Statistics Question

Parent Cafe
1

<p>This is NOT homework or anything forbidden, but I’m hoping someone can explan this to me in very simple language.</p>

<p>Son will apply to high school in the fall along with the other eighth graders. Each student is entitled to 12 choices and gets placed at the highest-ranked school that he chose and also chose him.</p>

<p>So if the admissions numbers are the following, what does it actually mean in terms of chances. I can’t figure out if the possibility of admission is exactly the percentile of seats/applicants or if the fact that each kid had 12 choices changes that. (No, I never took statistics and never went to college.)</p>

<p>School 1: 108 admitted out of 1168 applicants
School 2: 30 admitted out of 257 applicants
School 3: 60 admitted out of 134 applicants
School 4: 42 admitted out of 938 applicants</p>

2

<p>For your question there’s a difference between ‘admitted’, as in enrolled and will be attending, and ‘offered admission’ as in the person may have received multiple admission offeres but will end up choosing only one.</p>

<p>If your data is reflecting the latter, then it would reflect ‘chances of being accepted’. If it reflects the former, then you can’t tell from the data what the odds are of being accepted without more data.</p>

<p>For example, if the numbers are 100 admitted out of 1000 applicants it could be anywhere from a 10% chance of admission (if all ‘admitted’ decided to attend this school) to a 100% chance of admission (if all applicants were offered admission but only 10% of those chose to accept the offer).</p>

3

<p>Sorry. Each student can only receive one match and they are required to attend that program unless they go to private school, instead. And about 8% don’t receive a match at all.</p>

4

<p>To add to my train of thought, we have 8 choices for son so far, one of which is audition only (the first choice), and the rest are totally random. The percentiles of acceptance stated range from 5% to 40% with most in the 5-18% range. The 40% is an outlier because it’s not a desirable program. So what I’m really trying to figure out is with 7 random choices, no guarantee of any acceptance at all, and the admissions range generally under 20%, how likely is it that there could be no acceptance at all? My husband and I are arguing about this because I want to find a more “sure thing” program to add to the list and my husband thinks I’m reading these numbers wrong and that it will work out. Which, of course, it will, but I still want to have a better sense of what I’m reading.</p>

5

<p>zooser is the question that you are seeking advice for how to rank your choices? I believe you need to know more than the information you’ve given us - ie the program they are using which I believe tries to somehow optimize getting kids into one of their top five choices. [Insideschools.org</a> : Blogs](<a href=“http://insideschools.org/blog/2011/03/31/hs-admissions-48-get-1st-choice-10-get-no-match/]Insideschools.org”>http://insideschools.org/blog/2011/03/31/hs-admissions-48-get-1st-choice-10-get-no-match/)</p>

<p>I got screwed by this thing when choosing my housing after my freshman year in college. We got to rank our 13 choices and I got choice number 13. But that’s because the system was optimized to give as many people as possible their first choice and not making sure no one got a bottom choice.</p>

6

<p>Well if 8% don’t get any matches at all, what exactly happens to them? Do they not go to high school? Are they forced into a private school? Does the match-up committee assign them randomly? That is the question I would really want answered!</p>

7

<p>Assuming the selection is random (that it, the school isn’t looking at qualifications or applying some other algorithm such as distance):</p>

<p>If the chance of getting in is 0.1 (10%), it means the chance of <em>not</em> getting in is 0.9 (90%).</p>

<p>The chances of not getting into the top two are then 0.9*0.9, or 0.81, so the chance of getting into one of the top two is 1.0 - 0.81, 0.19 (19%).</p>

<p>Similarly, for three schools: 1.0 - 0.9<em>0.9</em>0.9 or 0.271 (27%).</p>

<p>Generally, for n schools: 1.0 - 0.9^n (^ means “raised to the power of”)</p>

<p>So for 8 schools, it would be 1.0 - 0.9^8 or 0.57 (57% chance) of getting admitted to one of the top 8.</p>

<p>If you have probabilities for each school, you can substitute them in.</p>

<p>The problem is, I doubt it is purely random. There is probably some mechanism where they try to give as many people as possible their highest choice as possible. So I don’t know if these probabilities mean much when combined.</p>

8

<p>

There is a second round of admission in which some match is guaranteed, but it might not be in the child’s borough.</p>

<p>

I don’t think so because less than half get the first choice.</p>

<p>

I’m trying to figure out if I should add in a couple of programs that he wouldn’t ever attend unless my husband or I lost our job and couldn’t send him to private school. Really, I’m just trying to get a sense for myself about whether I should prepare mentally for a bad outcome.</p>

9

<p>^Less than half could get their first choice if everyone puts the same school in first place and the school is too small to accommodate half the applicants. (Exaggeration, but you get the idea.) I’m sure there is a program that tries to optimize that as many people as possible don’t come away disappointed, but who knows what it is. I’ll leave the math to someone whose done this sort of thing though!</p>

10

<p>

</p>

<p>Statistics does not provide the answer to this question, because the schools are making choices, not picking randomly. So your best guess as to how likely your son is to be admitted to no school is 8%.</p>

11

<p>

That’s not necessarily true. If I read this correctly this is a public high school assignment process, so the result may be purely mathematical.</p>

12

<p>

Sorry, I wasn’t clear. The numbers are only for the schools he’s interested in that have random, computer generated selection. The other programs are things like auditions or tests, which I didn’t include.</p>

13

<p>Oh. OK, then it’s easy. To know whether he’d be admitted to none, just multiply the rejection chances. The rejection chance is the number rejected divided by the number of applicants.</p>

<p>So, for your four schools:</p>

<p>

</p>

<p>School 1, rejection chance = 1060/1168
School 2, 227/257
School 3, 74/134
School 4, 896/938</p>

<p>Multiply those, and we get (now I have to go get a calculator, no, wait, I’ll just use Google):</p>

<p>(1 060 / 1 168) * (227 / 257) * (74 / 134) * (896 / 938) = 0.422851474</p>

<p>So, the chance that he would be accepted at none of those four schools is about 42%.</p>

14

<p><a href=“http://www.nytimes.com/2011/05/08/nyregion/in-applying-for-high-school-some-8th-graders-find-a-maze.html[/url]”>http://www.nytimes.com/2011/05/08/nyregion/in-applying-for-high-school-some-8th-graders-find-a-maze.html&lt;/a&gt;&lt;/p&gt;

<p>Maybe this article will help. There is also a follow-up article. I think it said some unknown algorithm is used to assign the kids (it’s been awhile since I read it). I recall that a lot of kids don’t get any of their choices, and those that do spend nearly as much time gaming the system as one does to get into college.</p>

15

<p>Actually, thinking about it again, I didn’t account for the decisions of the schools not being independent. That is, two schools can’t pick the same student. That would change the odds. However, that probably doesn’t make much difference in this case. Multiplying the rejection chances together will give a pretty good answer, though it will be a bit pessimistic.</p>

16

<p>If z-kid doesn’t include School 3 on his list, the likelihood of matching goes waaaay down. As z-mom presents the problem, the likelihood of matching essentially reflects the likelihood of matching at School 3 plus a small chance at matching at one of the other schools.</p>

<p>One problem with that, however, is that we don’t actually know all the relevant information for gauging the success rate of School 3 applicants. We don’t know whether the 45% of applicants to School 3 who were successful all (or mostly) ranked School 3 in their top 5 choices. As I understand the system, a kid who ranked School 3 #1 or #2 – his “reach” school – might well be matched at School 3 over a stronger student who ranked it #11 or #12.</p>

<p>On the other hand, it may be that School 3 had 80 slots, and only succeeded in filling 60 of them in the match because the other 74 applicants all succeeded in matching with higher choices. Or perhaps 60 may have been its full complement, but it didn’t succeed in filling that until Round 2. School 3 could have an effective acceptance rate of 100%. I suspect that’s a lot closer to reality than 45%. Remember, at each of these schools about 90% of the applicants matched somewhere, and for each school a certain percentage will have matched at schools they liked more than the school in question. (As may well be true of z-kid if he aces the entrance exam for one of the exam schools.)</p>

17

<p>I’ve worked on design teams for various kinds of school lottery systems, and there’s more complexity here than you might be seeing. You need more information about the lottery system in general. 1. Does the system prioritize selections based on siblings? (This is common.) If so, the question for a given school is what number of students at your child’s grade level applied without sibling preference, and how many of those were offered admission. Some schools have so many sibling applicants that they have very few spaces available for the “general” population most years. Total school admissions are also unimportant – what matters is just for the grade you’re looking for. 2. Same thing, but for any other preference criteria the district may have. 3. If the algorithm first tries to match every student’s first choice with available openings (and this is the way a lot of district-wide lotteries work) then you need to know for the schools you are interested in how many students last year were admitted out of the 1st choice selections, and how many out of 2nd, 3rd,… – our district publishes a matrix buried deep in the district website, but the enrollment folks ought be able to point you in the direction of it. The key here is that very popular schools – call them A, B, C may always completely fill from 1st choices. Thus, you need to choose ONE of A,B,C to put as your first choice if you really want that school, and then don’t prioritize either of the others, because you won’t get them (since they weren’t your first choice) and since that then makes it even less likely that you’ll get your next choice since you ranked it lower and people who ranked it higher get the slots. It is a tough system – very different than if schools hold independent lotteries, and really tough if you don’t have a fallback alternative (think safety school) that you can include as your lowest ranked option that you are sure to get. </p>

<p>There’s more to it than this, but I hope it might give you a little bit better of an idea. In some districts, sibling preference only applies if you put that school as your top choice. In other districts, free & reduced lunch status comes into play. But whatever your district does, there should be documentation out there that defines the selection methodology, and it should be available to you.</p>

18

<p>

No preference to siblings.<br>

The preference is to students in the district and, since wer’re on Staten Island, almost no one outside of the district ever applies in from elsewhere, so I don’t think that would be statistically significant.

The FAQ says that none of the schools are informed as to what choice they are, so I don’t think that matters. The process, theoretically, stops when a school on the list matches the child. There is no promise of a first choice or any other choice on the list.</p>

<p>For this group of choices, the DOE swears that it is totally random. There are other possible choices for which the destination schools handpick based on test scores, attendance, etc., but this particular group is supposed to be random.</p>

<p>What I’m taking away is that we need to have a program on the list that isn’t particularly popular in order to guarantee a seat somewhere. My hope is that he will audition well and get one of the coveted music seats. But based on this conversation, I’m going to seek out less popular options and have him understand that sometimes we don’t get what we want and have to make the best of what is presented to us.</p>

19

<p>Zmom-- None of our schools are ever informed as to what rankings specific students use, but the lottery system absolutely takes those preferences into account. Given the parameters you’ve described, in many systems, the lottery would pull the first child -call him 1 (randomly) and see if that child’s first choice can be met. (Which, if the child is trying to get into a school with no slots at that grade level it might not be.) If matched, we’re done with that child 1. If not, child 1 goes into the holding pool to be dealt with after we’ve dealt with every other child’s #1 choice. And then we pick the next child randomly, and try to do the same. After we’re finished with everyone’s number 1 choice, we’re left with a pool of kids yet to be matched, and we throw away all their #1 choices and repeat the process for choice #2. Sometimes the kids are re-randomized at this point, sometimes not. We keep going like this until either all kids are matched, or until the kids left have no more choices that can be matched. </p>

<p>In most lottery systems, there is no advantage in not filling all your available slots as long as you’d be willing to attend that specific school/program. The absolute key is to make sure that if certain schools never (or very, very rarely) dip into the 2nd priority requests that you don’t include it unless it is your first priority school. If Schools A, B, C all fill 100% from 1st priority requests, and Schools D,E,F all fill completely from 1st or 2nd priority requests, and Schools G,H,I all fill completely from 1st, 2nd,3rd, and 4th priority requests, and schools J,K,L don’t always fill, then a good strategy is to put one school from A/B/C as your first choice (if one of them IS your first choice), one school from D/E/F as your second choice (if one of them IS your second choice outside of ABC), pick two of G/H/I for your third and fourth choices, and use J/K/L to round out your selections. (Obviously, don’t include any school you wouldn’t be willing to attend.) </p>

<p>Where most people go wrong is that they’ll put A/B/C /D/E/F/ down as their choices, not understanding that in the situation I’ve described, if their child doesn’t make it into A, s/he is not gong to get into B or C either, and then they don’t make it into D/E/F because those were all taken by kids who ranked D/E/F as either first or second choice.</p>

<p>It is a pernicious system from the student perspective, but it is the approach that maximizes schools filling up. The alternative, which I prefer, is that each school conducts a separate lottery, and then families see the results, choose the offer they like, and the system repeats – much like college admissions.</p>

20

<p>^ arabrab - Excellent discussion.</p>

<p>zoosermom - The bottom line is that only a thorough knowledge of how the selection software works (known as “internals”) will help you choose an optimal approach. It would be easy to design a “random” selection process where inverting the top four “random” choices would be the approach most likely to yield a “match.” Or another, where the student who makes only ONE school selection would have an advantage.</p>

<p>Frankly, I think you already have all the information you’re likely to get. Good luck to your S on Selection Day.</p>