How are Scaled Scores Translated into Percentiles

[TennisBoy78]

Hello guys. Looking to gain insight on how scaled scores are translated into percentiles. Here are my scores from my first PCAT test:

Verbal 407 63
Biology 402 57
Reading 396 43
Quantitative 383 25
Chemistry 400 54
Composite 398 47

After reading message boards, I've generally found people who make slightly higher scaled scores (like ten points) have their percentiles jump up considerably (like 20 points). I dont know if this is a difference of getting a few more questions right on each section (like 3-5) or if it is more. Yeah, I'll be working on that Quantitative for next time.

I called Harcourt but they dont publish any material that lists tables with raw scores and percentile translations. I know that test forms may be different, but it is just to get a feel.

Question: Does anyone know of where I can find tables listing raw (scaled) scores translation to percentiles? Like I said, I really think I am close to getting in the 70 pecentiles for biology and chemistry if I had answered just a few more right (3-5).

Next Question: Did anyone do much better their second time taking the PCAT? What did you do differently? I'm thinking of taking the Kaplan Classroom Course. Should this help me, and by how much?

Thanks!

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[bananaface]

The percentiles have to do with how everyone else taking the PCAT did on your test date, so there will be no standardized translation. For your test date 1% of people are placed in each percentile, with those scoring highest getting 99th percentile and thereon down. On one test date a specific raw score could put you in the 70th percentile while on another you could be 50th percentile. It all depends on your performance relative to your peers.

 

[TennisBoy78]

The percentiles have to do with how everyone else taking the PCAT did on your test date, so there will be no standardized translation. For your test date 1% of people are placed in each percentile, with those scoring highest getting 99th percentile and thereon down. On one test date a specific raw score could put you in the 70th percentile while on another you could be 50th percentile. It all depends on your performance relative to your peers.

One correction that is not true: More than 1% of people could score at the same percentile. Percentiles only mean that XX% of people scored AT or BELOW your score. This is how bell curves work, and percentiles for bell curves do not correspond to 1% of the population scoring at your score.

I know that other stuff is true, but that is not my question. My question pertains to tables of raw scores and percentiles. If there is none, that's fine. Harcourt couldn't produce one, so I wanted to know if others knew of any other source that could produce it. If you get a few more right in a particular section, your percentile can shoot up by more points that your raw score increase. This is the crux of my message. I want to know if anyone has more info on this.

 

[bananaface]

One correction that is not true: More than 1% of people could score at the same percentile. Percentiles only mean that XX% of people scored AT or BELOW your score. This is how bell curves work, and percentiles for bell curves do not correspond to 1% of the population scoring at your score.

I know that other stuff is true, but that is not my question. My question pertains to tables of raw scores and percentiles. If there is none, that's fine. Harcourt couldn't produce one, so I wanted to know if others knew of any other source that could produce it. If you get a few more right in a particular section, your percentile can shoot up by more points that your raw score increase. This is the crux of my message. I want to know if anyone has more info on this.

You are correct. If a clump of people score alike they might all get pulled down into the same percentile and not have exactly 1% in each percentile. For example, if 5% of people got a score of 200 all of them would be in the 0th percentile. And, a 201 would get 6th percentile. In reality, the numbers should not clump so badly.

There is no such table available to the public, as far as I know. I have heard about institutions having access to that data. You would probably have to go directly through Harcourt to get it, if they will release it at all.

 

[TennisBoy78]

You are correct. If a clump of people score alike they might all get pulled down into the same percentile and not have exactly 1% in each percentile. For example, if 5% of people got a score of 200 all of them would be in the 0th percentile. And, a 201 would get 6th percentile. In reality, the numbers should not clump so badly.

There is no such table available to the public, as far as I know. I have heard about institutions having access to that data. You would probably have to go directly through Harcourt to get it, if they will release it at all.

Harcourt does not produce any tables, as I called them. Don't know why they can't, because I feel that it would give me additional insight as to how much I should improve. Seems kind of illusionary to me that no one knows how many questions separates an average score from a score in the 80 percentile. I'm not shooting for a 90 something percentile because although it will enhance my application, my other credentials should make up for it.

Once again, from seeing other scores, a slightly higher raw score could translate into a larger percentile increase. The question is that I have yet to find out is: for each question answered correctly on average, how much does your raw score increase. If the answer was "5", that would mean me getting 6 more questions (per section) right to achieve the percentile increase that I need. Seems simplistic, but this could help me understand how close or how far I was from the prize.

Thanks!

Thanks!

 

[rkothari]

Harcourt does not produce any tables, as I called them. Don't know why they can't, because I feel that it would give me additional insight as to how much I should improve. Seems kind of illusionary to me that no one knows how many questions separates an average score from a score in the 80 percentile. I'm not shooting for a 90 something percentile because although it will enhance my application, my other credentials should make up for it.

Once again, from seeing other scores, a slightly higher raw score could translate into a larger percentile increase. The question is that I have yet to find out is: for each question answered correctly on average, how much does your raw score increase. If the answer was "5", that would mean me getting 6 more questions (per section) right to achieve the percentile increase that I need. Seems simplistic, but this could help me understand how close or how far I was from the prize.

Thanks!

Thanks!

I posted about this in composite inflation thread, I will copy paste it below:

Like previopus posters said it is not an average of your percentile for each section. This is what most people believe but not true. Your scaled scores for each sections are averaged and that average is given a percentile. For example every1 from 500-600 might get a 99% every1 from 490-500 might get 98% like that.

This is kinda unfair bc there is a wide gap in score range as you go up. For example a person with 450 might have a 99% and a person with 500 might still have 99% if 1% of people fall in between 450 and 500 score. Over years I have found that scoring range is very short at bottom and wide at the top like:

370-400 = 0 - 50 percentile Assuming the lowest any1 would get is 370 which is realistic.
400-410 = 50 to 70 percentile
410-430 = 70 to 90 percentill
Above 430 = 90 to 99 % percentile.

This is how scores ususally fall. Post yr scores and scaled score so you can cofnirm this,'


I would edit this to say that there is "clumping" as posters previously said. So in reality there may be 3% of people given 99% and then next percentile may be 95 % and no 96,97 or 98 percentile. (to take into account 3% of people).

If you got 99% percentile on the next, it does not mean you got 99% of question correct you need about 450/600 which is about 75% correct to get 99%. Hope this clears up.

 

[TennisBoy78]

I posted about this in composite inflation thread, I will copy paste it below:

Like previopus posters said it is not an average of your percentile for each section. This is what most people believe but not true. Your scaled scores for each sections are averaged and that average is given a percentile. For example every1 from 500-600 might get a 99% every1 from 490-500 might get 98% like that.

This is kinda unfair bc there is a wide gap in score range as you go up. For example a person with 450 might have a 99% and a person with 500 might still have 99% if 1% of people fall in between 450 and 500 score. Over years I have found that scoring range is very short at bottom and wide at the top like:

370-400 = 0 - 50 percentile Assuming the lowest any1 would get is 370 which is realistic.
400-410 = 50 to 70 percentile
410-430 = 70 to 90 percentill
Above 430 = 90 to 99 % percentile.

This is how scores ususally fall. Post yr scores and scaled score so you can cofnirm this,'


I would edit this to say that there is "clumping" as posters previously said. So in reality there may be 3% of people given 99% and then next percentile may be 95 % and no 96,97 or 98 percentile. (to take into account 3% of people).

If you got 99% percentile on the next, it does not mean you got 99% of question correct you need about 450/600 which is about 75% correct to get 99%. Hope this clears up.

Comments and questions: I will post a new board requesting scaled scores for testtakers. Hopefully if enough people respond, I will get a clearer picture. I will be very motivated to find more info on this.

I understand that percentiles do not correspond to the number of questions answered correctly (this is elementary). However, how do you know, for example, that a 450 scaled score corresponds to answering 75% of questions correct. If so, what other correlations are true (let's say for 50th percentile)?

I'm sorry to be so anal about this, but I honestly feel cheated by Harcourt for not having any empirical data that explains this more thoroughly. Different test versions may vary from one another in difficulty, so percentiles and scaled scores are not fixed. On the other hand, these people have to devise these exams so that the levels of difficulty from one version to the next should not vary widely.

Thanks for your input and hope that this opens more discussion on the topic.

 

[TennisBoy78]

Oh to the Harcourt people (if you are reading), I'm not the only one that wants to find this out. It would help us out to know more info.