On the Real Dangers of Marguerite Roza’s Fake Graph

In my last post, I ranted about this absurd graph presented by Marguerite Roza to a symposium of the New York Regents on September 13, 2011. Since that presentation (but before my post), that graph was also presented by the New York State Commissioner of Education to Superintendents of NY State School Districts (Sept. 26, slide #20). The graph and the accompanying materials are now part of a statewide push in New York to promote an apparent policy agenda, though I lack some clarity on the specifics of that agenda at this point in time.

Because this graph is now part of an ongoing agenda in New York and because critiques by other credible, leading scholars similar to my own but less ranting in style, which were submitted to state officials following the symposium have seemingly been ignored (shelved, shredded, or whatever) I feel the need to take a little more time to explain my previous rant. Why is this graph so problematic? And who cares? How could such a silly graph really cause any problems anyway? Let’s start back in with the graph itself.

How absurd is this graph?

So, here it is again, the Marguerite Roza graph explaining how if we just adopt either a) tech based learning systems or b) teacher effectiveness based policies we can get a whole lot more bang for our buck in public schools. In fact, we can get an astounding bang for our buck according to Roza.

Figure 1. Roza Graph


As I explained on my previous post, along the horizontal axis is per pupil spending and on the vertical axis are measured student outcomes. It’s intended to be a graph of the rate of return to additional dollars spent. The bottom diagonal line on this graph – the lowest angled blue line – is intended to show the rate of return in student outcomes for each additional dollar spent given the current ways in which schools are run. Go from $5,000 to $25,000 in spending and you raise student achievement by, oh… about .2 standard deviations. I also pointed out that it doesn’t really make a whole lot of sense to assume that there is no return to any type of schooling at $5,000 per pupil. It might be small, but likely something. It should really have been set to $0 for the intercept. It’s also likely that for any of the curves, that they should be… well… curves. You know, with diminishing returns at some point, though perhaps the returns diminish well beyond spending $25,000. But these are just small signs of the sloppy thinking going on in this graph.

The next sign of the sloppy thinking is that the graph suggests that one can use these ill-defined tech-based solutions to get FIVE TIMES the bang for the same buck – a full standard deviation versus only .2 standard deviations – when spending $25,000 per pupil.

So, how crazy is it to assert that these reforms can create a full standard deviation of improvement up the productivity curve – for example, if we spend $25,000 per pupil on tech-based systems as opposed to $5,000 per pupil on tech-based systems? Well, here’s the “standard normal curve” which, for fun, I obtained from the NY Regents Assessment study guide. That’s right, this is from the study guide for the NY Regents test. So perhaps the members of the Board of Regents should take a look. A full standard deviation of improvement would be like moving a class of kids from the 50%ile to the 84.1%ile. That’s no simple accomplishment!

Figure 2. Standard Normal Curve

Let’s put this bang for the buck into context. I joked in my previous post that this blows away Hoxby’s study findings regarding NYC charter schools and closing the Harlem-Scarsdale achievement gap. Hoxby, for example found that students lotteried into charter schools had cumulative gains over their non-charter peers of .13 to .14 standard deviations by grade 3, and annual gains over their non-chartered peers of .06 to .09 standard deviations. Sean Reardon of Stanford explains how the selected models and methods may have inflated those claims! But that’s my point here. Let’s compare Roza’s stylized claims with previous, bold, inflated claims but ones at least based on a real study.

Let’s assume that the bottom line on Roza’s chart represents traditional public schooling in NYC and that traditional public schools in NYC spend about $20,000 per pupil. Following Roza’s graph that would put those students at about .2 standard deviations above what they would have scored if their schools spent only $5,000 per pupil.  Roza’s graph suggests however, that if the same $20,000 per pupil was spent on tech-based learning systems, those students would have scored about .7 standard deviations higher than if only $5,000 was spent, which is also .5 (a half standard deviation) greater than spending on traditional schools. That is, shifting the $20,000 per pupil from traditional schooling to tech-based learning systems would produce an achievement gain that is over FIVE TIMES the annual achievement gains from Hoxby’s NYC charter school study. Of course, it’s not entirely clear what the duration of treatment is in relation to outcome gains in Roza’s graph. Perhaps she means that one could gain this much after 110, 12 or 20 years of exposure to $20,000 per pupil invested in tech-based learning systems?

Figure 3. Roza Graph with Notes

Why is this graph (and the related information) dangerous?

So, let’s assume that many features of the graph are just innocently and ignorantly sloppy. Not a comforting assumption to have to make for a graph presented to a major state policy making body and by someone claiming to be a leading researcher on educational productivity and representing the most powerful private foundation in the country. Setting the intercept at $5,000 instead of $0… Setting such crazy effect magnitudes on the vertical axis. All innocently sloppy and merely intended to illustrate that there might be a better way if we can just think outside the box on school spending.

I have no problem with the idea of exploring outside the box for options that might shift the productivity curve. I have a big problem with assuming… no… declaring outright that we know full well what those options are and that they will necessarily shift the curve in a HUGE way.

I have significant concerns when this type of analysis is used to promote a policy agenda for which there exists little or no sound evidence that the policy agenda is worthwhile either in terms of costs or benefits.

The remainder of the Roza presentation and the presentation that followed basically assert that large shares of the money currently in the public education system are simply wasted. This assumption is also simply not supportable – certainly not by any of the ill-conceived fodder presented at the Regents Symposium by Marguerite Roza or Stephen Frank of Educational Resource Strategies.

For example, Stephen Frank presented slides to suggest that any and all money in the education system that is spent on a) teacher pay for experience above base pay or b) teacher pay for degree levels (any and all degrees) above and beyond base pay c) any compensation for teacher benefits, is essentially wasted and can and should be reallocated.  Here’s one of the slides:

Figure 4. Stephen Frank (ERS) slide:

Essentially, what is being argued is that a school where all teachers are paid only the base salary and receive no health benefits or retirement benefits would be equally productive to a school that does provide such compensation (since we know that those things don’t contribute to student results). That is, it would be equally productive for less than half the expense! Thus, all of that wasted money could be spent on something else, spent differently, to make the school more productive. This is essentially the middle diagonal line of the productivity curve (straight line) chart – spending on teacher effectiveness.  But this is all based on absurdly bold assumptions and slipshod analysis (intentionally deceptive since it’s based on a district with a senior workforce).

I have written about this topic previously, and how pundits (not researchers by any stretch of the imagination) have wrongly extrapolated this assumption from studies that show no strong correlations between student outcomes and whether teachers have or do not have advanced degrees, or studies that show diminishing returns in tested student outcomes to teacher experience beyond a certain number of years. As I explained previously, studies of the association between different levels of experience and the association between having a masters degree or not and student achievement gains have never attempted to ask about the potential labor market consequences of stopping providing additional compensation for teachers choosing to further their education – even if only for personal interest – or stopping providing any guarantee that a teacher’s compensation will grow at a predictable rate over time throughout the teacher’s career.

It is pure speculation and potentially harmful speculation to make this leap.

Who’s most likely to get hurt?

So, let’s say we were to capitulate on these overreaching if not outright absurd and irresponsible claims? What’s the harm anyway? Why not simply allow a little speculative experimentation in our schools? Can’t do worse right? Wrong! We could do worse! Simply pretending that there’s a better way out there, pretending that the productivity curve can be massively adjusted, with no foundation for this assumption means that there is comparable likelihood that revenue-neutral “innovations” could do as much harm as good. Assuming otherwise is ignorant and irresponsible.

But perhaps more disturbingly, when we start talking about where to engage in this speculative experimentation to adjust the productivity curve – excuse me – productivity straight line – we are most often talking about experimenting with the lives and educational futures of the most vulnerable children and families. I suspect that NY State policymakers buying into this rhetoric aren’t talking about forcing Scarsdale to replace small class sizes and highly educated and experienced teachers with tech-based learning systems. This despite the fact that Scarsdale, many other Westchester and Long Island affluent districts are already much further to the right on the spending axis than the state’s higher need cities, including New York City as well as locations like Utica, Poughkeepsie and Newburgh.  Further, as I have discussed previously on this blog, New York State continues to provide substantial state aid subsidies to these wealthy communities while failing to provide sufficient support to high need midsized and large cities.

But instead of providing sufficient resources to those high need cities to be able to provide the types of opportunities available in Scarsdale, the suggestion by these pundits posing as researchers is that it’s absolutely okay… not just okay… but the best way forward… to engage in revenue neutral (if not revenue negative) speculative experimentation which may cause significant harm to the state’s most needy children.

And that is why this graph is so dangerous and offensive.



  1. I could understand where data could be found to form a graph relating cost/pupil and change in SD, but where did the data come from to form the other two graphs? Are we just drawing lines to suit our purpose?

    1. Indeed that appears to be what was done here – simply making up productivity advantages of imaginary – or at least very imprecisely characterized alternative technologies for schooling.

  2. Don’t forget the second line. They use that to justify APPR, the new teacher/principal evaluation system. And if you could combine the two in your Regents Reform Agenda…. Holy Doogie Howswer!

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