Accuracy & Error

Editor's Notes

• #4: Think about the last test you took. Did you obtain exactly the score you thought or knew you deserved? Was your score higher than you expected? Was it lower than you expected? What about your obtained scores on all the other tests you have taken? Did they truly reflect your skill, knowledge, or ability, or did they sometimes underestimate your knowledge, ability, or skill? Or did they overestimate? If your obtained test scores did not always reflect your true ability, they were associated with some error. Your obtained scores may have been lower or higher than they should have been. In short, an obtained score has a true component (actual level of ability, knowledge) and an error component (which may act to lower or raise the obtained score).
• #14: The standard deviation of the error score distribution, also known as the standard error of measurement, is 4. 43. If we could know what the error scores are for each test we administer, we could compute Sm in this manner. But, of course, we never know these error scores. If you are following so far, your neat question should be, “But how in the world do you determine the standard deviation of the error scores if you never know the error scores?”
• #16: Error scores are assumed to be random. As such, they cancel each other out. That is obtained scores are inflated by random error to the same extent as they are deflated by error. Another way of saying this is that the mean of the error scores for a test is zero. The distribution of the error scores is also important, since it approximates a normal distribution closely enough for us to use the normal distribution to represent it.
• #18: (Fig. 17.3 Should refresh your memory) We listed along the baseline the standard deviation of the error score distribution. This is more commonly called the standard error of measurement (Sm) of the test. Thus we can see that 68% of the error scores for the test will be no more than 4.32 points higher or 4.32 points lower than the true scores. That is, if there were 100 obtained scores on this test, 68 of these scores would not be “off” their true scores by more than 4.32 points. The Sm then, tells us about the distribution of obtained score around true scores. By knowing an individual’s true socre we can predict what his or her obtained score is likely to be.
• #19: (Fig. 17.3 Should refresh your memory) We listed along the baseline the standard deviation of the error score distribution. This is more commonly called the standard error of measurement (Sm) of the test. Thus we can see that 68% of the error scores for the test will be no more than 4.32 points higher or 4.32 points lower than the true scores. That is, if there were 100 obtained scores on this test, 68 of these scores would not be “off” their true scores by more than 4.32 points. The Sm then, tells us about the distribution of obtained score around true scores. By knowing an individual’s true socre we can predict what his or her obtained score is likely to be.
• #20: The careful reader may be thinking, “That’s not very useful information. We can never know what a person’s true score is, only their obtained score.” This is correct. As a test users, we work only with obtained scores. However, we can follow our logic in reverse. If 68% of obtained scores fall within 1 Sm of their true scores, then 68% of true scores must fall within 1Sm of their obtained scores. Strictly speaking, this reverse logic is somewhat inaccurate, it would be true 99% of the itme (Gullikson, 1987). Therefore the Sm is often used to determine how test error is likely to have affected individual obtained scores. That is, X plus or minus 4.32 (+4.32) defines the range or band
• #21: The careful reader may be thinking, “That’s not very useful information. We can never know what a person’s true score is, only their obtained score.” This is correct. As a test users, we work only with obtained scores. However, we can follow our logic in reverse. If 68% of obtained scores fall within 1 Sm of their true scores, then 68% of true scores must fall within 1Sm of their obtained scores. Strictly speaking, this reverse logic is somewhat inaccurate, it would be true 99% of the itme (Gullikson, 1987). Therefore the Sm is often used to determine how test error is likely to have affected individual obtained scores. That is, X plus or minus 4.32 (+4.32) defines the range or band
• #22: The careful reader may be thinking, “That’s not very useful information. We can never know what a person’s true score is, only their obtained score.” This is correct. As a test users, we work only with obtained scores. However, we can follow our logic in reverse. If 68% of obtained scores fall within 1 Sm of their true scores, then 68% of true scores must fall within 1Sm of their obtained scores. Strictly speaking, this reverse logic is somewhat inaccurate, it would be true 99% of the itme (Gullikson, 1987). Therefore the Sm is often used to determine how test error is likely to have affected individual obtained scores. That is, X plus or minus 4.32 (+4.32) defines the range or band
• #23: The careful reader may be thinking, “That’s not very useful information. We can never know what a person’s true score is, only their obtained score.” This is correct. As a test users, we work only with obtained scores. However, we can follow our logic in reverse. If 68% of obtained scores fall within 1 Sm of their true scores, then 68% of true scores must fall within 1Sm of their obtained scores. Strictly speaking, this reverse logic is somewhat inaccurate, it would be true 99% of the itme (Gullikson, 1987). Therefore the Sm is often used to determine how test error is likely to have affected individual obtained scores. That is, X plus or minus 4.32 (+4.32) defines the range or band