograms are visual representations of how well a group of students did on a test or quiz. Histograms can be easily drawn from a chart of grade breakdowns (number of A, B, C, D and F grades received on a test). These totals are later graphed on a chart. The resulting curve represents how the class did as a whole on a test.
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Computing Basic Statistics for Classroom Use

Figuring the mean
1. Add the grades of all students

2. Divide the total of the grades by the number of students

3. The result is the mean for that test or quiz.

Figuring the pass rate
1. Count the number of students in each grade category
In some systems, this will be A, B, C, D, F. Note that test and quiz grades can be out of any number, not just 100.

2. Divide the number of students who received a grade in all passing categories by the number of students who took the test.

3. The result is the pass rate for that class for that test.

Figuring the failure rate
1. Count the number of students in each grade category
In some systems, this will be A, B, C, D, F.

2. Divide the number of students who received a grade in all failing categories by the number of students who took the test.

3. The result is the failure rate for that class for that test.

Plotting a histogram
1. A histogram is a picture of your grade distribution or breakdown. It is a simple graph with two axes. One side (the vertical) represents the number of students who took the exam. The horizontal side has the range of grades received on the exam.

2. Create the vertical axis by showing how many students took the exam. For example, if you have 25 students in your class, have the bottom represent 0 and the top 25 with intervals of 5 students.

3. Create the horizontal axis by showing the range of possible grades. For example, you may have F on the left side, followed by D, C, B, and A in ascending order.

4. Plot the number of students who received each grade. Remember to note grades for which there were no scores at the zero level. Then, you can either use bars to depict the number of scores in each category or connect the dots at the top of each column (include the zeroes!).
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