You might also recall that the EVAAS is the system developed by the now late William Sanders (see here), who ultimately sold it to SAS Institute Inc. that now holds all rights to the VAM (see also prior posts about the EVAAS here, here, here, here, here, and here). It is also important to note, because this teacher teaches in North Carolina where SAS Institute Inc. is located and where its CEO James Goodnight is considered the richest man in the state, that as a major Grand Old Party (GOP) donor “he” helps to set all of of the state’s education policy as the state is also dominated by Republicans. All of this also means that it is unlikely EVAAS will go anywhere unless there is honest and open dialogue about the shortcomings of the data.

Hence, the attempt here is to begin at least some honest and open dialogue herein. Accordingly, here is what this teacher wrote in response to my request that (s)he write a guest post:

***

SAS Institute Inc. claims that the EVAAS enables teachers to “modify curriculum, student support and instructional strategies to address the needs of all students.” My goal this year is to see whether these claims are actually possible or true. I’d like to dig deep into the data made available to me — for which my state pays over $3.6 million per year — in an effort to see what these data say about my instruction, accordingly.

For starters, here is what my EVAAS-based growth looks like over the past three years:

As you can see, three years ago I met my expected growth, but my growth measure was slightly below zero. The year after that I knocked it out of the park. This past year I was right in the middle of my prior two years of results. Notice the volatility [aka an issue with VAM-based reliability, or consistency, or a lack thereof; see, for example, here].

Notwithstanding, SAS Institute Inc. makes the following recommendations in terms of how I should approach my data:

*Reflecting on Your Teaching Practice: Learn to use your Teacher reports to reflect on the effectiveness of your instructional delivery.*

*The Teacher Value Added report displays value-added data across multiple years for the same subject and grade or course. As you review the report, you’ll want to ask these questions:*

*Looking at the Growth Index for the most recent year, were you effective at helping students to meet or exceed the Growth Standard?**If you have multiple years of data, are the Growth Index values consistent across years? Is there a positive or negative trend?**If there is a trend, what factors might have contributed to that trend?**Based on this information, what strategies and instructional practices will you replicate in the current school year? What strategies and instructional practices will you change or refine to increase your success in helping students make academic growth?*

Yet my growth index values are *not* consistent across years, as also noted above. Rather, my “trends” are baffling to me. When I compare those three instructional years in my mind, nothing stands out to me in terms of differences in instructional strategies that would explain the fluctuations in growth measures, either.

So let’s take a closer look at my data for last year (i.e., 2016-2017). I teach 7th grade English/language arts (ELA), so my numbers are based on my students reading grade 7 scores in the table below.

What jumps out for me here is the contradiction in “my” data for achievement Levels 3 and 4 (achievement levels start at Level 1 and top out at Level 5, whereas levels 3 and 4 are considered proficient/middle of the road). There is moderate evidence that my grade 7 students who scored a Level 4 on the state reading test exceeded the Growth Standard. But there is also moderate evidence that my same grade 7 students who scored Level 3 did not meet the Growth Standard. At the same time, the number of students I had demonstrating proficiency on the same reading test (by scoring at least a 3) increased from 71% in 2015-2016 (when I *exceeded* expected growth) to 76% in school year 2016-2017 (when my growth declined significantly). This makes no sense, right?

Hence, and after considering my data above, the question I’m left with is actually *really* important: Are the instructional strategies I’m using for my students whose achievement levels are in the middle working, or are they not?

I’d love to hear from other teachers on their interpretations of these data. A tool that costs taxpayers this much money and impacts teacher evaluations in so many states should live up to its claims of being useful for informing our teaching.

]]>He, along with Andrew Bacher-Hicks (PhD Candidate at Harvard), Mark Chin (PhD Candidate at Harvard), and Douglas Staiger (Economics Professor of Dartmouth), just released yet another National Bureau of Economic Research (NBER) “working paper” (i.e., not peer-reviewed, and in this case not internally reviewed by NBER for public consumption and use either) titled “An Evaluation of Bias in Three Measures of Teacher Quality: Value-Added, Classroom Observations, and Student Surveys.” I review this study here.

Using Kane’s MET data, they test whether 66 mathematics teachers’ performance measured (1) by using teachers’ student test achievement gains (i.e., calculated using value-added models (VAMs)), classroom observations, and student surveys, and (2) under naturally occurring (i.e., non-experimental) settings “predicts performance following random assignment of that teacher to a class of students” (p. 2). More specifically, researchers “observed a sample of fourth- and fifth-grade mathematics teachers and collected [these] measures…[under normal conditions, and then in]…the third year…randomly assigned participating teachers to classrooms within their schools and then again collected all three measures” (p. 3).

They concluded that “the test-based value-added measure—is a valid predictor of teacher impacts on student achievement following random assignment” (p. 28). This finding “is the latest in a series of studies” (p. 27) substantiating this not-surprising, as-oft-Kane-asserted finding, or as he might assert it, fact. I should note here that no other studies substantiating “the latest in a series of studies” (p. 27) claim are referenced or cited, but a quick review of the 31 total references included in this report include 16/31 (52%) references conducted by only econometricians (i.e., not statisticians or other educational researchers) on this general topic, of which 10/16 (63%) are *not* peer reviewed and of which 6/16 (38%) are either authored or co-authored by Kane (1/6 being published in a peer-reviewed journal). The other articles cited are about the measurements used, the geenral methods used in this study, and four other articles written on the topic *not *authored by econometricians. Needless to say, there is clearly a slant that is quite obvious in this piece, and unfortunately not surprising, but that had it gone through any respectable vetting process, this sh/would have been caught and addressed prior to this study’s release.

I must add that this reminds me of Kane’s New Mexico testimony (see here) where he, again, “stressed that *numerous studies* [emphasis added] show[ed] that teachers [also] make a big impact on student success.” He stated this on the stand while expressly contradicting the findings of the American Statistical Association (ASA). While testifying otherwise, and again, he also only referenced (non-representative) studies in his (or rather defendants’ support) authored by primarily him (e.g, as per his MET studies) and some of his other econometric friends (e.g. Raj Chetty, Eric Hanushek, Doug Staiger) as also cited within this piece here. This was also a concern registered by the court, in terms of whether Kane’s expertise was that of a generalist (i.e., competent across multi-disciplinary studies conducted on the matter) or a “selectivist” (i.e., biased in terms of his prejudice against, or rather selectivity of certain studies for confirmation, inclusion, or acknowledgment). This is also certainly relevant, and should be taken into consideration here.

Otherwise, in this study the authors also found that the Mathematical Quality of Instruction (MQI) observational measure (one of two observational measures they used in this study, with the other one being the Classroom Assessment Scoring System (CLASS)) was a valid predictor of teachers’ classroom observations following random assignment. The MQI also, did “not seem to be biased by the unmeasured characteristics of students [a] teacher typically teaches” (p. 28). This also expressly contradicts what is now an emerging set of studies evidencing the contrary, also not cited in this particular piece (see, for example, here, here, and here), some of which were also conducted using Kane’s MET data (see, for example, here and here).

Finally, authors’ evidence on the predictive validity of student surveys was inconclusive.

Needless to say…

Citation: Bacher-Hicks, A., Chin, M. J., Kane, T. J., & Staiger, D. O. (2017). An evaluation of bias in three measures of teacher quality: Value-added, classroom observations, and student surveys. Cambridge, MA: ational Bureau of Economic Research (NBER). Retrieved from http://www.nber.org/papers/w23478

]]>In this piece, as taken from the abstract, they “studied how six high-performing, high-poverty [and traditional, charter, under state supervision] schools in one large Massachusetts city implemented the state’s new teacher evaluation policy” (p. 383). They aimed to learn how these “successful” schools, with “success” defined by the state’s accountability ranking per school along with its “public reputation,” approached the state’s teacher evaluation system and its system components (e.g., classroom observations, follow-up feedback, and the construction and treatment of teachers’ summative evaluation ratings). They also investigated how educators within these schools “interacted to shape the character and impact of [the state’s] evaluation” (p. 384).

Akin to Moore Johnson’s aforementioned work, she and her colleagues argue that “to understand whether and how new teacher evaluation policies affect teachers and their work, we must investigate [the] day-to-day responses [of] those within the schools” (p. 384). Hence, they explored “how the educators in these schools interpreted and acted on the new state policy’s opportunities and requirements and, overall, whether they used evaluation to promote greater accountability, more opportunities for development, or both” (p. 384).

They found that “despite important differences among the six successful schools [they] studied (e.g., size, curriculum and pedagogy, student discipline codes), administrators responded to the state evaluation policy in remarkably similar ways, *giving priority to the goal of development over accountability *[emphasis added]” (p. 385). In addition, “[m]ost schools not only complied with the new regulations of the law but also went beyond them to provide teachers with more frequent observations, feedback, and support than the policy required. Teachers widely corroborated their principal’s reports that evaluation in their school was meant to improve their performance and they strongly endorsed that priority” (p. 385).

Overall, and accordingly, they concluded that “an evaluation policy focusing on teachers’ development can be effectively implemented in ways that serve the interests of schools, students, and teachers” (p. 402). This is especially true when (1) evaluation efforts are “well grounded in the observations, feedback, and support of a formative evaluation process;” (2) states rely on “capacity building in addition to mandates to promote effective implementation;” and (3) schools also benefit from spillover effects from other, positive, state-level policies (i.e., states do not take Draconian approaches to other educational policies) that, in these cases included policies permitting district discretion and control over staffing and administrative support (p. 402).

Related, such developmental and formatively-focused teacher evaluation systems can work, they also conclude, when schools are lead by highly effective principals who are free to select high quality teachers. Their findings suggest that this “is probably the most important thing district officials can do to ensure that teacher evaluation will be a constructive, productive process” (p. 403). In sum, “as this study makes clear, policies that are intended to improve schooling depend on both administrators and teachers for their effective implementation” (p. 403).

Please note, however, that this study was conducted before districts in this state were required to incorporate standardized test scores to measure teachers’ effects (e.g., using VAMs); hence, the assertions and conclusions that authors set forth throughout this piece should be read and taken into consideration given that important caveat. Perhaps findings should matter even more in that here is at least some proof that teacher evaluation works IF used for developmental and formative (versus or perhaps in lieu of summative) purposes.

Citation: Reinhorn, S. K., Moore Johnson, S., & Simon, N. S. (2017). Educational Evaluation and Policy Analysis, 39(3), 383–406. doi:10.3102/0162373717690605 Retrieved from https://projectngt.gse.harvard.edu/files/gse-projectngt/files/eval_041916_unblinded.pdf

]]>In this article, Steinberg and Kraft (2017) examine teacher performance measure weights while conducting multiple simulations of data taken from the Bill & Melinda Gates Measures of Effective Teaching (MET) studies. They conclude that “performance measure weights and ratings” surrounding teachers’ value-added, observational measures, and student survey indicators play “critical roles” when “determining teachers’ summative evaluation ratings and the distribution of teacher proficiency rates.” In other words, the weighting of teacher evaluation systems’ multiple measures matter, matter differently for different types of teachers within and across school districts and states, and matter also in that so often these weights are arbitrarily and politically defined and set.

Indeed, because “state and local policymakers have *almost no empirically based evidence *[emphasis added, although I would write “no empirically based evidence”] to inform their decision process about how to combine scores across multiple performance measures…decisions about [such] weights…are often made through a somewhat arbitrary and iterative process, one that is shaped by political considerations in place of empirical evidence” (Steinberg & Kraft, 2017, p. 379).

This is very important to note in that the consequences attached to these measures, also given the arbitrary and political constructions they represent, can be both professionally and personally, career and life changing, respectively. How and to what extent “the proportion of teachers deemed professionally proficient changes under different weighting and ratings thresholds schemes” (p. 379), then, clearly matters.

While Steinberg and Kraft (2017) have other key findings they also present throughout this piece, their most important finding, in my opinion, is that, again, “teacher proficiency rates change substantially as the weights assigned to teacher performance measures change” (p. 387). Moreover, the more weight assigned to measures with higher relative means (e.g., observational or student survey measures), the greater the rate by which teachers are rated effective or proficient, and vice versa (i.e., the more weight assigned to teachers’ value-added, the higher the rate by which teachers will be rated ineffective or inadequate; as also discussed on p. 388).

Put differently, “teacher proficiency rates are lowest across all [district and state] systems when norm-referenced teacher performance measures, such as VAMs [i.e., with scores that are normalized in line with bell curves, with a mean or average centered around the middle of the normal distributions], are given greater relative weight” (p. 389).

This becomes problematic when states or districts then use these weighted systems (again, weighted in arbitrary and political ways) to illustrate, often to the public, that their new-and-improved teacher evaluation systems, as inspired by the MET studies mentioned prior, are now “better” at differentiating between “good and bad” teachers. Thereafter, some states over others are then celebrated (e.g., by the National Center of Teacher Quality; see, for example, here) for taking the evaluation of teacher effects more seriously than others when, as evidenced herein, this is (unfortunately) more due to manipulation than true changes in these systems. Accordingly, the fact remains that the more weight VAMs carry, the more teacher effects (will appear to) vary. It’s not necessarily that they vary in reality, but the manipulation of the weights on the back end, rather, cause such variation and then lead to, quite literally, such delusions of grandeur in these regards (see also here).

At a more pragmatic level, this also suggests that the teacher evaluation ratings for the roughly 70% of teachers who are not VAM eligible “are likely to differ in systematic ways from the ratings of teachers for whom VAM scores can be calculated” (p. 392). This is precisely why evidence in New Mexico suggests VAM-eligible teachers are up to five times more likely to be ranked as “ineffective” or “minimally effective” than their non-VAM-eligible colleagues; that is, “[also b]ecause greater weight is consistently assigned to observation scores for teachers in nontested grades and subjects” (p. 392). This also causes a related but also important issue with fairness, whereas equally effective teachers, just by being VAM eligible, may be five-or-so times likely (e.g., in states like New Mexico) of being rated as ineffective by the mere fact that they are VAM eligible and their states, quite literally, “value” value-added “too much” (as also arbitrarily defined).

Finally, it should also be noted as an important caveat here, that the findings advanced by Steinberg and Kraft (2017) “are not intended to provide specific recommendations about what weights and ratings to select—such decisions are fundamentally subject to local district priorities and preferences. (p. 379). These findings do, however, “offer important insights about how these decisions will affect the distribution of teacher performance ratings as policymakers and administrators continue to refine and possibly remake teacher evaluation systems” (p. 379).

Related, please recall that via the MET studies one of the researchers’ goals was to determine which weights per multiple measure were empirically defensible. MET researchers failed to do so and then defaulted to recommending an equal distribution of weights without empirical justification (see also Rothstein & Mathis, 2013). This also means that anyone at any state or district level who might say that this weight here or that weight there is empirically defensible should be asked for the evidence in support.

Citations:

Rothstein, J., & Mathis, W. J. (2013, January). Review of two culminating reports from the MET Project. Boulder, CO: National Educational Policy Center. Retrieved from http://nepc.colorado.edu/thinktank/review-MET-final-2013

Steinberg, M. P., & Kraft, M. A. (2017). The sensitivity of teacher performance ratings to the design of teacher evaluation systems. *Educational Researcher, 46*(7), 378–

396. doi:10.3102/0013189X17726752 Retrieved from http://journals.sagepub.com/doi/abs/10.3102/0013189X17726752

The case — *Houston Federation of Teachers et al. v. Houston ISD —* was filed in 2014 and just one day ago (October 10, 2017) came the case’s final federal suit settlement. Click here to read the “Settlement and Full and Final Release Agreement.” But in short, this means the “End of Value-Added Measures for Teacher Termination in Houston” (see also here).

More specifically, recall that the judge notably ruled prior (in May of 2017) that the plaintiffs *did* have sufficient evidence to proceed to trial on their claims that the use of EVAAS in Houston to terminate their contracts was a violation of their Fourteenth Amendment due process protections (i.e., no state or in this case district shall deprive any person of life, liberty, or property, without due process). That is, the judge ruled that “any effort by teachers to replicate their own scores, with the limited information available to them, [would] necessarily fail” (see here p. 13). This was confirmed by the one of the plaintiffs’ expert witness who was also “unable to replicate the scores despite being given far greater access to the underlying computer codes than [was] available to an individual teacher” (see here p. 13).

Hence, and “[a]ccording to the unrebutted testimony of [the] plaintiffs’ expert [witness], without access to SAS’s proprietary information – the value-added equations, computer source codes, decision rules, and assumptions – EVAAS scores will remain a mysterious ‘black box,’ impervious to challenge” (see here p. 17). Consequently, the judge concluded that HISD teachers “have no meaningful way to ensure correct calculation of their EVAAS scores, and as a result are unfairly subject to mistaken deprivation of constitutionally protected property interests in their jobs” (see here p. 18).

Thereafter, and as per this settlement, HISD agreed to refrain from using VAMs, including the EVAAS, to terminate teachers’ contracts as long as the VAM score is “unverifiable.” More specifically, “HISD agree[d] it will not in the future use value-added scores, including but not limited to EVAAS scores, as a basis to terminate the employment of a term or probationary contract teacher during the term of that teacher’s contract, or to terminate a continuing contract teacher at any time, so long as the value-added score assigned to the teacher remains unverifiable. (see here p. 2; see also here). HISD also agreed to create an “instructional consultation subcommittee” to more inclusively and democratically inform HISD’s teacher appraisal systems and processes, and HISD agreed to pay the Texas AFT $237,000 in its attorney and other legal fees and expenses (State of Texas, 2017, p. 2; see also AFT, 2017).

This is yet another big win for teachers in Houston, and potentially elsewhere, as this ruling is an unprecedented development in VAM litigation. Teachers and others using the EVAAS or another VAM for that matter (e.g., that is also “unverifiable”) do take note, at minimum.

]]>Accordingly, she is gathering stories from educational practitioners including teachers, principals, and staff, who are new to the profession as well as seasoned professionals, about their experiences working in such environments.

While it may not be the easiest sell to a producer, this topic has it all: absurdism, humor, and the pathos of seeing good people fighting for autonomy, caught in a storm of externally imposed aims.

Hence, if you have an especially good anecdote, an insider perspective, if you want to help her turn these stories into art, so that she and her creative colleagues can reach out to others and make these stories known, please send contact her directly via email at:

She is trying to get “it” as right as she can. Some of you out there may be the key!

Thank you in advance!

]]>Related, three articles were recently published online (here, here, and here) about how in Louisiana, the state’s old and controversial teacher evaluation system as based on VAMs is resuming after a four-year hiatus. It was put on hold when the state was in the process of adopting The Common Core.

This, of course, has serious implications for the approximately 50,000 teachers throughout the state, or the unknown proportion of them who are now VAM-eligible, believed to be around 15,000 (i.e., approximately 30% which is inline with other state trends).

While the state’s system has been partly adjusted, whereas 50% of a teacher’s evaluation was to be based on growth in student achievement over time using VAMs, and the new system has reduced this percentage down to 35%, now teachers of mathematics, English, science, and social studies are also to be held accountable using VAMs. The other 50% of these teachers’ evaluation scores are to be assessed using observations with 15% based on student learning targets (a.k.a., student learning objectives (SLOs)).

Evaluation system output are to be used to keep teachers from earning tenure, or to cause teachers to lose the tenure they might already have.

Among other controversies and issues of contention noted in these articles (see again here, here, and here), one of note (highlighted here) is also that now, “even after seven years”… the state is *still* “unable to truly explain or provide the actual mathematical calculation or formula’ used to link test scores with teacher ratings. ‘This obviously lends to the distrust of the entire initiative among the education community.”

A spokeswoman for the state, however, countered the transparency charge noting that the VAM formula has been on the state’s department of education website, “and updated annually, since it began in 2012.” She did not provide a comment about how to adequately explain the model, perhaps because she could not either.

Just because it might be available does not mean it is understandable and, accordingly, usable. This we have come to know from administrators, teachers, and yes, state-level administrators in charge of these models (and their adoption and implementation) for years. This is, indeed, one of the largest criticisms of VAMs abound.

]]>More specifically, Virginia SGP “pressed for the data’s release because he thinks parents have a right to know how their children’s teachers are performing, information about public employees that exists but has so far been hidden. He also want[ed] to expose what he sa[id was] Virginia’s broken promise to begin [to use] the data to evaluate how effective the state’s teachers are.” The “teacher data should be out there,” especially if taxpayers are paying for it.

In January of 2016, a Richmond, Virginia judge ruled in Virginia SGP’s favor. The following April, a Richmond Circuit Court judge ruled that the Virginia Department of Education was to also release Loudoun County Public Schools’ SGP scores by school and by teacher, including teachers’ identifying information. Accordingly, the judge noted that the department of education and the Loudoun school system failed to “meet the burden of proof to establish an exemption’ under Virginia’s Freedom of Information Act [FOIA]” preventing the release of teachers’ identifiable information (i.e., beyond teachers’ SGP data). The court also ordered VDOE to pay Davison $35,000 to cover his attorney fees and other costs.

As per an article published last week, the Virginia Supreme Court overruled this former ruling, noting that the department of education did not have to provide teachers’ identifiable information along with teachers’ SGP data, after all.

See more details in the actual article here, but ultimately the Virginia Supreme Court concluded that the Richmond Circuit Court “erred in ordering the production of these documents containing teachers’ identifiable information.” The court added that “it was [an] error for the circuit court to order that the School Board share in [Virginia SGP’s] attorney’s fees and costs,” pushing that decision (i.e., the decision regarding how much to pay, if anything at all, in legal fees) back down to the circuit court.

Virginia SGP plans to ask for a rehearing of this ruling. See also his comments on this ruling here.

]]>Well, at least one school district in Florida is kissing the state’s six-year infatuation with its VAM-based teacher accountability system goodbye. I could have invoked a much more colorful metaphor here, but let’s just go with something along the lines of a sophomoric love affair.

According to a recent article in the *Tampa Bay Times* (see here), “[u]sing new authority from the [state] Legislature, the Citrus County School Board became the first in the state to stop using VAM, citing its unfairness and opaqueness…[with this]…decision…expected to prompt other boards to action.”

That’s all the article has to offer on the topic, but let’s all hope others, in Florida and beyond, do follow.

]]>She used R (i.e., a free software environment for statistical computing and graphics) to simulate correlation scatterplots (see Figures below) to illustrate three unique situations: (1) a simulation where there are two indicators (e.g., teacher value-added and observational estimates plotted on the x and y axes) that have a correlation of r = 0.28 (the highest correlation coefficient at issue in the aforementioned post); (2) a simulation exploring the impact of negative bias and a moderate correlation on a group of teachers; and (3) another simulation with two indicators that have a non-linear relationship possibly induced or caused by bias. She designed simulations (2) and (3) to illustrate the plausibility of the situation suggested next (as written into Audrey’s post prior) about potential bias in both value-added and observational estimates:

* If there is some bias present in value-added estimates, and some bias present in the observational estimates…perhaps this is why these low correlations are observed. That is, only those teachers teaching classrooms inordinately stacked with students from racial minority, poor, low achieving, etc. groups might yield relatively stronger correlations between their value-added and observational scores given bias, hence, the low correlations observed may be due to bias and bias alone.*

Laura continues…

Here, Audrey makes the point that a correlation of r = 0.28 is “weak.” It is, accordingly, useful to see an example of just how “weak” such a correlation is by looking at a scatterplot of data selected from a population where the true correlation is r = 0.28. To make the illustration more meaningful the points are colored based on their quintile scores as per simulated teachers’ value-added divided into the lowest 20%, next 20%, etc.

In this figure you can see by looking at the blue “least squares line” that, “on average,” as a simulated teacher’s value-added estimate increases the average of a teacher’s observational estimate increases. However, there is a lot of variability (or scatter points) around the (scatterplot) line. Given this variability, we can make statements about averages, such as “on average” teachers in the top 20% for VAM scores will likely have on average higher observed observational scores; however, there is not nearly enough precision to make any (and certainly not any good) predictions about the observational score from the VAM score for individual teachers. In fact, the linear relationship between teachers’ VAM and observational scores only accounts for about 8% of the variation in VAM score. Note: we get 8% by squaring the aforementioned r = 0.28 correlation (i.e., an R squared). The other 92% of the variance is due to error and other factors.

What this means in practice is that when correlations are this “weak,” it is reasonable to say statements about averages, for example, that “on average” as one variable increases the mean of the other variable increases, but it would not be prudent or wise to make predictions for individuals based on these data. See, for example, that individuals in the top 20% (quintile 5) of VAM have a very large spread in their scores on the observational score, with 95% of the scores in the top quintile being in between the 7th and 98th percentiles for their observational scores. So, here if we observe a VAM for a specific teacher in the top 20%, and we do not know their observational score, we cannot say much more than their observational score is likely to be in the top 90%. Similarly, if we observe a VAM in the bottom 20%, we cannot say much more than their observational score is likely to be somewhere in the bottom 90%. That’s not saying a lot, in terms of precision, but also in terms of practice.

The second scatterplot I ran to test how bias that only impacts a small group of teachers might theoretically impact an overall correlation, as posited by Audrey. Here I simulated a situation where, again, there are two values present in a population of teachers: a teacher’s value-added and a teacher’s observational score. Then I insert a group of teachers (as Audrey described) who represent 20% of a population and teach a disproportionate number of students who come from relatively lower socioeconomic, high racial minority, etc. backgrounds, and I assume this group is measured with negative bias on both indicators and this group has a moderate correlation between indicators of r = 0.50. The other 80% of the population is assumed to be uncorrelated. Note: for this demonstration I assume that this group includes 20% of teachers from the aforementioned population, these teachers I assume to be measured with negative bias (by one standard deviation on average) on both measures, and, again, I set their correlation at r = 0.50 with the other 80% of teachers at a correlation of zero.

What you can see is that if there is bias in this correlation that impacts only a certain group on the two instrument indicators; hence, it is possible that this bias can result in an observed correlation overall. In other words, a strong correlation noted in just one group of teachers (i.e., teachers scoring the lowest on their value-added and observational indicators in this case) can be relatively stronger than the “weak” correlation observed on average or overall.

Another, possible situation is that there might be a non-linear relationship between these two measures. In the simulation below, I assume that different quantiles on VAM have a different linear relationship with the observational score. For example, in the plot there is not a constant slope, but teachers who are in the first quintile on VAM I assume to have a correlation of r = 0.50 with observational scores, the second quintile I assume to have a correlation of r = 0.20, and the other quintiles I assume to be uncorrelated. This results in an overall correlation in the simulation of r = 0.24, with a very small p-value (i.e. a very small chance that a correlation of this size would be observed by random chance alone if the true correlation was zero).

What this means in practice is that if, in fact, there is a non-linear relationship between teachers’ observational and VAM scores, this can induce a small but statistically significant correlation. As evidenced, teachers in the lowest 20% on the VAM score have differences in the mean observational score depending on the VAM score (a moderate correlation of r = 0.50), but for the other 80%, knowing the VAM score is not informative as there is a very small correlation for the second quintile and no correlation for the upper 60%. So, if quintile cut-off scores are used, teachers can easily be misclassified. In sum, Pearson Correlations (the standard correlation coefficient) measure the overall strength of linear relationships between X and Y, but if X and Y have a non-linear relationship (like as illustrated in the above), this statistic can be very misleading.

Note also that for all of these simulations very small p-values are observed (e.g., p-values <0.0000001 which, again, mean these correlations are statistically significant or that the probability of observing correlations this large by chance if the true correlation is zero, is nearly 0%). What this illustrates, again, is that correlations (especially correlations this small) are (still) often misleading. While they might be statistically significant, they might mean relatively little in the grand scheme of things (i.e., in terms of practical significance; see also “The Difference Between”Significant’ and ‘Not Significant’ is not Itself Statistically Significant” or posts on Andrew Gelman’s blog for more discussion on these topics if interested).

At the end of the day r = 0.28 is still a “weak” correlation. In addition, it might be “weak,” on average, but much stronger and statistically and practically significant for teachers in the bottom quintiles (e.g., teachers in the bottom 20%, as illustrated in the final figure above) typically teaching the highest needs students. Accordingly, this might be due, at least in part, to bias.

In conclusion, one should always be wary of claims based on “weak” correlations, especially if they are positioned to be stronger than industry standards would classify them (e.g., in the case highlighted in the prior post). Even if a correlation is “statistically significant,” it is possible that the correlation is the result of bias, *and* that the relationship is so weak that it is not meaningful in practice, especially when the goal is to make high-stakes decisions about individual teachers. Accordingly, when you see correlations this small, keep these scatterplots in mind or generate some of your own (see, for example, here to dive deeper into what these correlations might mean and how significant these correlations might really be).

*Please contact Dr. Kapitula directly at kapitull@gvsu.edu if you want more information or to access the R code she used for the above.

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