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World Series Winners and Losers: Playing the Percentages

13 Nov

Don’t be fooled by last week’s denouement of the World Series; the baseball season never really ends. The looks at the data from what was once boomed as the National Pastime just don’t stop, including some looks at the World Series itself, e.g. a survey put together by Joel Pozin of the regular-season winning percentages of Series participants dating back to the first series in 1903. It’s here:

Regular Season Winning Percentages of World Series Champions vs. Losers_ 1903-2017 Joel Pozin

The survey in fact contributes one of three small, public-domain Series’ datasets Pozin makes available on the collaboration-fostering data.world site (you’ll need to sign up for free for access to the other two workbooks; note that the percentage data for 1904 and 1994 aren’t there, because the World Series weren’t contested those years. In addition, I’ve appended percentage win-percentage data for the 2017 season to the sheet here.)

The other two workbooks recount the Series winner and loser percentages in their discrete sheets, but they do something else as well: they bare the formulas that return the team winning percentages, formulas that do a slightly different math from that performed by Major League Baseball’s number crunchers. A winning percentage, after all, emerges from a rather simple act of division: Wins/All games played. But Pozin has taken account of the mini class of games that, for whatever reason, culminated in a tie or draw, games that baseball officialdom simply bars from the win-loss calculation. Pozin, on the other hand, admits them to the All-games-played denominator, and assigns a .5 for each tie to the numerator. Pozin’s outcomes thus don’t invariably comport with the canonical percentages, though the differences of course aren’t game-changing, so to speak. But differences they are.

Those formulas themselves are interesting, however. On the loser sheet, for example, the 1903 Series runner-up Pittsburgh Pirates won 91 games, lost 49, and tied one, those respective accumulations committed to cells C2:E2 in the losers’ worksheet. The formula in F2 then declares:

=ROUND((C2+E2/2)/SUM(C2:E2),3)

(Note that the sheet featuring Series winners formulates its denominators this way instead, e.g.: (C2+D2+E2) ). The single tied game recorded in E2 is halved and added to the win figure in C2 to build the formula’s numerator; but in addition, the rounding of the result to three decimals quantifies the value in F2 to exactly what we see – .649, or .6490000.

But one could opine that the cause of exactitude could have been slightly better served with

=(C2+E2/2)/SUM(C2:E2)

followed by a formatting of the result to three decimals, thus preserving the quotient’s precision. The ROUND function forces a substantive pullback in precision – because after applying ROUND, the number you see is truly and only .649. But does my nit-pick here matter? Maybe.

And while we’re deliberating about things formatting, the winning percentages expressed in the workbooks in their Excel-default, 0.649 terms could be made to assume the baseball standard .649 deportment per this custom format:

series1

Now back to the winners and losers in the master sheet I’ve offered for download. A simple inaugural inquiry would have us calculate and compare the average winning percentage of the winners and losers. Rounded off to the usual three decimals I get .619 and .614 respectively, a dissimilitude that is neither great nor surprising. World Series competitors, after all, are the champions of their respective leagues, and so could be regarded as more-or-less equivalently skilled. And while of course only one team can win, the best-of-seven-game motif (in fact four series proceeded on a best-of-nine basis) could be ruled as too brief to define the truly superior squad.

But additional comparisons may point to other interesting disparities. If we pivot table and group the winning percentages in say, ten-year tranches:

Rows: Year

Values: ChampWinRatio (Average)

LoserWinRatio (Average)

(Remember that no Series was played in 1904 and 1994, and that the custom format we commended above must be reintroduced to the pivot table if you want it in play here. In addition, of course, the 2013-2022 tranche, forced by our grouping instruction to embody the ten-year amplitude, comprises only five years’ worth of data).

I get:

series2

Note the rather decided scale-down in winning percentages set in motion during the 1973-1982 tranche. Do these smallish but apparently real curtailments hint at a press toward parity among baseball’s teams that dulled the advantage of elite clubs? Perhaps the advent of free agency following the 1975 season, in which teams’ contractual hold on their players was relaxed, played its part in smoothing the distribution of talent.

But another, if distantly related, exposition of the trend could also be proposed. Baseball rolled out a post-regular-season playoff system in 1969, one that now qualifies ten of its 30 teams each season; and that broadened inclusiveness overwrites any guarantee that the clubs with the best regular-season records will find themselves in the fall classic.  The 1973 National League champion New York Mets, to call up the extreme example, beached up in the Series with a regular-season winning percentage of .509. But they won the playoff.

Now let’s return to my quibble about the deployment of the ROUND function, and my counter-suggestion for simply calculating win percentages without it and formatting the numbers to three decimals instead. Working with Joel Pozen’s rounded figures, we can write an array formula that’ll count the number of World Series victors whose regular-season percentage exceeded that of the losers each year:

{=SUM(IF(C2:C114>E2:E114,1))}

The formula assigns the value of 1 to each value in the C column – the one containing Series winners’ percentages – that tops the corresponding value in E, the losers’ column, and then adds all the 1’s (note: the formula can surely be written in alternative ways). I get 57, meaning that according to Pozin’s percentages a jot more than half of all the 113 World Series wins went to the team with the higher regular-season percentage.  Again, not a shocker, but worth demonstrating.

Now if we array-calculate the number of Series winners with the lower of the regular-season winning percentages:

{=SUM(IF(C2:C114<E2:E114,1))}

I get 53 – but there are 113 Series for which to account here, and 57 plus 53 computes to 110.   It turns out then then that in three Series – the ones played in 1949, 1958, and 2013 – the competing teams appear to have achieved the same regular-season win percentage.

And for two seasons, 1949 and 2013, the winner-loser identity is inarguable – the teams in those years had precisely the same numbers of wins and losses. But if we actuate my formulaic alternative, in which the drawn-game half-win-credit is retained but the ROUND function is shed for the reasons advanced above, we learn that the 1958 winner New York Yankees played to a .596774 percentage (rounded to six decimals), because they played a tie game that year; but the losing Milwaukee Braves steamed into the Series with a .597402. Seen that way, the 1958 Braves are the 54th losing team to best the winner’s regular-season mark.

The difference here of course is hair-splittingly slim. But if your head-of-the-class high school average was .000628 points greater than that of the runner-up, would you be willing to share your valedictorian honors by agreeing to a round-off?

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Girls, Boys, and NYC Math Scores: An Addendum

31 Oct

Sloth has its limits. I had, if you must know, entertained a couple of questions about the way in which I managed the New York City math test data in my previous post, but place momentum in the service of lassitude and I decided  that for the time being I couldn’t be bothered. Now I’m bothered.

What’s bothering me, at last, is a concern we’ve certainly voiced before in other posts – namely, the fact that my score analyses to date have ascribed equal weight to each record in the data set, irrespective of the number of students populating the listed schools. That forced parity thus imparts disproportionate influence to smaller schools. But because the data set is so sizable, I had originally assumed that a proper weighting of the student populations would exert only a small corrective effect on the test averages.

That assumption isn’t terribly untoward; but because the girls’ test averages evince only slight – if tenacious – superiorities over the boys’, a second, suitably weighted look at the scores might the responsible view to take via a calculated field, in the interests of learning if the results might materially change as a consequence.

To start, then, I visited next-available column S, titled it RealScores (of course the name is your call), and entered, in S2:

=IF(H2=”s”,””,F2*G2)

 The formula simply multiplies every school’s mean score in G by the number of its students posted to F, returning the total number of score points, as it were, to be divided by the total number of students identified by a pivot table breakout (e.g, Borough).

 The IF statement in which the formula is couched replaces each “s” entry (see the previous post below for explication) with a textual cipher (“”), and not 0. That latter numeric would have been processed by any average, thus artificially depressing the results. And the absence of a test result assuredly does not strike an equivalent to zero, as any student will tell you.  

And those “s” rows release an interesting subtlety into the equation. The calculated field, which I’ve I advanced above (I’ve called it actscore) is written thusly:

math1a

That is, the field simply divides the RealScores field we instituted earlier by the total number of students tested (the Number Tested field). The “s” records contain no scores – but they continue to cite student numbers in Number Tested. Unaccompanied as they are by no scores, those numbers thus add ballast to the denominator in our calculated field, and in turn artificially drag down the averages.

The way out – one way out – is to sort the Mean Scale Score (in G) Smallest to Largest, if you’ve clicked on a number in the field. The s entries should fall to the bottom of the field, the first s landing in row 36045. Hang a left to F36045, enter a 0 there, and copy it down the remainder of the column. Now the calculated field will add nothing from the s records – literally – to the Number Tested denominator, obviating the downward pull of the averages to emerge.

Got all that? In any case, now we can go on to construct the same pivot tables that featured in the preceding post, and compare the new recalculated results here with those in that post.

Averages by Gender and Year:

math2a

Averages by Borough and Gender:

math3a

One we didn’t directly bring to the previous posts, Averages by Grade and Gender (we had added Year to the mix there):

math4a

The signal conclusion here is the preservation, per all permutations, of the girls’ edge. The averages are all a touch higher this time around, however, a concomitant of higher scores that appear to obtain in the larger schools – the ones contributing larger numbers to the averages.

Now I’m not so bothered. But I’m still missing a sock.

Girls, Boys, and NY City Math Scores: No Mean Feat

27 Oct

Are boys better at math than girls? The question is hard-wired for controversy of course, but stammer a first response by trotting out SAT (Scholastic Aptitude Test) scores and the answer is yes. Boys consistently outscore girls by roughly 30 points a year on the nationally-administered exam (national in the US, that is), an extraordinarily dogged interval that bucks the ebb and flows of SAT score aggregates:

math1

(Screen shot source: the above-linked web site, reproducing the chart in turn from the College Board that conducts the SAT.)

And, as the linked site above continues, the advantage enforces itself even as high school girls outperform boys academically overall. (None of this suggests that conclusions are necessary or unitary; see this demurral, for example.)

Is that the last word on the subject? Of course it isn’t, and for additional testimony we can swing our protractors over to the New York City Open Data site and its compilation of New York State Math Test results by gender for city schools, reported for the years 2013-17 (the test is described here). Click the Data Dictionary link to call up a workbook offering the data and supplementary worksheet tabs clarifying their fields.

Next click the Master tab and 47,000 rows worth of score data are yours for the analyzing, including at least three parameters just begging for your attention: student grade, year of exam, and gender, which the sheet curiously entitles Category. The test scores themselves – scaled to enable cross-grade comparisons – fill column G, a normalization that would thus appear to support some rather global aggregations, e.g. average score for all students by year or gender, or even borough (that parameter is in fact concealed in the DBN field in A and must be dredged from the school code entries, a chore we’ve performed in a previous post).

You’ll note, however, that 485 records, a touch more than 1% of them all, substitute an “s” code in lieu of actual test scores, a replacement impelled by privacy considerations (see the discussion in cell B12 of the DatasetInfo tab). In fact, we’ve encountered this stricture before in a different demographic context; see this post, for example. But in any case, those alpha proxies will simply be ignored by any computation, thus freeing the 99% of the number-bearing entries for any closer, quantifying look.

But there’s another perturbation roiling the data that the formulas won’t automatically overlook: the All Grades posts in the Grade field that, in effect, subtotal schools’ math averages by year and gender, e.g., the scores for all girls at P.S. 015 in 2013 across all grades. There are more than 11,000 such records among the data and I’d allow they could, and probably should, be deleted, because they perpetrate the old double-count snag that must be cleared. Again, any and all aggregating tasks performed upon the score data could be made to emerge from a pivot table, and the promise of eliminating 187,000 cells from the worksheet should prove irresistibly appealing.

But I am mustering a show of resistance, or ambivalence, to any plan for expurgating some of the Level fields in columns H through Q. These count the number of students per school per year and per class, whose testing outcomes position them atop one of four levels of accomplishment defined by New York State, and as detailed in the ColumnInfo sheet (the higher the number the greater the proficiency). The Level % fields – for example, could have, under other spreadsheet-organizational circumstances, been easily derived from the N-field data via a standard pivot-table sited % of Column/Row Total – had all the level scores been assigned their own record beneath the same, circumscribing field. But the data don’t behave that way, and so perhaps the sheet is doing us a favor by folding the % fields into the data set (in fact, had all the Level_N numbers been assembled beneath a single field heading, the Number Tested field could have likewise been bid a farewell, because a pivot table would return numbers tested as a sub or grand total). So in light of the prevailing realities, leaving all those fields alone might be a prudent thing.

But I think the time has come for us to actually do something with the data. For a broad-stroked inaugural look, we could average all test scores by gender and year, via this pivot table:

Rows: Year

Columns: Category

Values: Mean Scale Score (Average, figured to two decimal points)

I get:

math2

No female shortfall here. On the contrary, girls’ average scores top boys for each of the available years, by more than a point each year. (On the other hand, we also need to inspect a nuance dotting the large student numbers here: the obvious fact that many of the scores issue from the same students. After all, a third-grade student in school A in 2013 likely reappeared as a fourth-grade student in school A in 2014.)

But is there any evidence of a progressive slimming of the girls’ edge with age? SAT scores, after all, chart a significantly older demographic: the cohort of university-eligible students, the one that affirms that insistent 30-point male differential. Our data, on the other hand, emanate from test-takers hailing from grades three through eight, bidding us to wonder: Does a male margin begin to pull away any time within our data? An answer calls for an introduction of the Grade parameter to the table, but because a three-variable output (Year, Category, and Grade) will begin to clutter the table, I’d opt to cast Grade into a Slicer and successively tick the six grades for which the numbers are available:

math3

Click through the grades and the girl score superiority prevails throughout, indeed broadening unevenly across the older grades and cresting with a 3.07-point average excess in grade 6.

We could also examine borough-wide variation in the numbers, by extracting the respective borough codes from the DBN data in column A. The codes occupy the third position in each code entry, and so if we wend our way to the-next-free-column R and name it Borough, we can enter in R2:

=MID(A2,3,1)

Copy down R, and the borough indicators are isolated:

K- Brooklyn (for Kings County)
M-Manhattan
Q-Queens
R-Richmond (Staten Island)
X-The Bronx

Then draw up this pivot table:

Rows: Borough

Columns: Category

Values: Mean Scale Score (Average, to two decimals)

I get:

math4

Here both gender and borough disparities mark the data, the former most conspicuous in the Bronx. Among the boroughs Queens rises to the top, its average score separating itself from fifth-place the Bronx by more than 20 points. Indeed, the Queens boy average exceeds every other girl’s mean, save that of Queens, of course.

These findings contribute but a sprinkling of pixels to the larger picture, but contributory they are. Accounting for the relative male math predominance at later phases of the educational process serves up a famous analytical challenge; winners of the near-impossible William Lowell Putnam Mathematical Competition, for example – 120-point university-level exam on which the median score is often 0 – are nearly all male, but I don’t know what that means, either.

All of which begs the next question: I’m a guy – so why is it when I divide my number of socks by 2 I always get a remainder of 1?

US Visa Data, Part 2: An Excel Application

16 Oct

Promenade down the wage_rate_of_pay_from field lining the H-1B visa data set (the visas have rather newsworthy of late; see, for example this New York Times piece) and you’ll likely saunter away with the impression that the jobs attaching to the H-1Bs are impressively compensated (the partner wage_rate_of_pay_to field that reports the apparent upper ranges among the proposed salaries is more spottily filled). These sound like pretty good, if impermanent gigs, and as such there might be something to learn by say, breaking out wages by state – once you try your hand at cinching a loose end or two that, bad metaphor notwithstanding, poses a knotty problem demanding your expert attention. (You’ll also learn that a very small proportion of visa applications – around 2% – aren’t seeking H-1Bs at all, but rather variant visas tied to country agreements with Chile, Australia, and Singapore.)

You’ll discover that the wage_unit_of_pay field in fact stocks a number of units, or demarcations of time, by which pay is calculated, e.g., Bi-Weekly, Year, etc. The problem points to a banal but integral data-quality matter. The pay figures in wage_rate_of_pay overwhelmingly key themselves to the Year unit – more than 93%, in fact – but more than 32,000 visas stipulate an hourly compensation, and some of these report wage units of pay that clearly can’t be clocked against 1/24th of day. Auto-filter wage_unit_of_pay for Hour, and you’ll bare 55 pay figures equalling or exceeding $48,000 – and if those rates are hourly, only one question remains to be asked: where can I download an application form? And the far smaller Bi-Weekly tranche likewise hands up a little cache of implausible compensations, as do the few Month position (can we definitively say that the $265,000 slot entertained by the Texas IPS PLLC firm in San Antonio is truly monthly? That application was withdrawn, by the way.) The Week pay data seem at least imaginable, however).

It would appear that these sore thumbs really mean to convey yearly salaries, and I know of no graceful means for redressing, apart from substituting Year in the suspect cells, and that isn’t graceful. Ok; I suppose some field-wide IF statement, e.g. if the number in wage_unit_of_pay exceeds 10000 AND the unit reads Bi-Weekly OR Hour, then enter Year in lieu of Hour with an accompanying Copy>Paste Values atop wage_unit_of_pay might placate the purists, but I’m not sure practicality would be best served that way.

In reality, of course, we can’t know if even the plausible compensation figures are right, and in view of the enormousness of the data set a press toward simplicity might bid us to merely work with the Year item, with a pivot table that goes something like this:

Row: employer_state

Values: wage_rate_of_pay_from (Average)

wage_rate_of_pay_from (again, this time Count)

Slicer: wage_unit_of_pay (select Year)

Sort the averages largest to smallest, and I get in excerpt:

visas1

Nice work, if you can get it. That’s Alaska heading the average salary hierarchy, though its visa-owning workforce is diminutive. Among the heavy hitters, Washington state (WA) – home of Microsoft, for one thing – checks in with an average emolument of $113,139; and indeed, an auto-filter tells me that over 4,000 of the Washington visas were requested by that very firm (you may happen to note, by the way, that one Microsoft-attesting record spells its headquarters city Redmnond, another data-quality eyebrow raiser. And there’s those 14 state blanks, too, though they sure pay well, if anonymously). The overall Year salary offer – and remember we’re working with the wage_rate_of_pay_from, the lower of the two salary tiers: over $87,000.

But inspection of the averages will affirm considerable interstate variation – e.g. major employer Texas, whose $79,823.51 mean thrusts it down to 46th place, though largest hirer California looks good with an average over $102,000. Accounting for the dispersions across the salary band might make for a story worth writing.
And if you’re interested in principal employers, try this table:

Rows: employer_name (Filter, Top 10)

Values: employer_name (Count). Sort largest to smallest.

I get:

v2

Tech consultant giant Infosys and Tata rank first and second among the visa-sponsoring firms; Microsoft barely makes the top 10. But pad the table with the wage_rate_of_pay_from field, and again deploy a Slicer and tick its Year item, and we see:

v3Big bucks emanating from Redmond, no matter how you spell it.

And since I’ve lazed past the discrepant-time-unit problem by confining my pivot tabling to Year figures only, let me at least consider a workaround that would more-or-less reconcile the Year, Bi-Weekly, etc. units, provided all their salary data were in working order, so to speak. In order to say, map all the salary proposals to the Year baseline, I’d draw up this lookup table:

visas2

The idea here calls for looking up the wage_unit_of_pay for all cells, and multiplying the associated pay figure by the appropriate looked-up value. These, of course, are standardized educated guesses, assuming for example that a 2000-hour annual work investment is to be multiplied by the hourly rate and that a bi-weekly term comprises 25 paydays.

Those suppositions could, for any given visa case, be way off, but absent meaningful supplementary information, they’d have to do.

But for the reasons detailed above we didn’t go that route anyway. I don’t know about you, but I’m happy enough with 494,672 records.

US Visa Data, Part 1: An Excel Application

4 Oct

If you want to be a legal alien in the United States you’ll need a visa. If you’re technically skilled the visa of choice is the H-1B, described by the Public Enigma open data site as”…a non-immigrant visa that allows U.S. companies and organizations to temporarily employ foreign workers in specialty occupations.”

If you want to learn more about the speciality cadre join Enigma for free, carry out the requisite click-throughs (the H-1B data are advertised on their home page) and you’ll find yourself here:

visa1

Opt for the 2017 edition, click the ensuing Open in Data Viewer button, and then click in turn the Export Dataset button centered of the trio of links below (though you can’t get this far unless you join Enigma and sign in):

visa2

Then break for tea time while the data mows a swath through your RAM and as last overtakes your screen; and with 528,000 visa application records amassing 154 MB, that’s a lot of Liptons.

Yes, you’ll have to perform the usual column auto-fit necessities, and you may want to think about which fields could be safely sheared from the data set, in the interests of a healthful file downsizing. (You may also want to rename the character-ridden worksheet tab.) It seems to me we could do quite nicely -at least – without employer_phone, employer_phone_ext, agent_attorney_name, agent_attorney_city, agent_attorney_state, and the wholly desolate pw_wage_source_year. These truncations have the effect of scaling my workbook down to a svelte 86 MB. (You may want to retain employer_country, though; several nations other than the United States are listed therein.)

Once having thinned the file we can go to work, starting with a simple resume of number of visa requests by state. My pivot table looks like this:

Rows: Employer_state

Values: total_workers (sum; sort largest to smallest)

total_workers (again, here % of Column Total)

You may also want to filter out the very small number (25) of blank records.

Note, by the way, that total_workers doesn’t always register one worker per visa request; a great many of the applications record multiple applicants.

My pivot table looks like this, in excerpt:

visa3

High-population, hi-tech California submits nearly a quarter of all of the H1B applications, with the top three states, including Pennsylvania and Texas, handing in 52% of them all.  Grand total of H1Bs: over a million.

(Note that the output comprises 57 rows, because the application data counts the District of Columbia (DC) the nation’s capital, not accorded state status), and US territories: Puerto Rico (PR), the Virgin Islands (VI), Guam (GU), Micronesia (FM), the Northern Mariana Islands (MP), and American Samoa (AS).)

And what proportion of application requests were approved? The pivot table should furnish the answer:

Rows:  case_status

Values: case_status (count, % of Column Totals).

total_workers (sum, % of Column Totals)

I get:

visa4

We find nearly 89% of the applications win governmental approval, with another 7% or so securing the okay even as the submission was withdrawn, for whatever reason. The certifications in turn accredit an even larger set of actual applicants; including the certified withdrawals, over 96% of the individuals seeking the H1B visa acquired it, at least for the time frame within which we’re working. Thus we see, latter-day controversy and clamor over immigration notwithstanding, that these visa applicants, ones in possession of specialist skill sets, are almost always shown the open door – remembering at the same time, however, that by definition they aren’t long-term immigrants.

We can next quickly recapitulate the average wait time distancing an H1B visa application from its decision date, via a pretty straightforward array formula asking us in effect to simply subtract all submission from decision dates, stored in the case_submitted and decision_date fields respectively. In the interests of key-stroke economy I named the fields sub and dec, and entered, somewhere:

{=AVERAGE(dec-sub}

That pert expression subtracts each submission from its corresponding decision date and averages them all. I get an average wait of 31.21 days per application, though a scan of individual waits discloses very substantial variation.

I then wondered about the comparative handful of application denials. Do they evince notably different wait times, in view of the fact that these entries culminate in rejection? For an answer I named the case_status field stat and entered this array formula, again somewhere:

{=AVERAGE(IF(stat=”DENIED”,dec-sub))}

The formula nests an IF statement into the mix, figuring the application wait times for those entries in case_status that read DENIED. In any case, I get a denial average wait of 4.06 days, a far swifter set of judgments. Perhaps those applications triggering denials are so egregiously ill-suited that the decision becomes easy – though that’s merely plausible speculation.

In the meantime, I’m getting excited about filing my own visa request. After all, my specialist skill set is formidable – how many left-handed spreadsheet devotees have so few Twitter followers? I’m stoked.

But I just remembered. I’m ineligible for a visa; I’m a US citizen.

America’s Schools, Part 2: Eyeing the Pupil Data

19 Sep

The question with which we wound up the previous post bears repeating, so let me repeat it: does a cognizance of the data quality issues that compromise the US school dataset inflict a failing grade upon the the workbook? That is, are we right to proceed with a look at the data just the same and give them a proper hearing, or should we bail out and take our pivot tables elsewhere?

I’d allow that the answer I submitted in that post bears repeating too – i.e., something like a yes. It seems to me that an analysis should properly go ahead, because the weight of the records – all 97,000 or so of the usable ones (let’s remember that number) – should, in virtue of its very size, synergize a plausible summary of the shape and quantity of America’s schools. Again, of course, the numbers are “wrong”; but they’re invariably wrong for any demographic take built on US census data, which after all date from 2010. Still, some general picture of the country’s institutional landscape should be there for the limning, if we’re persuaded.

We can commence, then, by performing a simple count and break out of schools by state:

Rows: STATE

Values: STATE (Sorted, Largest to Smallest)          

I get, in excerpt:

school1

 You’re not likely to be surprised by the above. American’s most populous state, California, predictably registers the most schools, though a check of Wikipedia’s state population totals furnished both for 2010 census aggregates and 2016 estimates points to a relation between population and school numbers that isn’t quite linear. Note in addition that our pivot table makes no place for the 28 schools in American Samoa, and in this case it could have; you’ll recall that we provisionally banished that territory’s records from the data because of the unavailability of its student totals. But here because we’re counting school names alone, the AS data could have been accommodated – simply because its school names, at least, are indeed listed.

Next, we could just as easily consider the average number of students per school by state, but before pressing ahead entertain a pre-verification surmise: namely, do the more populous states average more students per school? That’s a sensible conjecture, but one that must by no means invariably follow; after all, it’s possible that the sparser states simply maintain fewer schools, whose average size compares with the denser ones.

Let’s see. You can leave STATE alone in Values, and add to it ENROLLMENT, ticking Average. Then sort the results by ENROLLMENT. I get, in part:

school2

That’s Guam at the head of the class, its 40 schools averaging 781 students per institution (again, the bundle of 55 “STATEs” owes its hyper-count to the inclusion of American territories). At bottom sits the scantly populated Montana, whose per-school average of 171 makes it easy for teachers to space their students at exam time, if nothing else.

The disparities here, then, affirm a most mixed set of students-per-school averages, recalling the question if the numbers of schools by state indeed correlate with average school size. A rough read on that relationship becomes available with CORREL, in my case looking like this:

=CORREL(B4:B58,C4:C58)

And that expression evaluates to .3117, mustering a loose but meaningful association between the two variables – that is, as the number of schools across the states ascend, so does average class size. At least slightly.

And what of teacher-student ratios across the states? Again, the incipient question, one we’ve submitted several times in the past, needs to be asked and answered: does one calculate the ratios by according equal weight to every school irrespective of absolute school size, or does one realize a grand average of all of a state’s students divided by all its teachers (apparently defined here as Full Time, and so perhaps  deeming two half-time instructors as one full-timer) instead?

In fact, both alternatives are credible. There may be good analytical reason to treat schools as equally-sized entities in the averages, in the same way, for example, that we would could compare the standards of living of residents in different countries. And weighting 100 and 1000-student schools equivalently can’t be worse than granting one vote to every country in the United Nations General Assembly or apportioning two US Senators to each state, can it?

But before we tangle with the numbers we need to broaden our look at the FT_TEACHER field, because a measurable batch of records there reports faculty complements at zero or in the negative numbers. Sort the field Largest to Smallest, and lower a blank row atop the first zero. But you know that routine.

Now if we play the above option, by in effect averaging each student-faculty ratio, we need to title the next available column (where that is depends on how many fields you deleted in last post) StuStaffRatio or something like it, and simply enter a formula in row 2 dividing ENROLLMENT by FT_TEACHER and copy down (again, column references may vary). Back in the pivot table, you need to rewrite the range coordinates of the source data set (in PivotTable Tools>Analyze>Change Data Source.), and follow up by recruiting StuStaffRation into Values, averaging the results to two decimal points. I get, in excerpt, after sorting the field Largest to Smallest:

school3

The inter-state variation is considerable, and it’s most noteworthy that, large school sizes notwithstanding, Guam has managed to insure a pleasingly low (13.75) student-to-teacher proportion – so low you can’t see it in the screen shot – with California faring worst, at 23.76.

Now a suitable null hypothesis might foretell a perfect correlation between average enrollments and faculty sizes, irrespective of the absolute state numbers involved. Thus alerted to that prospect, we could write

=CORREL(C4:C58,D4:D58)

I get .4076, pretty serviceable by social-scientific standards, but surely not a 1. In other words, some positive association obtains between school student sizes and their teaching teams.

And speaking of school numbers, if you sort the ENROLLMENT field Largest to Smallest you’ll discover the honors going to the Ohio Virtual Academy, an online institution that serves Kindergartners through 12th graders and 11640 students – somewhere (its governmental web page counts 11278 as of the 2014-15 school year).

That means there’s some crossing-guard monitors in Ohio with a whole lot of time on their hands.

America’s Schools, Part 1: Some Truants Among the Data

8 Sep

The segue is inadvertent, but calling up a census of America’s schools look right after our look at New York school attendance data with makes for a deft transitioning, if I may say so myself, and I think I’ve just granted permission to do so.

This nationwide listing -105,000 institutions strong – is curiously archived in a site putatively devoted to information about hurricane Harvey. I’m not sure about the placement, but that’s where it is.

And it’s pretty big, as you’d expect, counting 105,087 schools in its fold and pitching 24 MB at your hard drive, after a download and a save as an Excel workbook. (Note: the data unroll stats for the country’s public – that is, government operated – schools only. The very large number of private and sectarian institutions diffused across the US are thus excluded from the inventory.) And if you run a simple SUM at the base of column AC, the field storing student enrollment numbers, you’ll wind up with 50,038,887, and that’s pretty big, too.

But of course, that number can’t get it exactly right. For one thing, the overview introducing to the workbook tells us that the data feature “…all Public elementary and secondary education facilities in the United States as defined by…National Center for Education Statistics…for the 2012-2013 year”. And since then a few hundred thousand little Justins and Caitlins will have moved on to other venues, to be replaced by littler Treys and Emmas – and the turnover just can’t be equivalent. Moreover the (apparent) Source Dates recorded in X track back to 2009 in many cases, though I don’t completely know how those dates are to be squared with the 2012-2013 reporting period.

Now apart from the as-usual column autofits in which the dataset obliges you, you may also want to shear those fields likely not to figure in any analysis, though that of course is something of a judgement call. In view of the virtual equivalence of the X and Y data in A and B with those in the LATITUDE and LONGITUDE parameters in S and T, I’d do away with the former pair. I’d also mothball ADDRESS2 (and maybe ADDRESS, too – will you need their contents?) I’d surely dispense with the NAICS_CODE entries, as each and every cell among them declaims the same 611110. And I think VAL_METHOD, VAL_DATE, SOURCE (storing basic information about the school committed to web sites), and probably SHELTER_ID could be asked to leave as well, lightening my workbook by about 5.3 MB all told. On the other hand, WEBSITE appears to have done nothing but clone the contents of SOURCE and as such could assumedly be dispatched as well, but I’ve since learned that the sites offer up some useful corroborating information about the schools, and so I’d retain it. But a field I would assuredly not delete, in spite of my early determination to do so, is COUNTRY. I had misled myself into believing the field comprised nothing but the USA legend, but in fact it entertains a smattering of other geopolitical references, e.g. GU for Guam, PR for Puerto Rico, and ASM for what I take to be American Samoa, for example.

I’m also not sure all the Manhattan schools (the ones in New York county, that is) display their correct zip codes for what it’s worth, and it might be worth something. The Beacon High School on West 61st Street is zip-coded 10022, even as it belongs, or belonged, to 10023 (though that wrong zip code informs a review of the school by US News and World Report); but the error may be excused by an updated reality: the Beacon School moved to West 44th Street in 2015, calling the timeliness of our data into a reiterated question. I’m equally uncertain why the Growing Up Green Charter School in Long Island City, Queens is mapped into New York county.

More pause-giving, perhaps, are the 1773 schools discovered inside New York City’s five counties – New York, Queens, the Bronx, Brooklyn (Kings County), and Richmond (or Staten Island; note that a Richmond county appears in several states in addition to New York). You’ll recall that our posts on New York’s attendance data, drawn from the city’s open data site, numbered about 1590 institutions. Thus any story-monger would need to be research the discrepancy, but in any case it is clear that the dataset before us errs on the side of inclusiveness.

But a lengthier pause punctuates a Largest-to-Smallest sort of the ENROLLENT field. Drop down to the lowest reaches of the sort and you’ll find 1186 schools registering a population of 0, another 1462 reporting -1, 4493 sighting -2 persons on their premises, and 91 more submitting a contingent of -9. Moreover, you’ll have to think about the 5399 schools counting a POPULATION (a composite of the ENROLMENT and FT_TEACHER fields) of -999. It’s not too adventurous to suggest that these have been appointed stand-ins for NA.

In addition, we need to think about the schools declaring only 1 or 2 students on their rolls. Consider for example the Marion Technical Institute in Ocala Florida and its 1 student and 34 full-time teachers. Visit its web site, however, and we encounter a more current student enrollment of 3 and a FTE (full-time equivalent) instructional complement of 37 (as of the 2015-16 school year), not very far from what our database maintains. But at the same time many of the 1-student schools are accompanied by FT_TEACHER values of 1 or 0 as well, and these microscopic demographics demand scrutiny. The web site for Bald Rock Community Day school in Berry Creek, California, for example, reveals no enrolment/teacher information, for example.

What to do, then? It seems to me that any school disclosing a negative or zero enrollment – and now sorting the ENROLLMENT field highest-to-lowest will jam all of these to the bottom of the data set – be disowned from the data set via our standard interpolation of a blank row atop 97407, where the first zero figure sits. We’ve thus preserved these curious entries for subsequent use should their other fields prove material.

And all that begs the larger question tramping, or trampling, through the data: How much time, effort, and money should be properly outlaid in order to support the vetting of 100,000 records? Multiple answers could be proposed, but there’s a follow-on question, too: In light of the issues encountered above, hould the data in the public schools workbook should be analysed at all?

Well, if we’ve come this far, why not?