Wednesday, September 6, 2017

What is 'rational?'




I left a comment at a very interesting blog post at http://www.ivigilante.com/where-rationality-ends/. Here's what I wrote:

An interesting article! I think that you brought up rationality in a sense that has more to do with academic notions of what is “ideal” than with the real world. It’s understandable, since most formal education (particularly in economics departments!) focuses on this notion!

Herbert Simon was, as far as I’m aware, the first academic to point out that expecting people to act ‘rationally’ is futile. He won a Nobel Prize for his work on bounded rationality, too, so it’s not like his work went unrecognized. A brief summary: http://www.economist.com/node/13350892
As this page correctly observes, people’s behavior often fails to adhere to even the most basic principles of logic, which leaves humans looking pretty stupid IF you believe that logic–i.e. ‘rationality’–is the best standard to which we should compare behavior.
 

But Gerd Gigerenzer and others (including me) argue the opposite! Rather than saying, ‘Gee, people are pretty dumb because they don’t make decisions the way a computer would make a decision,’ we argue instead that people use shortcuts that are typically well-suited for the real world of vast uncertainty and severe time pressure.

Some interesting reading on Gigerenzer’s approach, which he calls “ecological rationality:” https://hbr.org/2014/06/instinct-can-beat-analytical-thinking and https://www.edge.org/conversation/gerd_gigerenzer-smart-heuristics


In the instance of the gas station that you described above, I’d say you were acting in an ecologically rational manner, probably using a heuristic. I’d guess that your deliberation went something like this:
“This old-timey gas station has ridiculously long lines. I hate long lines! Screw it, I’ll go elsewhere and pay a bit more for my gas. The savings of about $1.00 per fill-up isn’t worth my time and aggravation.”


A standard economic model would require that you sit down and calculate whether the savings of $1 or $2 is actually worth your time and aggravation. Which would, of course, require that you assigned a numerical value to your aggravation, knew how much time you’d spend waiting, and how much of that waiting time you’d actually spend on side hustles (vs. something unproductive), how much money you’d make from the time spent on your side hustle, etc…


When it’s spelled out like that, it becomes painfully obvious that nobody behaves like “homo economicus,” because performing such actions is, in itself, terribly inefficient–not to mention far more imprecise than big-time thinkers would like to admit [i.e. how much IS your aggravation worth? And what if you estimate a 15-minute wait, but it’s actually a 25-minute wait, which causes extra frustration? How much extra frustration would that cause, and what negative effects would that stress have on your health? And, more to the point, how much would it cost to address those negative health effects? Because, remember, we need numbers in order to make the equation work…].


So, to the point of your article: if you buy into Gigerenzer’s notions, rational thought often DOESN’T require complexity–as long as you’re holding people to the standard of ecological rationality, rather than logical-mathematical rationality. 

The example above illustrates how ridiculous it is to expect people to make 'rational,' calculated decisions every time they're faced with a choice. Can you imagine stopping to do a calculation like this every time you had to do something?! You'd never accomplish anything, because you'd suffer from "paralysis by analysis."

http://www.cogniview.com/blog/wp-content/uploads/2013/03/Analysis_Paralysis.jpg 

Thus, assuming that your goal is to be productive, it is therefore irrational to be rational!!!

To use the above example of waiting in a long line in order to save $0.10 per gallon on gas, you'd have to quantify everything: how much is your time worth? How much is your frustration worth? How much gas would your car would use at idle while you wait in line for a pump to open up? What is the 'opportunity cost' of  spending time waiting in line for a pump, waiting to pay at the counter, and trying to merge back onto the highway? Furthermore, as another commenter noted at the above article by I, Vigilante, what is the potential cost—in money, in time, and in trouble—of credit-card skimming, or the risk of total identity theft?

By the very nature of calculation, you need to fill in numbers here. But how can you quantify frustration in monetary terms? The very act of filling in this kind of equation requires enough guesswork to make the entire procedure an exercise in futility!

That's a hidden fact about math: it requires certainty about each term in the equation. Once you introduce guesswork, the equation becomes meaningless. It will still give you an answer, but to quote a popular proverb on the subject: "Junk in, junk out."

Essentially, acting in an ecologically rational manner is to adapt your behavior to suit the situation. Since every situation has different characteristics, it is foolish to behave the same way in all situations!

There are times in which deliberation and care are necessary before embarking on a course of action; there are other times in which quick, decisive action is needed. It is therefore impossible, on a practical level, to know in advance which kind of approach is best for solving a particular problem. One must first identify the nature of the problem, and any important features that may make this particular problem unique/different from similar situations one has already faced.


Academics tend to dislike such arguments, since this renders it impossible for researchers to determine in advance what the "correct" answer should be. After all, a researcher needs to present his or her ideas to skeptical peers! So it is far more defensible to tell your peers: "The correct answer is X, because this equation, based on principles of formal logic, has determined that the correct answer is X."

After all, the above approach has the appearance of airtight inevitability! If you say, "This equation yields X, therefore, the correct answer is X," you're much less likely to spark a heated debate than if you introduce the obvious subjectivity of "Situation P requires this equation, whereas Situation Q requires that equation. Since here, we have Situation P, this equation is necessary, so the correct answer is X. But if we changed these features, we'd have Situation Q, and the correct answer would be Y." An audience member could easily challenge you by objecting that we don't really have Situation P—we actually have Situation Q, or maybe Situation R. This debate could derail your entire presentation and make you look silly in front of a room full of your peers at a conference!

But is the point of research to avoid disagreement, or to advance knowledge?...

My overarching point is this: when academic research demonstrates that most people arrive at the wrong answer to a question, the participants' errors may be an artifact of the research process, NOT something inherently wrong with the human mind!

Next time a researcher tries to tell you that you're irrational, you shouldn't necessarily believe it...

https://www.walldevil.com/wallpapers/w02/853524-comics-nerd-philosophy-question-everything-stick-figures-xkcd.jpg

Wednesday, August 9, 2017

Multiple Regression Explained



How to interpret multiple regression

Regression is useful for making a predictive model. Let's say there's a positive linear correlation between K and N, but you suspect that Factors L and M also contribute to Outcome N


Make up a storysay, that Factors K, L, and M represent intelligence, persistence, and amount of sleep per night and N refers to a course grade.

So, to test the relative impacts of Factors K, L, and M on Outcome N, you can feed each factor into a regression model, and test whether each factor increases the fit. That is, a correlation between Factor K and Outcome N yields a Pearson's r of .64 and R2 of .4096. 

But, when you run a regression testing the effect of Factors K and L on Outcome N, you find an R2 of .5625, with a significant change in the R2 value. That means that Factors K and L together do a better job of explaining the relationship than Factor K alone. 

Then, you run a regression with Factors K, L, and M together, and find an R2 of .5929, with no significant changethis means that Factor M does not help to explain the relationship. Outcome N is due mostly to Factors K and L; Factor M is an unimportant predictor of Outcome N.

Voilà! There's regression in a nutshell! 

And, if you're confused about the math...remember in middle school or high school math, when you learned about "rise over run" and learned the formula y = mx + b? Yeah, that's a simple linear regression. With multiple regression, you can add multiple terms, such that y = ax1 + bx2 + cx3...+ z. But it's still the same concept, just with more predictors than that lone "mx" term.

In case you missed it, there are some fantastic, easy-to-use, and FREE stats programs available now! I review them here.
For more help explaining statistical concepts and when to use them, 
please download my freely available PDF guide here!
https://drive.google.com/open?id=0B4ZtXTwxIPrjUzJ2a0FXbHVxaXc

Saturday, August 5, 2017

When to use a chi-square

 
 
When to use a chi-square

Not clear about when you should use a chi-square vs. when to use a t test? 

First, you should check out my free, downloadable PDF, A Practical Guide to Psych Stats.

Now that that's out of the wayif you're still not sure, how about a tasty example? 
Let's say that we want to know whether a bag of Original Skittles has a truly random distribution of colors. If so, we’d expect to find roughly equal numbers of red, green, purple, yellow, and orange Skittles, right? 

A chi-square goodness-of-fit test [that is, a one-variable chi-square] can help us evaluate this. If there are 18 red, 13 green, 18 purple, 19 yellow, and 17 orange, the chi-square goodness-of-fit test tells us whether this distribution is different enough from an even distribution of 17 apiece (85 Skittles / 5 colors) that we can reject the notion that the colors are evenly distributed. 

If you're really curious about my made-up numbers, by the way, here's a straightforward, easy-to-use online calculator to help you: http://www.socscistatistics.com/tests/goodnessoffit/Default2.aspx

***
Now, let's say we’re looking for differences in the proportion of red Skittles to the other colors in a bag of Original vs. a bag of Tropical Skittles. 



In this case, we have two categorical variables [Original vs. Tropical Skittles, and unequal distribution of colors], so we would need a chi-square test for independence. The additional category makes the calculation a little more complex (but not if you use statistical software to handle the dirty work! 😊), but ultimately, we're looking at the same thing as before: are there roughly equal numbers of each type Skittles in each bag?

In case you missed it, there are some fantastic, easy-to-use, and FREE stats programs available now! I review them here.
For more help explaining statistical concepts and when to use them, 
please download my freely available PDF guide here!
https://drive.google.com/open?id=0B4ZtXTwxIPrjUzJ2a0FXbHVxaXc

Wednesday, July 26, 2017

The AI Apocalypse?



The AI Apocalypse?

Is AIartificial intelligence—hype or substance? Can machines think? Can they ever 
achieve consciousness? Will the AI "Singularity" eventually destroy us all?
 

Monday, May 1, 2017

Life Lessons



At the end of every semester, I hold a session for my students in which I talk about non-academic stuff. Since there are no classes and, often, no guidance on the everyday ins and outs of adulthood, somebody's gotta do something about this, right?

Right?!?!

So, I decided to do something about it! And I've made it available to everyone for free, right here! I've posted the PDF of my slideshow here, since I like to make things freely available for all!

To get my narration, however, you'll have to be one of my students...


https://drive.google.com/open?id=0B4ZtXTwxIPrjQW1VcXRFc0F4ZTg


Addition on Sept. 5, 2017 - I feel vindicated after discovering this John Oliver bit about retirement, which echoes much of what I wrote about finance in the above slides:


Nothing like watching an episode of Last Week Tonight a year after it hit YouTube! More like Last Year Tonight, amirite?...OK, maybe I should leave the comedy to the comedians :/

Wednesday, April 19, 2017

...And the winner is



...And the winner is...

In the ever-changing landscape of social media today, have you wondered lately what forms of social media college students are using most often?

The students in my Spring 2017 stats class were wondering this very question! So, as a brief introduction to research (and as an example of the one-way ANOVA, which we had recently covered), I offered my class the option to get a couple extra credit points for surveying 5 of their friends about their social media usage.

Read on for a snapshot of social media usage among college students right now!

Limitations

I intentionally designed the survey with a couple weaknesses, to give the students some practice at identifying those limitations. We used a 7-point Likert-type scale [it's pronounced LICK-ert, by the way! In case that link goes dead, here's a cached version].
  1. Only the endpoints on this scale were labeled: a 1 indicated "I never use this form of social media" and a 7 indicated "I use this form of social media multiple times per day."

    Not having any labels for the intermediate values is a weakness because it introduces an unacceptable amount of error based on how people interpret a particular number—how do we know that you and I interpret a value of "6" the same way?

    Answer: we don't. Hence, this is a weakness. And a rather serious one!
     
  2. Another major weakness is that these students each asked about 5 friends at Bowling Green State University.

    Given that this is a Psych Stats course, many students are Psych majors. Given that fact, they probably have a disproportionately high number of friends who also major in psychology. Are Psych majors representative of all BGSU students, let alone all college students?

    Not necessarily; hence, the sampling procedure is another major limitation of this study.

    For purposes of a class demonstration, this flawed sample is fine. But it severely limits the ability to generalize the results to all BGSU undergraduate students, let alone college students nationwide. Or, at least, the sampling procedure inspires some doubt about generalizibility.
     
  3. A third limitation is that I only included 5 forms of social media, rather than a more complete list. One student suggested including Tumblr, which is defensible—but for simplicity's sake, I shot that idea down.

    Respondents gave self-report data (on the aforementioned 1-7 scale) regarding their usage of: Facebook, Snapchat, Instagram, Twitter, and Pinterest. That's it.

    So, usage of LinkedIn, reddit, tumblr., Google+, flickr, SoundCloud, and other social networking sites were left out of the picture here. Even MySpace has stuck around, as musicians sometimes use it to gain additional exposure for their work. These sites are not captured in this survey.

Nonetheless, some data is better than no data! As far as student engagement goes, this data is also better than made-up data, because we're looking at real responses from real people—even if the survey methodology is less-than-ideal!

Results

The results of the survey are posted in .csv format on my Google Drive, publicly accessible here. I did the analysis in JASP, which I've previously recommended for many use cases (the complete analysis is available here) and in the even newer program jamovi (that analysis is available here).

Here's the [un-editable] graph generated by JASP:

And here are the descriptive stats:

A couple highlights:
  • Snapchat is the clear winner, with the highest mean (5.671) and the lowest SD (1.819)
  • Instagram takes second place, Facebook is a close third, and Twitter lags behind. Pinterest is a distant last place in this sample
  • The F-ratio was 'statistically significant': F(4, 360) = 22.08, p < .001
  • For effect size, I used eta-squared: Eta-squared = 0.197
  • A post-hoc analysis (with Tukey correction) reveals that Pinterest is significantly different from all others (duh!) and Snapchat is significantly different from Twitter. Instagram and Twitter are also significantly different.
     
  • Statisticians will note that Levene's test reveals a violation of the assumption of equality of variance. Strictly speaking, this means that we should not run an ANOVA; instead, we should use a non-parametric alternative like the Kruskal-Wallis H-test.

    In my experience, though, this rarely yields a fundamentally different result. And after you run the H-test, you still need a post-hoc test anyway!

For convenience's sake, I've screencapped the post-hoc test as well. [Click to enlarge image]

I ran the post-hoc test in the brand-new stats program jamovi, which allows you to run the post-hoc test with no correction or with several of the most frequently-used correction procedures. I like how jamovi let me do the analysis both ways, and showed the results side-by-side.

You can see that a post-hoc analysis with no correction for multiple comparisons yields a significant difference for Facebook vs. Snapchat. It also shows that Facebook and Twitter are almost, but not quite, significantly different (p = .055). Should we ignore this result because it didn't meet the sacred .05 criterion?

I'd say that we should consider it in the context of the study. What are we looking for? Patterns in usage of social media among college students (specifically, college students at BGSU).

What are we trying to accomplish? Well, let's suppose I'm trying to advertise a product or service to college students, in which case I want my ad to be seen by as many college students as possible, for as few $$$ as possible.

Even if the difference between Facebook and Twitter usage isn't significant at the conventional alpha level of .05, if we're talking about efficiency of time, effort, and money, it's close enough that I'd certainly consider advertising on Facebook instead of Twitter!

So is Tukey's correction (or another multiple correction procedure) necessary here? It's certainly debatable; I fall on the "no" side of things—after all, if there's a significant ANOVA, then there's clearly a significant difference somewhere, right? Multiple correction procedures reduce power, so if you use a correction like Tukey's test, you could end up with a significant ANOVA but no significant post-hoc results!

And significance is kind of overblown, anyway... 

_________________

Remember, if you're interested in a more nuanced analysis, you can download the .csv file linked above and run the analyses yourself! I suggest using JASP or jamovi, which are both free of cost and open-source!

ResearcherID