Data and Truth

Tuesday July 15, 2014

A presentation at csv,conf.

I would like to approach some ideas about data and truth through a specific example. Some theoretical frameworks will be mixed in. By the end I'll have made a few recommendations.

How many NYC public school English
Language Learner (ELL) students
took the state math test in 2008?

The specific question to get us started is this: "How many New York City public school English Language Learner (ELL) students, that is, students identified as not speaking English fluently, took the New York State math test in 2008?

You'll notice that this is a very specific question, and this is because I'm cheating. I've aligned the question to the data I happen to have.

Just for fun, take it as a Fermi problem - how many do you think there were? Can you estimate the answer?

Way of Knowing:

But before we officially start trying to answer the question with data, I want to start introducing some "ways of knowing" that I'm borrowing from Balenky and friends. These are going to be systems of epistemology - ways of understanding knowledge. "Silence" refers to alienation from knowledge, which might sound strange. Especially with regard to math, statistics, anything data related, you have likely met people who feel these things are quite "other" to them You, on the other hand, are on the very opposite of that spectrum. I'd like to offer, and it may be the most important point in the talk, that it is a fundamental problem that we as humanity are missing the involvement of so many people.

Way of Knowing:
 Subjective Knowledge

Next up is "subjective knowledge", which is important but relevant to data work mostly in as much as they might seem to devalue one another. Probably a good deal more could be said about this relationship.

There is a file, `ell.csv`

We have a file, ell.csv! It was obtained first as an Excel file from the New York City Department of Education's web site. I've saved the relevant bit as CSV and you'll have to take my word that this process resulted in the "right" data, whatever that means.

d = read_csv('ell.csv')

I'll read in the data. What do you think? How much closer are you to an answer to our starting question?

You can't see data

The point here is that you haven't got a data sense. Data might as well be ultraviolet light, because it is totally invisible to you. Except it's worse, because UV light we can at least try to project somehow sort of reasonably into something that you do have a sense for handling, but for data we really haven't got anything like that, in general.

For your consideration: Numbers are visualizations. Letters are visualizations. Means are visualizations, p-values are visualizations, root mean squared errors are visualizations. And, of course, visualizations are visualizations. We have a lot of visualizations, but we don't have nearly enough, and many of those we do have are awful.

I think one thing we need is better tools, and I'll give some small examples later on.

In [1]: d.ix[0:4, 0:5]
      DBN Grade  Year Category  Number Tested
0  01M015     3  2006      ELL              4
1  01M015     3  2006       EP             35
2  01M015     3  2007      ELL              8
3  01M015     3  2007       EP             23
4  01M015     3  2008      ELL              6

So let's visualize some of this data that I've promised. "DBN" is a school identifier. "Grade" and "Year" you can make sense of, perhaps. "ELL" we talked about earlier, and "EP" is "English Proficient". "Number Tested" is what we're looking for! Great!

In [2]: d['Number Tested'][(d['Category'] == 'ELL') &
                           (d['Year']     == 2008)].sum()
Out[2]: 110956

So we can write these two lines and get an answer. Here is is: about 110,000.

How many things could have gone wrong here? Have we answered the question we started with? How close is this answer to the truth? Do you know enough to answer these questions?

Way of Knowing:
 Received Knowledge

Say I'm a data journalist and I got a number for my story, or I'm an education policy student, or I'm anyone at all, and now this number is published somehow and it is far easier to find than the data itself. Many people will not even think to ask to see this number's credentials. It isn't just dangerous that the credentials aren't out there - it's dangerous that people aren't asking. These are problems of "received knowledge".

Way of Knowing:
 Procedural Knowledge

Or you might be concerned with aspects of the procedure that rather miss the point. Do I have structured provenance data for the number? Are those students "Thing > Person"s? These are the failings of "procedural knowledge".

Way of Knowing:
 Constructed Knowledge

Even with just this one data source and this one question, things are more complicated than that. We'll call a complete and nuanced view of knowledge and belief "constructed knowledge". What we really need is a more complete understanding. Let's look in the data for some of the easy bits.

In [3]: sorted(d['Grade'].unique())
Out[3]: ['3', '4', '5', '6', '7', '8', 'All Grades']

Looking at what grades are in this file, we see that there are grades 3-8, which I can tell you is what it should be - those are the grades with New York State math tests. But we also have "All Grades" rows, which immediately suggests that our first answer was off by a factor of two.

 + Internal checks for consistency
 - Consistency is not truth
 - Redundancy
 o Views

Are the subtotal rows good or bad? On the one hand, it gives us something to check - if the provided totals are wrong, then certainly something is wrong, somewhere. But if they're right, it really only gives us a good feeling and perhaps increases a general sort of respect for someone somewhere. It's not really evidence that the data is "true".

The redundant data certainly isn't needed and introduces more places for mistakes to happen both in production and use. The fundamental problem, as is often the case, is that the data we see is really a view of other data, and we'd like to reduce the number of these indirections. So these rows really shouldn't be in there. But this is a point you may not succeed in making with whoever produces the file.

In [4]: d['Number Tested'][(d['Category'] == 'ELL') &
                            (d['Year']     == 2008) &
                            (d['Grade']    != 'All Grades')].sum()
Out[4]: 55478

So let's re-calculate. 55 thousand or so. Is this the right answer then?

In [5]: sorted(d['Category'].unique())
Out[5]: ['ELL', 'ELLs', 'EP']

Let's look at the "Category" column just a little more carefully. We thought there were just "ELL" and "EP", but also there's "ELLs". How strange.

In [6]: (d['Category'] == 'ELLs').sum()
Out[6]: 6

There are six of these "ELLs". Strange indeed. At this point you can look into what's going on, and you will almost certainly conclude that someone edited the source file by hand at some point. Of course we have no record of this, of who it was or when it happened, and we are really just guessing about the process that brought the data to us. I want to suggest that this guessing is something important.

Information Source
 + Transmitter
    + Signal
       + Receiver
          + Destination

Here is Shannon's general model of communication, going from information source via transmitter to some signal, and then from signal via receiver to destination. You can find this model many places. Try doing it for spoken language. It also has a fractal quality. Try doing it for brain to vocal cord. And so on.

Phenomena of Interest
 + Data Creation
    + Data
       + Analysis
          + System of Beliefs

Here I've re-written Shannon's model to be the data process we often need to think about. Whatever we're interested in is the phenomenon of interest, which is leading via some data creation process to some data, perhaps a CSV. Then some sort of analysis happens which leads to an updated system of beliefs inside the head of some human, perhaps you.

While Shannon was mostly concerned with noise affecting his signal, we're mostly concerned with what's happening in the data creation and analysis steps. Problems can enter in either phase, and probably both. Note especially that correct analysis depends on correct understanding of the data creation process.

In [7]: d['Number Tested'][(d['Category'].isin(['ELL', 'ELLs'])) &
                           (d['Year']     == 2008) &
                           (d['Grade']    != 'All Grades')].sum()
Out[7]: 55487

With our hard-earned guess about the "ELLs" labels, we can now get yet another answer to our initial question. 55,487. So precise.

Notice how ugly our code is already for this simple question. So fragile. Really it would be better to fix the data at its source, wouldn't it? We can probably agree about the "ELLs" thing at least, can't we?

In [8]: d.ix[[1235], 0:5]
         DBN Grade  Year Category  Number Tested
1235  01M363     4  2006      ELL              1

[1 rows x 5 columns]

But the problems we have seen are still superficial. How do we know if this data is true? Was there exactly one fourth-grade ELL student tested at 01M363 in 2006? I don't know. You probably don't know. The people running the data system probably don't know. A teacher might know. That student might know.

In [9]: read_csv('world_cup_2014_final.csv')
        team  score
0    Germany      0
1  argentina      1

[2 rows x 2 columns]

But let's look at some data that people care about much more than the education of New York City's youth. As you can plainly see, this data has a serious problem. Argentina is not capitalized!

(Note that this talk was given two days after this match was played, with actual scores the reverse of those given.)

The point here is that many of the things that we think of to fix in data are not really the difficult things. There's no way to know that the score is wrong unless you know that the score is wrong, in this case. We need eyes on the data. We need distributed validation. We need people.

Data should be easy to change.
It isn't easy.
∴ We need to fix something.

Say we have the people. It's still far too hard for them to make corrections. I'll mention two reasons.

One is related to authority-based epistemology, wherein the data is correct because it comes from an "authoritative" source. This is especially pernicious when the authority is an organization - a human released that incorrect data, but now that it has the stamp of the organization even the humans in the very same organization may not be able to change it.

The second reason is that systems aren't set up to be changed flexibly. Too often available data is a view of underlying systems and we're playing wack-a-mole. We need to find better ways to design and expose data systems.

Data must never change.

So say the data is corrected. This is a disaster! Now some things have been corrected, but our code was adapted to those things so the fixes may have broken our code, and of course there are new problems that we couldn't have anticipated.

Attempting to ensure that data meets whatever expectations we've developed, we might write assertions about the data. This is another kind of wack-a-mole, in that we can't really test everything that we assume. To be clear, I think we should write more tests rather than fewer, especially when code is used on data that necessarily changes. But for analysis that we want to be reproducible, the data must not change.

In [10]: assert((d['Category'] == 'ELLs').sum() == 6)

Computer scientist types are sometimes excited about homoiconicity, which we can think of as having your code also be data. I think that we should flip this around and think of our data as also being code. Then you don't need a million assertions to check that each piece of the data is the data you expect. If the data is in another file, you do one assertion that the file is the same file you thought it was, and you can go on then to use assertions in useful expressive ways.

In [11]: sha('ell.csv')
Out[11]: '846bb60a6e5df37281ffe79eec2087044d900860'

In [12]: assert(sha('ell.csv') == '846bb60a6e5df37281ffe79eec2087044d900860')

One way to knit your data into your code is to write an assert on a hash of your data. The hash of a file is, for practical purposes, unique to the file, but small enough to include in your source. So if the data changes, the hash will change, and the assertion will fail. It's effectively the same thing as copying all your data into your source file as a literal, but it takes fewer lines of code. This is reproducible.

I'll note that this kind of trick is also what git uses for ensuring your version controlled files aren't fiddled with, and it's related to how the blockchain of cryptocurrencies like BitCoin ensure that history isn't fiddled with. I think it may turn out that the block chain idea is useful for public records beyond currency.

How do we assert?

I still think we should be assertive in working with data, and I want to propose a way of doing it that sucks less, as a possible interface idea. Read Evaluate Print Loops are very useful tools, and things like IPython notebook are nice as well. But coding with a REPL you have a lot of back and forth, and with IPython notebook especially it's easy to get tangled up because you have exactly one current state of the system and you can't really rewind it or otherwise access earlier points.

1 + 1
assert(1 + 1 ==

What if we used assertions as the interface? Now, this may seem to have all the sexiness of a paper tape adding machine. But note that I'm not switching to a REPL, but I am getting my output, and as I go I'm creating a confirmable record of what I've done.

x = 16

assert(x / 2 ==
x = 24

x / 2

It would also be nice if there was some intelligence to this system, so that if I go back and change something I don't have untrue assertions lying around.

assert(sha('ell.csv') ==

And it's very easy to do my data assertions.

assert(sorted(d['Category'].unique()) ==
       ['ELL', 'ELLs', 'EP'])

d['Category'][d['Category'] == 'ELLs'] = 'ELL'

assert(sorted(d['Category'].unique()) ==
       ['ELL', 'EP'])

This sort of thing would make it very natural to write code that reads like a narrative, or better yet an argument, showing what was the case, what was done, and what the result is, all confirmable.

Data that changes and doesn't change

Now we still have this problem of data needing to change and also absolutely not being allowed to change. How do we resolve this? Well, physics also has this problem, and the solution is time. We need a system that can always have the same answer for questions like "what did we know on some date at some time?". What can do this?


SQL, and really most databases, is almost always a disaster when it comes to this. If your work pulls data from SQL, your work is not reproducible, and it may not even be consistent for a single run.


In this sense, it's a benefit of CSV that it's so often used as a snapshot format - for the most part a CSV file will not change on its own. You can do worse than to keep around copies of every CSV you ever use and treat them as immutable. Storage space is cheap, they say.

git checkout `git rev-list -n 1 --before="2014-05-01" master`

Of course some real versioning system would be better. Git is not the worst thing. It can get you the system as of whatever date/time, but it's a little clunky, and there are other issues that make it less than ideal for some data sets. But still, for many data sets git-controlled CSV is a great solution.


The Dat Project promises to do versioning, and I really hope to see it do it very well. It's still early. So far versioning behavior is a little strange as far as I can tell. There's also the issue of unique IDs, which is something you might not think about if you're storing data in rows of CSV. This affects the next candidate as well.

 * time baked in
    * (as-of db t)
 * triples
 * datalog
 * proprietary

Datomic is a database that has the time feature that I think should be a requirement for every data system: you can always get the state of the data "as of" any time. So if I run my analysis today and get a result, I can be guaranteed that I can get the same result if I do it again tomorrow. You have no such guarantee with a SQL database or with CSV files in DropBox, for example.

Datomic makes some other interesting choices. First, it decides that the structure of data is fundamentally triples, not rows or objects. I'm not sure this is right for every problem, but Datomic is very clear about its opinion. A related choice is that you query the database using datalog. And most unfortunately, Datomic is proprietary software.

I don't know yet whether Dat will be anything like the Free version of Datomic, but I want this as-of time feature somewhere!

The most exciting phrase to hear in science,
the one that heralds new discoveries, is not
"Eureka" but "That’s funny..."      (Asimov)

Wrapping up, I want to connect to what I think is the purpose of working with data, which is to learn something about the world. Of course, with data much of the time when we say "That's funny..." it's because there's something wrong with the data. Here's an example.

giant rubber duck

So: Is the duck real? Call me naive, but when I first saw this picture I thought this was Photoshop wizardry. This is a real duck. Some of you already know, and some of you may not believe me. Talk to the people around you. Google it. It's a team effort.

The Data Explorers Club

So the final point is that while there is data out there that is unbelievable, some of those are discoveries! I would like to see more discoveries. I would like it very much if building knowledge from data became a popular hobby. Call it The Data Explorers Club.

Thank you.

This is how life will be. I must be wholehearted while tentative,
fight for my values yet respect others, believe my deepest values
right yet be ready to learn. I see that I shall be retracing this
whole journey over and over - but, I hope, more wisely.   (Perry)

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