Wisdom of the Cloud

Many summers ago when I started out in the Craft, I could log onto the trusty DEC-20 literally anywhere in the world, and use SPSS or BMDP to analyse data. Nowadays, I have to have IBM SPSS or Stata installed on the right laptop or computer, and bring it with me, wherever I may roam, and wonder dreamily  if I could just access my licensed stats packages from anywhere, like a library, a beach, a forest, a coffee shop.

One option would to subscribe to a stats package in the Cloud! Iin terms of main line stats packages, https://www.apponfly.com/en/ has R (free plus 8 euro’s ($A12.08) per month for platform, NCSS 10 at 18/27.19 per month + platform, IBM SPSS 23 Base 99/149.54 ditto and Standard (adds logistic regression, hierarchical linear modelling, survival analysis etc) for 199/300.59 per month + platform.

Another option, particularly if you’re more into six sigma / quality control type analyses, is Engineroom from http://www.moresteam.com at $US275 ($A378.55) per year.

Obviously,  compare the prices against actually buying the software , but to be able to log in from anywhere, on different computers, and analyse data,  sigh, it’s almost like the summer of ’85!

John and Betty’s Journey into Statistics Packages*

In past days of our lives, those who wanted to learn a stats package, would attend courses, and bail up/bake cakes for statisticians, but would mainly raise the drawbridge, lock the computer lab door and settle down with the VT100 terminal or Apple II or IBM PC and a copy of the brown or update blue SPSS Manual, or whatever.

Nowadays, folks tend to look things up on the web, something of a mixed blessing, and so maybe software consultants will now say LIUOTFW (‘Look It Up On The Flipping Web’) rather than the late, great RYFM (‘Read Your Flipping Manual’).

And yes, there are some great websites, and great online documentation supplied by the software venders, but there are also some great books, available in electronic and print form. A list of three of the many wonderful texts available for each package (IBM SPSS, SAS, Stata, R and Minitab) can be downloaded from the Downloadables section on this site.

IBM SPSS (in particular), R (ever growing), and to a slightly lesser extent SAS, seem to have the best range of primers and introductory texts.
IMHO though, Stata could do with a new colourful, fun primer (not necessarily a Dummies Guide, although there’s Roberto Pedace’s Econometrics for Dummies (Wiley, New York, 2013) which features Stata), perhaps one by Andy Field, who has already done superb books on SPSS, R and SAS.

While up on the soapbox, I reckon Minitab could do with a new primer for Psychologists / Social Scientists, much like that early ripsnorter by Ray Watson, Pip Pattison and Sue Finch, Beginning Statistics for Psychology (Prentice Hall, Sydney, 1993).

Anyway, in memories of days gone by, brew a pot of coffee or tea, unplug email, turn off the phone and the mobile/cell, and settle in for an initial night’s journey, on a set or two of real and interesting data, with a good stats package book, or two!

*(The title of this post riffs off the improbably boring and stereotyped 1950’s early readers still used in Victorian primary (grade) schools in the 1960’s
http://nla.gov.au/nla.aus-vn4738114 (think Dick and Jane, or Alice and Jerry), as well as the far more entertaining and recent John and Betty’s Journey into Complex Numbers by Matt Bower http://www.slideshare.net/aus_autarch/john-and-betty )

“AIC/BIC not p” : comparing means using information criteria

A basic principle in Science is that of parsimony, or reducing complexity where possible, as typified in the application of Occam’s Razor.

William of Occam (or Ockham), a philosopher monk named after the English town that he came from, said something to the effect of ‘pluralitas non est ponenda sine necessitate’ (‘plurality should not be posited without necessity’). In other words, don’t increase, beyond what is necessary, the number of entities needed to explain something.

Occam’s Razor doesn’t necessarily mean that ‘less is always better’, it merely suggests that more complex models shouldn’t be used unless required, to increase model performance, for example. As is commonly, but probably mistakenly believed to have been proposed by Albert Einstein, ‘everything should be made as simple as possible, but not simpler’.

 

Common methods of measuring performance or ‘bang’, taking into account the cost, complexity or ‘buck’, are the Akaike Information Criterion (AIC), Bayesian or Schwarz Information Criterion (BIC), Minimum Message Length (MML) and Minimum Description Length (MDL).

Unlike the standard AIC, the latter three techniques take sample size into account, while MDL and MML also take the precision of the model estimates into account, but let’s just keep to the comparatively simpler AIC/BIC here.

An excellent new book by Thom Baguley ‘Serious Stats’ (serious in this case meaning powerful rather than scarey) http://seriousstats.wordpress.com/ shows how to do a t-test using AIC/BIC in SPSS and R.

I’ll do it here using Stata regression, the idea being to compare a null model (e.g. just the constant) with a model including the group. In this case we’re looking at the difference between headroom in American and ‘Foreign’ cars in 1978. (well, it’s Thursday night!).

Here’s the t-test results

(1978 Automobile Data)
——————————————————————————
Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
———+——————————————————————–
Domestic |      52    3.153846    .1269928    .9157578    2.898898    3.408795
Foreign |        22    2.613636     .103676    .4862837     2.39803      2.829242

 

Domestic has slightly bigger mean headroom (but also larger variation!), p value is 0.011, indicating that the probability of getting a difference in means as large as or larger than the one above (0.540), IF the null hypothesis, that the populations means are actually identical, holds, is around 1 in a 100.

 

Using the method shown in Dr Thom’s book (Stata implementation on my Downloadables page) we get

 

Akaike’s information criterion and Bayesian information criterion

—————————————————————————–
Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
————-+—————————————————————
nullmodel |     74   -92.12213   -92.12213      1     186.2443    188.5483
groupmodel |     74   -92.12213   -88.78075      2     181.5615    186.1696

 

AIC and BIC values are lower for the model including group, suggesting in this case that increasing complexity (the two groups), also commensurately increases performance (i.e. need to take into account the two group means for US and non-US cars, rather than assuming there’s just one common mean, or universal headroom)

Of course, things get a little more complex when comparing several means, having different variances etc (as the example above actually does, although means still “significantly” different when differences in variances taken into account using separate variance t-test).  Something to think about, and more info on applying AIC/BIC to variety of statistical methods can be found in refs below, particularly 3 and 5.

 

Further Reading (refs 2,3,4 and 5 are the most approachable, with Thom Baguley’s book referred to above, more approachable still)

      1. Akaike, H., A new look at the statistical model identification. IEEE Transactions on Automatic Control, 1974. 19: p. 716-723.
      2. Anderson, D.R., Model based inference in the life sciences: a primer on evidence. 2007, New York: Springer.
      3. Dayton, C.M., Information criteria for the paired-comparisons problem. American Statistician, 1998. 52: p. 144-151.
      4. Forsyth, R.S., D.D. Clarke, and R.L. Wright, Overfitting revisited : an information-theoretic approach to simplifying discrimination trees. Journal of Experimental and Artificial Intelligence, 1994. 6: p. 289-302.
      5. Sakamoto, Y., M. Ishiguro, and G. Kitagawa, Akaike information criterion statistics. 1986, Boston, MA: Dordrecht.
      6. Schwarz, G., Estimating the dimension of a model. Annals of Statistics, 1978. 6: p. 461-464.
      7. Wallace, C.S., Statistical and inductive inference by minimum message length. 2005, New York: Springer.
      8. Wallace, C.S. and D.M. Boulton, An information measure for classification. Computer Journal, 1968. 11: p. 185-194.

 

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Expected Unexpected: Power bands, performance curves, rogue waves and black swans

Many years ago, I had a ride of a Kawasaki 500 Mach III 2-stroke motorcycle, which along with its even more horrendous 750cc version was known as the ‘widow-maker’. It was incredibly fast in a straight line, but if it went around corners at all, the rider had long since fallen (or jumped) off!

It also had a very narrow ‘power band’ http://en.wikipedia.org/wiki/Power_band, in that it would have no real power until about 7,000 revs per minute, and then all of a sudden it would whoop and holler like the proverbial bat out of hell, the front wheel would lift, the rider’s jaw drop, and well, you get the idea! In statistical terms, this was a nonlinear relationship between twisting the throttle and the available power.

A somewhat less dramatic example of a nonlinear effect is the Yerkes-Dodson ‘law’ http://en.wikipedia.org/wiki/Yerkes%E2%80%93Dodson_law, in which optimum task performance is associated with medium levels of arousal (too much arousal = the ‘heebie-jeebies’, too little = ‘half asleep’).

Various simple & esoteric methods for finding global (follows a standard pattern such as a U shape, or upside down U) or local (different parts of the data might be better explained by different models, rather than ‘one size fits all’) relationships exist. A popular ‘local’ method is known as a ‘spline’ after the flexible metal ruler that draftspeople once fitted curves with. The ‘GT’ version, Multivariate Adaptive Regression Splines http://en.wikipedia.org/wiki/Multivariate_adaptive_regression_splines. is available in R (itself a little reminiscent of a Mach III cycle at times!),  the big-iron ‘1960’s 390 cubic inch Ford Galaxie V8′ of the SAS statistical package and the original, sleek ‘Ferrari V12’ Salford Systems version.

Other nonlinear methods are available http://en.wikipedia.org/wiki/Loess_curve, but the thing to remember is that life doesn’t always fit within the lines, or follow some human’s idea of a ‘natural law’.

For example, freak or rogue waves, that can literally break supertankers in half, were observed for centuries by mariners but are only recently accepted by shore-bound scientists, similarly the black swans (actually native to Australia) of the stock market http://www.fooledbyrandomness.com/

When analysing data, fitting models, (or riding motorcycles), please be careful!