Transcript Worked problems for standard scores, percentiles, and stanines

Tommy is coming in at the 16th percentile. He needs to stop that partying.
Picabo is at the 99+ percentile. She needs to watch those steroids.
Picabo is definitely better than Tommy. Whoa! Actually, they are the same—
they both skied at the same speed, 100 mph.
Only when compared to the norms for their gender do we see a difference in their
performance.
In this case, however, there is an absolute standard of comparison. This is a case
of criterion-referenced measurement.
So, what’s going on here? 80% correct gets Mort to the 36th %tile in History,
while only 45% correct gets him to the 74th %tile in Science.
The answer, actually, is quite simple. The History test is, by definition, easier.
More examinees got a higher percentage of the items correct on the History
test than on the Science test.
On the History test the average student probably got a score closer to 85% correct,
while on the Science test, the average student was more likely to have had a
score lower than 45% correct.
The correct answer is B. Dick, who scored 70 of 75 items correct did best on the
test. His score is clearly better than Harry’s. Harry, who got 70% of the items
correct only got 52 or 53 items correct.
The only thing we have to check is whether Dick scored above or below Tom’s
70th percentile. To check this we first have to calculate his standard score. A
simple calculation reveals that Dick’s standard score is 1. He scored one
standard deviations above the mean. Since one standard deviation above the
mean equates to the 84th percentile, Dick clearly outscored Tom.
Equation for computing a standard score (z);
z = (Raw Score – Mean Score) / Standard Deviation
The answer is D: Not enough information is given.
The two girl’s standardized test scores were obtained from different norm groups
and are, hence, not comparable. In order to be able to compare two
individuals’ norm-referenced scores (standard scores, percentiles, grade
equivalent scores, etc.) the scores have to be compared to the same norm
group. Rosemary’s scores are from a test normed in Virginia; Angela’s from a
test normed in Texas. It is possible that an above-average performance on, say,
a math test in Texas would be equivalent to a below-average performance on a
similar test in Virginia.
The correct answer is B: Only Rosemary is clearly better at English than at math.
The difference between Rosemary’s standard scores in math and English (.25 and
1.2) correspond, roughly, to a difference in percentiles of 51 %tile for math
and the 90th %tile for English. The difference in Angela’s standard scores for
math and English, on the other hand, correspond, again roughly, to a
difference between the the 79th %tile and the 83ed %tile.
Choice C is incorrect for reasons given for the previous item. The girls’ test scores
come from test normed on different populations and, hence, are not
comparable.