Believe it or not, I could not stay away and put together this description of my efforts yesterday. My goal is to make sense of the 2015 SI%chart which seems to conflict with the 2015 Concordance charts and with the anecdotal evidence from high schools in GA, OK and IL. I know that this is a goal most of you have.
My plan is to try to convert this chart so that it defines ‘percentile’ in the same way that the 2014 SI % chart defines it.
Here goes my second attempt at an explanation of what I am doing:
Partial copy of 2015 SI% chart:
(with added definition as given by Compass Report)
Score 2015 SI chart What it means
(definition B)
214 99+ 99+% of students scored at or below this score
213 99 99% of students scored at or below this score
212 99 99% of students scored at or below this score
211 99 99% of students scored at or below this score
210 99 99% of students scored at or below this score
209 99 99% of students scored at or below this score
208 99 99% of students scored at or below this score
207 99 99% of students scored at or below this score
206 99 99% of students scored at or below this score
205 99 99% of students scored at or below this score
204 98 98% of students scored at or below this score
203 98 98% of students scored at or below this score
202 98 98% of students scored at or below this score
201 97 97% of students scored at or below this score
200 97 97% of students scored at or below this score
199 96 96% of students scored at or below this score
What this chart tells us:
OK, this SI% chart does not tell us the total number of test takers that took the test. However, one of the important things it is telling us is that the scores 202-204 have been scored by an entire 1% of test takers. It also tells us that the scores 200-201 are held by an entire 1% of test takers. We don’t know what number of test takers are in this band, but we know that each band equals 1%. We also don’t know how many of the 1% of test takers scored at the 3 individual spots for the band 202-204. The CB has not given us that information. It may be that each of the three scores garnered .333% of test takers or it may be that the 1% of scores were distributed unevenly. All we can assume is that an entire 1% of test takers had scores in those 3 ranges. Same with the band of scores 201-202. We do not know if test takers scored those two scores evenly, each garnering .5% of test takers, or if the scores were distributed unevenly. One thing seems certain: that each of the individual SI units 204, 203,202, and 201 will not have the equivalent fraction of a %ile since in one band it is 3 scores that at up to 1% and in the other band it is 2 scores that add up to 1%.
Crucial assumption:
If we know the exact fraction of a %ile of test takers that scored at each individual SI score unit, then Do Not move on with my explanation. But please do report how we know that information.
Assuming I am right so far, then I move on to Converting the definition within the parameters of the information given:
So with this in mind, if I want to understand the information in this 2015 chart in terms of the older, 2014 definition of percentiles, I will need to understand the scores as they correlate ONLY to the percentage of students that scored below them and not to the band of students who scored in the same percentile with them. I can not break up a band, though, because I do not know how the scores are distributed within the band. If I move only one SI score unit down, I might move .3% or .1% or .5%. We don’t know how to do this because the CB does not give us that number. It could result in factually incorrect statements. Thus, working only with the numbers that they give us, I think it is reasonable to translate like this:
Score 2015% Def B Converted to Def A
204 98 98% of students scored at or below this score → 97% of students scored below this score
203 98 98% of students scored at or below this score → 97% of students scored below this score
202 98 98% of students scored at or below this score → 97% of students scored below this score
201 97 97% of students scored at or below this score → 96% of students scored below this score
200 97 97% of students scored at or below this score → 96% of students scored below this score
If this conversion seems reasonable, then the 2015 SI% chart, once fully converted, looks VERY MUCH like the 2014 SI % chart. In addition, it corresponds more closely to the conversion charts. In addition, it accommodates predictions which make sense of the anecdotes of high scores at single high schools in GA, OK and IL. The biggest place for confusion with this method is where to begin the 99+ range of scores. As there is no range higher in the 2015 Chart and bc the high end scores have changed since 2014, the transition spot for 99 to 99+ will require other theorizing.