Right Versus Left Brain: What Does the Spinning Dancer Teach Us?

(source: http://www.freakonomics.com/2007/10/23/right-versus-left-brain-what-does-the-spinning-dancer-teach-us/)

Last week I linked to an intriguing visual of a spinning dancer. It is intriguing because some people see her spinning clockwise, whereas others see her spinning counter-clockwise. Moreover, some people are able to make the direction of her spin switch. The article asserts that the direction she spins is an indicator of whether your thinking is dominated by the right side of your brain (clockwise) or the left side of your brain (counter-clockwise).
According to funderstanding.com, left-brain people are supposed to be logical, sequential, rational, analytical, objective, and look at parts. These folks should see her spinning counter-clockwise. Right-brain people, meanwhile, are supposed to be random, intuitive, holistic, synthesizing, subjective, and look at wholes. She should spin clockwise in this case.
For me, the spinning is decidedly clockwise, which presumably makes me right-brained. I guess my college roommates, who nicknamed me “The Rational Man,” would be surprised and disappointed by the spinning dancer’s verdict. My wife Jeannette, watching the dancer next to me, saw her spin counter-clockwise. (As a result, her new nickname is “The Rational Woman,” though I don’t think it will stick.)
My initial sample of two people (my wife and myself) did not seem to fit with these predictions. So, in the interest of collecting more data, I asked blog readers to list their college majors along with the dancer’s spinning direction. We then tallied the data for the first 219 respondents who provided usable data. We divided people into the following broad categories based on their college majors: economics, hard sciences, engineering/math/computer science, non-economics social scientists, and the humanities.
The theory, I think, would predict that economists, engineers, and scientists would likely be dominated by left-brain thinkers who see her spinning counter-clockwise, whereas humanists and non-economics social scientists would have more right-brain thinkers. Here’s how the numbers actually break down as to who initially sees her spinning counter-clockwise among Freakonomics blog readers. The higher this number, the more rational you are supposed to be (with the number of observations in parentheses):

Engineers/mathematicians/computer programmers: 21.8% (N=55)
Economists: 26.7% (N=60)
Scientists: 31.0% (N=29)
Social Scientists: 36.2% (N=47)
Humanities: 42.9% (N=28)

Admittedly, these are not large sample sizes, but the results could hardly be more off from the theory’s apparent predictions. Ironically, it appears that the theory does have some power to order people as to how logical they might be — you just have to reverse your interpretation of which direction of spin corresponds to right-brained thinking. Perhaps the author of the article just got confused?
The initial article also misses on its other prediction — namely, that the dancer will spin counter-clockwise for most people. In fact, in our data only 30 percent of the people saw her spinning counter-clockwise when they first looked. Again, this is consistent with the original author mixing up clockwise and counter-clockwise.
As it turns out, I should have asked our commenters to list their genders as well. In most cases, we could make an informed guess of gender based on names. Women turned out to be 36 percent counter-clockwise, versus 30 percent for men (and 23 percent for people whose gender we couldn’t tell from their comment). From a cursory search of the Internet, it seems like this result also contradicts what we would expect.
I often joke about how the information provided by someone who is incredibly terrible at predicting the future (i.e., they always get things wrong) is just as valuable as what you get from someone who is good at predicting the future. I used this strategy with some success by betting the opposite of my father whenever he’d bet a large sum of money on a football team that was sure to cover the spread.
It looks like the spinning dancer is just terrible enough as a predictor to be of value.

The Logic of Causal Order (J.A. Davis, 1985)

“Which variables shall I include in this run? Shall I run X against Y or Y against X? Should I control for this? And if I control for this, must I also control for that?

à Substantive empirical matters: the more you know about social stratification, presidential voting, job satisfaction, or whatever, the easier it will be to plan your run.

Logical rules:

Rules about causal order in a set of variables: assumptions about which is the “cause” and which is the “effect” when you look at the relationship between two variables.

Three ideas:

1. the idea of indirect effects;

2. the idea of causally spurious effects; and

3. the idea of signed effects.

Two variables

Variable X is a cause of Variable Y when

-         change in X (sooner or later) produces change in Y

-         or (because some Xs don’t change) Ys tend to line up with the fixed values of
X.

Examples:

Employment is a cause of earnings: People who get (lose) jobs increase (decrease) their earnings.

Martial status is a cause of sociability patterns: when people get married they cut their frequency of visits to bars and taverns.

Race is a cause of party: Blacks are more likely to become Democrats than are whites.

Education is a cause of occupational prestige: People who hold college degrees are more likely to get high-status jobs. 

PE Test for Linear vs. Log-Linear Specifications.

Description

petest performs the MacKinnon-White-Davidson PE test for comparing linear vs. log-linear specifications in linear regressions.

Usage

petest(formula1, formula2, data = list(), vcov. = NULL, ...)

Arguments

formula1	either a symbolic description for the first model to be tested, or a fitted object of class "lm".
formula2	either a symbolic description for the second model to be tested, or a fitted object of class "lm".
data	an optional data frame containing the variables in the model. By default the variables are taken from the environment which petest is called from.
vcov.	a function for estimating the covariance matrix of the regression coefficients, e.g., vcovHC.
...	further arguments passed to coeftest.

Details

The PE test compares two non-nest models where one has a linear specification of type y ~ x1 + x2 and the other has a log-linear specification of type log(y) ~ z1 + z2. Typically, the regressors in the latter model are logs of the regressors in the former, i.e., z1 is log(x1) etc.
The idea of the PE test is the following: If the linear specification is correct then adding an auxiliary regressor with the difference of the log-fitted values from both models should be non-significant. Conversely, if the log-linear specification is correct then adding an auxiliary regressor with the difference of fitted values in levels should be non-significant. The PE test statistic is simply the marginal test of the auxiliary variable(s) in the augmented model(s). In petest this is performed by coeftest.
For further details, see the references.

Value

An object of class "anova" which contains the coefficient estimate of the auxiliary variables in the augmented regression plus corresponding standard error, test statistic and p value.

References

J. MacKinnon, H. White, R. Davidson (1983). Tests for Model Specification in the Presence of Alternative Hypotheses: Some Further Results. Journal of Econometrics, 21, 53-70.
M. Verbeek (2004). A Guide to Modern Econometrics, 2nd ed. Chichester, UK: John Wiley.

See Also

jtest, coxtest, encomptest

Examples

if(require("AER")) {
## Verbeek (2004), Section 3
data("HousePrices", package = "AER")

### Verbeek (2004), Table 3.3
hp_lin <- lm(price ~ . , data = HousePrices)
summary(hp_lin)

### Verbeek (2004), Table 3.2
hp_log <- update(hp_lin, log(price) ~ . - lotsize + log(lotsize))
summary(hp_log)

## PE test
petest(hp_lin, hp_log)}

---