I'll start this post to be very clear that I agree the MCAT is probably a pretty good indicator of medical school and step success, at least in terms of passing. However my issue is not with your interpretation of the specific paper, but the interpretation in general is not accurate in the areas I pointed out and gave references for in several areas. The term prediction and predictive ability are specific terms with specific meaning in statistics and there is far more to demonstrating those qualities than you suggested with a pearson correlation or R-squared (somewhat of a redundant argument).
I'm not only concerned with that specific paper. There are other papers showing the validity of the MCAT for predicting medical school performance. The AAMC has people dedicated to looking into this. The plots I've provided in previous posts were all from the AAMC's MCAT validity studies. My central claim is that the MCAT is a medium-to-strong predictor of medical school performance, especially step-1. The way to assess this is by judging the predictive validity of the MCAT. If you thought I made unjustifiable interpretations from that single paper, fine. But I'm not concerned with that single paper per se; the predictive validity of the MCAT is what matters.
I agree that the MCAT is probably the best currently available, validated measure designed to order test takers based on a combination of factors in several domains. This includes the utility of the test to separate likely successful and unsuccessful students for medical school admissions.
Roughly half of the variance in Step 1 scores is explained by variance in MCAT scores. That is what R-squared tells you. I think there are shared factors leading to both of these differences. The 50% number isn't essential - it's a substantial proportion.
I understand the interpretation of R-squared as you can see in my prior posts. You may think there are shared factors and there might be, but there might not be, and you also claimed same causality of these differences, which is a much bigger stretch.
The predictive power of a test for some outcome measure is judged by the results of using a correlation or linear regression. In the study I cited, yes, they looked at both the MCAT and step-1 retrospectively. There are studies where they tracked medical students throughout medical school and residency and compared their step-1 performance to what the MCAT results predicted. This is assessing predictive validity.
I can't restate what I've previously said, but predictive ability is not at all defined by correlation and within a regression you need to look at out-of-sample R-squared (assuming OLS), calibration, and certain quantiles of prediction error to see if it is actually predicting well. A single, in-sample Pearson correlation doesn't tell you this, especially not in a multivariable setting.
All else being equal, the stronger the correlation, the more likely it is that the relationship is causally connected. That's indisputable.
Not only indisputable, it's easily proven incorrect.
The below are two, ridiculously obvious non-causal associations. The top one has a much higher correlation. These are pretty similar in other material regards (like plausibility). Your argument that the top panel is more likely causal doesn't hold water.
Yes, correlation does not always equal causation, but there's a greater likelihood of a real relationship when the correlation is .95 rather than zero.
Again, not true. Nonlinear relationships can have zero or very non zero correlations (Pearson and Spearman) but strong nonlinear relationships. If the non linear one is causal then your point is shown not generally true. You're circularly falling into the correlation = causation trap. It's not even an outlier case for correlation to not equal causation-- it's pretty much the norm (even if we ignore the fact that you keep ignoring non linear associations).
The fact that there are tons of spurious and specious correlations doesn't negate the verity that many linear relationships are in fact causally connected.
Sure, no one is arguing that. Nonlinear relationships may also be causal.
You posted the suicides by hanging and US spending on science and technology. Those two things are patently disparate. There's no intuitive basis to presume those two things would be casually connected.
Right, you're proving my point that your interpretation, in this paper and in general, is incorrect.
But here, we're talking about the MCAT and Step-1. They both are 8-hour exams where people have to answer multiple-choice questions that test the knowledge of the test-takers as well as their reasoning skills. These are very similar tasks. There's no a priori reason why you'd expect a correlation between these two things to be specious, whereas there is for suicide hangings and research spending.
Right. They are both proxies for intelligence, work ethic, content exposure, and probably some other factors, but the point being is that randomizing students to receive a 525 on the MCAT will not tend to cause higher Step 1 scores; if it did, then you'd have a stronger argument for causality. This is literally how randomized experiments (well designed clinical trials) work and why observational studies are much further from generating good causal inference than people in medicine think. If you really think this is causal, you'd stand by the notion that randomly assigned MCAT scores will tend to produce certain Step 1 scores and medical school performance (which we know is clearly false). When we randomize patients to receive an ARB or placebo and there is a large enough difference in blood pressures after medication, we might conclude its the ARB...
If you can predict Step-1 scores with the MCAT, then the MCAT's legitimacy as a tool is validated.
Prediction and validation isn't really binary; like I said sure you can always get predictions, but how is your method better than tossing darts or flipping a coin? There are several things that need to be looked at before we can actually make that claim. Is the MCAT likely a decent predictor? I think so, because it has a plausible relationship to important factors of Step 1 scores, but they really haven't shown it to be a great one. No one has attempted to quantify how close predicted and actual step 1 scores are based on some MCAT-employing prediction model (again on new data).
If you want to argue that this isn't sufficient to show a causal relationship, that's your prerogative. I can't imagine a sensible argument as to why these two things would have such a strong, linear relationship and still not be causally connected. From a practical perspective, the MCAT does what it was designed to do.
It's not my prerogative, exactly. My point was that your interpretations were largely incorrect. Again, I'm not arguing with your conclusion, I'm saying your presented rationale isn't particularly strong.
I admit I haven't read enough on prediction models. My understanding is that the predictive validity of a test is judged by the strength of its linear relationship with some outcome variable. It's what psychologists use for all sorts of research. While some psych research is nonsense, not all of it is. Some of the fundamental statistical techniques used by researchers of all stripes were developed by psychologists.
I think if you back up you'll see the issue here. You're stuck on linear and a single number that doesn't contain the information you need to make the assessment. Just because tons of people do it incorrectly doesn't mean it's right. Most clinicians with publications incorrectly and often egregiously employ and interpret statistical methods, but that doesn't mean it's right. Clinicians, like psychologists, are not statisticians. I agree that there are numerous methods developed by psychologists (often who have a very quantitative background including graduate statistics courses in a stat department), but that's neither here nor there when we're talking about well established methods of evaluating predictive ability. Psychologists aren't the ones pushing the envelop on that front; they gave us mystical things like factor analysis (although the same guy gave us more useful stuff like Spearman's rho) and terribly flawed and popular "agreement" statistics like Kappa.
I posted data showing a linear relationship throughout the entire plot. It wasn't from the one paper though, it's the AAMC data.
It might be linear, but we don't know, that's why we use statistics and probability.
Okay fair enough, you don't like the one paper. You made good points, some of my conclusions from that single article may have been unjustified. You sharpened up some of my arguments, thank you for that. Nonetheless, the aggregate of data from multiple papers substantiates my basic claim. The AAMC data and the other paper above in this post both address your skepticism with respect to predictive validity.
Again, I like the idea of MCAT being useful to predict step 1, but your data and the papers don't support the predictive utility. There are tons of missing pieces; at the very least, out of sample measures like R-squared, the model standard deviation, quantiles of prediction errors, calibration plots...What you're doing right now is the equivalent of declaring
secondary hypertension because you measured a single blood pressure of 144/80 in a healthy adult around 30 years old...there's a lot missing to that picture.
You think physicians are that statistically illiterate? I'd believe it; it's not emphasized nearly enough in undergrad or medical school. I think two semesters of statistics should be a requirement for pre-meds rather than calculus.
As a group, yes. I agree at least 2 semesters of applied statistics should be a requirement, but ideally some lower level mathematics (through calc and linear algebra). Startling how many kids in my class complained they needed to "memorize these 7 pharm formulas" that came from plugging in and manipulating 2-3 original formulas...and the fact that for some reason courses like this tend to teach students problem solving skills they lack. Honestly, psychology and sociology should have been back-burnered as a requirement instead of statistics and mathematics because the schools do an okay job teaching the psych and people skills stuff (and those two subjects aren't rocket science), but the schools fail horribly at teaching statistics to their students (mainly blind leading the blind).
What happened? You go from agreeing with that comment to giving the Borat?