Standard scores:

Standard scores are "transformed scores". Raw tests scores ( number correct) are converted to reflect equally where they fall with respect to the mean. earned These scores allow "raw scores" on any test to be compared. These makes interpretation of test scores clearer. One can determine where a person's score falls in comparison to a person's overall ability, in comparison to another person, or in comparison to the group. They are especially important when using tests that have been standardized on large populations reflective of the demographic characteristics of the population as whole.

You must understand the basics of standard scores to understand completely how and why test scores are used in the GED model.

Most educational and psychological tests report test results using standard scores. Standard scores are based on the bell curve. It is important to understand the mean and the standard deviation to understand how these standard test scores are used. If you look at the bell curve you can see that test scores can easily be compare using the standard score model.

Some basic facts

Most educational and psychological test results are reported in standard scores. Standard scores are derived from z scores.
Most tests use standard scores(SS) with a mean of 100 and a standard deviation of 15.
A standard score of 100 is at the mean or the 50% percentile. A standard score of 85 is one standard deviation below the mean; i.e., significantly below the mean. a standard score of 115, is one standard deviation above the mean; i.e., significantly above the mean.
68% of the population falls with one standard deviation above the mean and one standard deviation below the mean. This is the Average range. This is often stated in terms of z score of a range from -1 to +1.
Since standard scores are consistent across tests a person's s cores can be compared across tests. A person with an IQ or standard intelligence score of 110 would be expected to have a reading achievement score within the same range. If the reading achievement standard score were 90, a 20 point difference would be indicated (110-90=20 points). This difference is greater than one standard deviation. This difference is a significant difference.
Most educational and achievement subtest scores have a mean of 10 and a standard deviation of 3.

They are easy to understand!!!!!

Here are some numbers to practice with if you want more information about how this works.

The simplest type of standard score is called a z-score. This score is an indication of the deviation of a score from the mean, or average score, or a group of scores in relation to the standard deviation. Let's see how this works. Below is a list of raw test scores that was earned on an exam.

                Jeff         78
                Bill           67
                Mary        92
                Paul         91
                Martha     62
                Donna      94
                Fred         98
                Robert      51
                Rachel      72
                Barbara     81
                Peter        61
                Leroy        85
                Daren        88
                Suzy        42
                Ron           78
                Rick           78
                Terri          80
                John          78
                Mike          68
                Tory          82

Suppose the school said all grading had to be on a bell curve; i.e, A,B,C,D,F.

How would I assign the grades for this class?

The grades need to be transformed.

Here is the formula that is applied to calculate a z score.

standard score(z score)= raw score(test grade)(X)-mean(M)
standard deviation (S.D.)

1. Find the mean of this class. The mean is the total of all of the raw scores divided by the number of people who took the test.

The mean for this class is 76.3

2. Next find the standard deviation; i.e., the measure of the variability of a distribution of scores.

To calculate the standard deviation follow the following steps:

Calculate the mean
Calculate the deviation score by subtracting the mean from each test grade.

                78-76.3
                67-76.3
                92-76.3
   etc.

You will see that the mean on this exam was 76.3 and the standard deviation was 14.07. In order to determine where a test grade would fall if a standardized sample were used the data is now converted to a z score. This score will assume a mean of 100 and a standard deviation of 14. The z score for each person is obtained by taking that person's score and subtracting the mean and then dividing by the standard deviation.

Thus if Jeff's score were calculated a z-score of 78-76.3/14.07=.12. Jeff's score is very close to the mean.

If we look at Suzy's score, on the other hand, the picture is different. Her z score is 42-76.3= 34.3/14.07= -2.43. In short, Suzy's score is more than 2 standard deviations below the mean. It is significantly discrepant from the mean.

Look at Fred's score. He has a z-score of 1.54. His score is significantly above the mean but you should see that even with such a high test score grade it is not as high above the mean as Suzy's is below. The sample of test takers was not randomly drawn and is therefore not representative of a large population of people. The distribution is skewed because of the large number of high scores on this test.

Using this method it would be possible to compare the relative performance of the scores each training session earned on the certification test. Would this have been a good procedure; i.e., to standardize the scores of each class and award passing status based on the standardized, z score of each participant within a class? NO! Do you understand why not? If not you should review more about statistics in an introductory statistic textbook. This issue will also be better further clarified in the session on the bell curve.The problem you should ask yourself is what are the characteristics of the small sample from which the test scores were taken?

Those who write and develop reliable and valid intellectual and achievement tests make certain that the sample is representative of the overall population demographics; i.e. that the test scores fall along a normal distribution-- bell curve.

This page designed & maintained by Kathleen Ross-Kidder, Ph.D., Department of Psychology, The George Washington University, Washington, D.C., Psychological consultant to GEDTS

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