Book Series on "Statistical Reasoning in Science & Society"

Back in early 2016, the American Statistical Association (ASA) made an announcement in its newsletter, Amstat News, about the introduction of an important new series of books. In part, that announcement said:

"The American Statistical Association recently partnered with Chapman & Hall/CRC Press to launch a book series called the ASA-CRC Series on Statistical Reasoning in Science and Society. 

'The ASA is very enthusiastic about this new series,' said 2015 ASA President David Morganstein, under whose leadership the arrangement was made. 'Our strategic plan includes increasing the visibility of our profession. One way to do that is with books that are readable, exciting, and serve a broad audience having a minimal background in mathematics or statistics.' 

The Chapman & Hall/CRC press release states the book series will do the following:

• Highlight the important role of statistical and probabilistic reasoning in many areas

• Require minimal background in mathematics and statistics

• Serve a broad audience, including professionals across many fields, the general public, and students in high schools and colleges

• Cover statistics in wide-ranging aspects of professional and everyday life, including the media, science, health, society, politics, law, education, sports, finance, climate, and national security

• Feature short, inexpensive books of 100–150 pages that can be written and read in a reasonable amount of time."

Seven titles have now been published in this series -

Measuring Society, by Chaitra H. Nagaraja (2019)
Measuring Crime: Behind the Statistics, by Sharon L. Lohr (2019)
Statistics and Health Care Fraud: How to Save Billions, by Tahir Ekin (2019)
Improving Your NCAA® Bracket with Statistics, by Tom Adams (2018)
Data Visualization: Charts, Maps, and Interactive Graphics, by Robert Grant (2018)
Visualizing Baseball, by Jim Albert (2017)
Errors, Blunders, and Lies: How to Tell the Difference, by David S. Salsburg (2017)

Readers of this blog should be especially interested in Chaitra Nagaraja's recently published addition to this series. Chaitra devotes chapters in her book to the topics of  Jobs, Inequality, Housing, Prices, Poverty, and Deprivation. I particularly like the historical perspective that Chaitra provides in this very readable contribution, and I recommend her book to you (and your non-economist friends). 

© 2019, David E. Giles

Interpolating Statistical Tables

We've all experienced it. You go to use a statistical table - Standard Normal, Student-t, F, Chi Square - and the line that you need simply isn't there in the table. That's to say the table simply isn't detailed enough for our purposes.

One question that always comes up when students are first being introduced to such tables is:

"Do I just interpolate linearly between the nearest entries on either side of the desired value?"

Not that these exact words are used, typically. For instance, a student might ask if they should take the average of the two closest values. How should you respond?

Not All Measures of GDP are Created Equal

A big hat-tip to one of my former grad. students, Ryan MacDonald at Statistics Canada, for bringing to my attention a really informative C.D. Howe Institute Working Paper by Philip Cross (former Chief Economic Analyst at Statistics Canada).

The paper is titled, "What do the Different Measures of GDP Tell us?"

We all know what's meant by Gross Domestic Product (GDP), don't we? O.K., but do you know that there are lots of different ways of calculating GDP, including the six that Philip discusses in detail in his paper, namely:

• GDP by industry
• GDP by expenditure
• GDP by income
• The quantity equation
• GDP by input/output
• GDP by factor input

So why does this matter?

Well, for one thing - and this is one of the major themes of Philip's paper - how we view (and compute) GDP has important implications for policy-making. And, it's important to be aware that different ways of measuring GDP can result in different numbers.

For instance, consider this chart from p.16 of the Philip's paper:

My first reaction when I saw this was "it's not flat". However, as RMM has commented below, "the line actually shows us the fluctuations of industries that are more intermediate compared with industries (or the total) that includes only final goods. Interesting and useful for business cycle analysis..."

Here's my take-away (p.18 of the paper):

"For statisticians, the different measures of GDP act as an internal check on their conceptual and empirical consistency. For economists, the different optics for viewing economic activity lead to a more profound understanding of the process of economic growth. Good analysis and policy prescription often depend on finding the right optic to understand a particular problem."

Let's all keep this in mind when we look at the "raw numbers".

© 2016, David E. Giles

Multivariate Medians

I'll bet that in the very first "descriptive statistics" course you ever took, you learned about measures of "central tendency" for samples or populations, and these measures included the median. You no doubt learned that one useful feature of the median is that, unlike the (arithmetic, geometric, harmonic) mean, it is relatively "robust" to outliers in the data.

(You probably weren't told that J. M. Keynes provided the first modern treatment of the relationship between the median and the minimization of the sum of absolute deviations. See Keynes (1911) - this paper was based on his thesis work of 1907 and 1908. See this earlier post for more details.)

At some later stage you would have encountered the arithmetic mean again, in the context of multivariate data. Think of the mean vector, for instance.

However, unless you took a stats. course in Multivariate Analysis, most of you probably didn't get to meet the median in a multivariate setting. Did you ever wonder why not?

One reason may have been that while the concept of the mean generalizes very simply from the scalar case to the multivariate case, the same is not true for the humble median. Indeed, there isn't even a single, universally accepted definition of the median for a set of multivariate data!

Let's take a closer look at this.

Actually Computing the Sample Variance!

I always enjoy the posts from John Cook on his The Endeavour blog. John's a knowledgable guy and there's a lot on his blog that's of interest to econometricians. Take a look for yourself!

Back in 2008, John had a post that's relevant to something I've been blogging about recently. It also reminded me of some important issues associated with computation - issues that we used to worry about a great deal in the bad old days of "hand calculations", and computers with short word-lengths and very limited memory

One thing that needs to be stressed to students is that the algebraic formulae that they learn about are not necessarily expressed in the form that's most appropriate computationally. By "appropriate", I'm referring to both computational accuracy and computational speed. There are actually lots and lots of examples that illustrate the point that I want to make. However, let's just consider the "simple problem" of computing the variance of a sample of data.

Variance Estimators That Minimize MSE

In this post I'm going to look at alternative estimators for the variance of a population. The following discussion builds on a recent post, and once again it's really directed at students. Well, for the most part.

Actually, some of the results relating to populations that are non-Normal probably won't be familiar to a lot of readers. In fact, I can't think of a reference for where these results have been assembled in this way previously. So, I think there's some novelty here. But we'll get to that in due course.

I can just imagine you smacking your lips in anticipation!

What's the Variance of a Sample Variance?

This post is really pitched at students who are taking a course or two in introductory economic statistics. It relates to a couple of estimators of the variance of a population that we all meet in such courses - plus another one that you might not have met. In addition, I'll be emphasising the fact that some "standard" results depend crucially on certain assumptions. Not surprisingly - but  not always made clear by instructors and text books.

The Greenfield Challenge

The European Network for Business and Industrial Statistics has the objective of "...connecting individuals and organisations, interested in theoretical developments and practical applications in the field of business and industrial statistics." They achieve this through their electronic network, and an annual Spring Conference.

The co-called "Greenfield Challenge", which is now an annual event, arose from a challenge laid down by Tony Greenfield in his George Box Medal acceptance speech in 2009:

"My challenge to you is that you will tell some audience about work you have done, and completed successfully because you used a statistical method. But that audience must be of people who are not statisticians.

And you will have spoken to those people through publications that are for the wider public, through magazines or newspapers, or from a public platform. You might even write a short story or a play.… That is my challenge: Tell the world, outside your circle, of work you have done, and done successfully because you used statistics."

Fighting words!

You can read more about the responses to this challenge from members of the ENBIS community here.



I really like this challenge. It seems to me that it would be equally applicable to the econometrics community.

What do you think?

© 2012, David E. Giles

Happy Birthday, "Your Better Life Index"

One year ago, the OECD released its Your Better Life Index. The Index sought to provide comparative data relating to well-being that go beyond the traditional economic output measures such as GDP.

I analyzed some of the YBLI data in a few posts last year - here, here, and here.

The YBLI has been re-released (updated) today. The OECD tells us:

"Some of the key takeaways from the new version of the Index include:

• No matter which countries people live in, they value the most some combination of  health, education and life satisfaction.
• Men and women who have used the Index value basically the same things.
• The wealthier you are, the more likely you are to make your voice heard in elections, but not by a huge margin.
• Men work more in the labour market and make more money than women, but women are better in other areas, they live longer, are better educated and in most places they are also happier.
• Inequality isn’t just about money, it affects other topics in Your Better Life Index."

BTW, if you have an interest in these issues, then the Freedom and Flourishing blog that Winton Bates writes should be on your reading list.

 

© 2012, David E. Giles

Complex Survey Data in Econometrics

It's easy to forget that many of the standard results that we learn in statistics are based fairly and squarely on the assumption that the data are obtained by using simple random sampling.

In reality, this is rarely the case. Stratified  and cluster sampling are routinely used by our statistical agencies, and frequently the sampling process is much more complicated than that. So-called "Complex Survey" designs, which involve multi-stage stratification and clustering are very common.

This is something to watch out for in practice.

An Irish Economic Statistician

Today, of all days, it seems appropriate to mention an outstanding Irish statistician - one who made seminal contributions to "economic statistics", as well as to mathematical statistics. I'm referring to Robert ("Roy") Charles Geary.

More on Shortest Confidence Intervals

I was (pleasantly) surprised by the number of "hits" my recent post on "Minimizing the Length of a Confidence Interval" attracted. As has often been the case, a lot of visitors came by way of  Mark Thoma's excellent blog, Economist's View. (Thanks, Mark!) 

In that post one of the things I discussed was the issue of constructing a "shortest length" confidence interval in the case where the distribution of the pivotal statistic that's used to start off the interval is asymmetric. In such cases, we have a more difficult task on our hands than when the distribution is symmetric, and uni-modal. In response to this, we usually construct "equal tails" confidence intervals in the asymmetric case.

I'm not going to repeat the previous post! Instead, I'm going to share a few lines of R code that I've put together to deal with this issue in the case of an asymmetric distribution that's of great practical importance to econometricians.

On the Asymptotic Properties of Sample Means

Last month, in a post titled "Extracting the Correct Mean(ing) From the Data" (here), I discussed some aspects of the arithmetic, geometric, and harmonic sample means.

In a subsequent comment, I was asked if the geometric mean (GM) and harmonic mean (HM) are consistent estimators of E[X], the (arithmetic) mean of the population. My first reaction was that they are, but a little further reflection shows otherwise.

Minimizing the Length of a Confidence Interval

Right now I'm teaching an introductory course on statistical inference for Economics students. We've been dealing with confidence intervals, starting off (as usual) with one for the mean of a Normal population.

For a given confidence level, the shorter the interval is, the more "informative" it is. The question that then arises is how to make the interval as short as possible, everything else being equal? Good question!

Extracting the Correct Mean(ing) From the Data

We've all taken, and/or taught, an introductory course in descriptive statistics where we encounter measures of "central tendency", variability, summarizing grouped data, and so on. In such courses students are usually told about three ways of calculating the mean, or average, of a sample. These are the Arithmetic Mean, Geometric Mean, and Harmonic Mean. In my experience, economists often fail to use the most appropriate of these three measures. I think this is because often we don't provide enough motivation and explanation in those introductory courses.

Still Searching for the Number of Weeks in a Year

When I put up a post titled "How Many Weeks Are There in a Year" back in April, little did I know how many hits it would get. For a while I was intrigued to see that visitors kept arriving. They still do - every day, without fail.

Then I realized the reason why. It wasn't because the readers of this post were in search of econometric enlightenment. Oh no! There was a much more obvious reason. They genuinely want to know the answer to the question posed in the title of that post!

A quick look at the blog "stats" revealed that there are some popular web search strings that lead these poor souls, no doubt kicking and screaming, to this site.

National Debt & Regression Models - Units of Measurement Matter!

In a recent post, titled "Debt and Delusion", Robert Shiller draws attention to a very important point amid the current bombardment of news about the debt crisis (crises?).

Referring to the situation in Greece, he comments:

 "Here in the US, it might seem like an image of our future, as public debt comes perilously close to 100% of annual GDP and continues to rise. But maybe this image is just a bit too vivid in our imaginations. Could it be that people think that a country becomes insolvent when its debt exceeds 100% of GDP?

That would clearly be nonsense. After all, debt (which is measured in currency units) and GDP (which is measured in currency units per unit of time) yields a ratio in units of pure time. There is nothing special about using a year as that unit. A year is the time that it takes for the earth to orbit the sun, which, except for seasonal industries like agriculture, has no particular economic significance.

We should remember this from high school science: always pay attention to units of measurement. Get the units wrong and you are totally befuddled.

If economists did not habitually annualize quarterly GDP data and multiply quarterly GDP by four, Greece’s debt-to-GDP ratio would be four times higher than it is now. And if they habitually decadalized GDP, multiplying the quarterly GDP numbers by 40 instead of four, Greece’s debt burden would be 15%. From the standpoint of Greece’s ability to pay, such units would be more relevant, since it doesn’t have to pay off its debts fully in one year (unless the crisis makes it impossible to refinance current debt)." .........

On the Correlation Between Crime and Punishment

In two previous posts (here and here) I've taken a look at the OECD's 50^th anniversary present to all of us - their "Better Life Index" (BLI). One of the eleven components of that Index is titled "Safety" - and according to the OECD this component

"...... largely reflects the risks of people being physically assaulted or falling victim to other types of crime. Crime may lead to loss of life and property, as well as physical pain, post-traumatic stress and anxiety. The biggest impact of crime on people’s well-being appears to be through the feeling of vulnerability that it causes."

The BLI site also notes that

"Across the OECD, one person in six reported falling victim to a conventional crime, with physical assault accounting for nearly a quarter of all conventional crime. In terms of perceived safety, one out of four people in the OECD report feeling unsafe on the street after dark."

In addition, the average homicide rate across the OECD countries is 2.2 murders per 100,000 inhabitants.

An interesting question that arises is whether or not the relative safety level matches the relative incarceration rate.

An Even Better Life?

Last week, in a post titled, It's a Wonderful Life, I discussed the OECD's recently released "Better Life Index" (BLI). The index is made up of eleven different components that are then aggregated, with equal weights, into a single BLI, which you can see here. In addition, the OECD provides an interactive tool so you can select your own weights across the 11 measures, and then make cross-country comparisons.

At the end of that earlier post I noted that one question that I hadn't addressed  was: "What's really driving the variability in the country rankings?" I promised to return to this question - so here we are.

How Many Weeks are There in a Year?

What a question (you'd think)! Well, bear with me, because I have some news for you. I've previously blogged about the decline and fall of our higher education system, but there's always room for a little embellishment. One thing that I've learned over my years of teaching econometrics and economic statistics is that you should always expect the unexpected. It goes with the territory.

Here's a situation that I encountered a few years ago when I was teaching a first-level undergraduate economic statistics course. I recount it simply to illustrate the point that I learn something every time I step into the classroom,  and certainly not out of disrespect for any particular individual(s). This is how it went down.