Score Statistics

1. Overview
2. Displaying Statistics
3. Interpreting Statistics
4. Letting Students See Statistics
5. Calculating Scores
6. Example Statistics

1. Overview

Post'Em calculates a variety of basic statistics for you: average, standard deviation, highest and lowest scores, score range, and count of students for each activity. See the section below on interpreting statistics.

If you supply a list of maximum scores, Post'Em will calculate percentage scores. If you also supply a list of weights, Post'Em will calculate weighted average scores. See the section below on calculating scores.

If you need more complex statistics such as z-scores, percentile rankings, and measures of distribution of scores, you can use a spreadsheet or statistics program to perform additional calculations.

2. Displaying Statistics

From the Post'Em Main Menu, select Display Statistics and click OK.
1. You can choose to display all students (the default) or search for a student by typing part or all of the student's username.
2. You can choose to display the statistics in a table format for printing (the default), or in text format which you can then save as a comma-delimited (.csv) file and import into a spreadsheet or statistical program.
3. Click the check box if you would like students to see these statistics. For more information and considerations, see below.)

Click the Display button.

3. Interpreting Statistics

Score statistics are grouped into tables.

• Students can see one to three tables: raw scores, possibly percentage scores, and possibly weighted average scores.
• Instructors see three to seven tables, since there are separate tables for individual and aggregate scores, and a table with summary statistics at the bottom.

1. Raw Individual Scores
   These are the student scores that the instructor uploaded to Post'Em.

   Username (in blue)

   Usernames of all students in the scores file will be listed.

   Other columns (in green)

   You will see all columns in the scores file that contain at least one number. Text columns such as letter grades and comments are excluded. (They can be seen on the Display Scores screen.)

2. Raw Aggregate Scores
   These statistics are computed by Post'Em using the scores the instructor uploaded.

   Maximum

   The highest possible score for this activity.
   This row will only appear if the instructor has included it in the scores file.

   Weight

   The importance of each activity, as a percent or fraction of the total grade.
   This row will only appear if the instructor has included it in the scores file.

   Average

   The average or mean student score for this activity.

   • Average is computed as the sum of all scores for the activity divided by the number of non-blank scores for the activity.
   • Blank scores are not included when calculating the average and other statistics.
   • Note that a blank score is not treated the same as a zero score.

   Std. Dev.

   A statistical measure of the variability (spread) of student scores for this activity.

   • The standard deviation is calculated by finding the sum of the squares of differences of non-blank scores from the mean, dividing by the number of non-blank scores, and taking the square root.
   • For example, if there are two scores, 60 and 80, the average is 70 and the standard deviation is 10.
   • About two thirds of the scores lie within one standard deviation of the mean. For example, if the average is 70 and the standard deviation is 10, if there are many scores, about 68% of the scores will lie between 60 and 80.

   Highest

   The highest student score for this activity.

   Lowest

   The lowest non-blank student score for this activity.

   Range

   The difference between the highest and lowest score.

   Count

   The number of students who have a non-blank score for this activity.

   Blank

   The number of students who have a blank score for this activity.

3. Percent Individual Scores
4. Percent Aggregate Scores
   • These are the same as the above scores, except that the numbers are expressed as percentage.
   • These will only appear if the instructor has included a Maximum row in the scores file.
   • To get a percentage score, divide the raw score by the maximum score and multiply by 100.
5. Weighted Average Individual Scores
   • If the instructor has included both a Maximum and Weight row in the scores file, Post'Em will calculate weighted averages.
   • The weighted average (Average %) is the sum of the products of percentage scores and weights, divided by the sum of the weights.
   • The non-blank weighted average (Average Nonblank %) only considers the student's non-blank scores.
6. Weighted Average Aggregate Scores
   • These are calculated in the same ways as the Raw Aggregate Scores above, except that they summarize the average scores of all students.
7. Weighted Average Aggregate Scores

4. Letting Students See Statistics

As always, students can only see their own scores and never the scores of other individual students, but you can permit them to also see aggregate score statistics for the class.

Some advantages of letting students see class statistics:

• Students can see how they are doing compared with other students.
• Students can be reassured that they have completed all the assignments that their classmates have completed.
• Students who perform well are rewarded by seeing their high class standing, and excellent students may try harder to achieve the highest score.
• Students who do not perform well may see the need for improvement and more effort.

Some disadvantages:

• If the class size is very small, students might be able to guess who received what score. You should probably not let students see statistics if the class size is smaller than 5 students.
• Like norm-referenced grading, comparing scores with other students may promote harmful forms of competition that reduce cooperation. If one student's success requires another's failure, students will be reluctant to help each other learn.
• Students who perform relatively well may become complacent and not work to their full potential.
• Students who do not perform relatively well may become discouraged and not focus on their positive achievements.
• Students may have difficulty interpreting the statistics and may ask many questions about statistics that are time-consuming to answer.

Whether to let students see the statistics depends on your opinion of their pedagogical usefulness and the circumstances of your class. You may want to consult research on the topic to further inform your decision. Use this feature at your own risk.

5. Calculating Scores

Post'Em can also calculate an overall weighted score for each student.

• If you supply maximum scores for each activity, Post'Em calculates percentage statistics.
  To do this, simply include a row in your scores file with the maximum scores. The first (left-most) cell in the row should contain the word Maximum.
• If you also supply weights for each activity, Post'Em also calculates weighted average scores.
  To do this, simply include a row in your scores file with the weights. The first (left-most) cell in the row should contain the word Weight. The weights could be percentages or decimal numbers, and they do not have to add up to 100.
• If the weights are all the same and the maxima are all the same, the overall score is simply the average of all student scores.
• If the weights are the same as the maxima, the overall score is the sum of all scores divided by the sum of the maxima.

6. Example Statistics

For example, assume you have a class with two students whose usernames are student1 and student2. There are two tests worth 100 points and a final exam worth 200 points. The tests each count as 20% of the grade, and the final counts as 60%.

You would upload a scores file like this:

Username,Test1,Test2,Final
student1,90,80,180
student2,85,92,170
Maximum,100,100,200
Weight,20,20,60

You would see the following statistics:

Score Statistics:

1. Raw Individual Scores:

2. Raw Aggregate Scores:

3. Percent Individual Scores:

4. Percent Aggregate Scores:

5. Weighted Average Individual Scores:

6. Weighted Average Aggregate Scores:

7. Totals:

If you allowed students to see statistics, your student student1 would see:

Score Statistics:

Raw Scores:

Percentage Scores:

Weighted Average Scores: