andrew_gelman_stats andrew_gelman_stats-2011 andrew_gelman_stats-2011-1078 knowledge-graph by maker-knowledge-mining
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Introduction: Tables are commonly read as crude graphs: what you notice in a table of numbers is (a) the minus signs, and thus which values are positive and which are negative, and (b) the length of each number, that is, its order of magnitude. The most famous example of such a read might be when the mathematician Srinivasa Ramanujan supposedly conjectured the asymptotic form of the partition function based on a look at a table of the first several partition numbers: he was essentially looking at a graph on the logarithmic scale. I discuss some modern-day statistical examples in this article for Significance magazine . I had a lot of fun creating the “calculator font” for the above graph in R and then writing the article. I hope you enjoy it too! P.S. Also check out this short note by Marcin Kozak and Wojtek Krzanowski on effective presentation of data. P.P.S. I wrote this blog entry a month ago and had it in storage. Then my issue of Significance came in the mail—with my
sentIndex sentText sentNum sentScore
1 Tables are commonly read as crude graphs: what you notice in a table of numbers is (a) the minus signs, and thus which values are positive and which are negative, and (b) the length of each number, that is, its order of magnitude. [sent-1, score-1.133]
2 The most famous example of such a read might be when the mathematician Srinivasa Ramanujan supposedly conjectured the asymptotic form of the partition function based on a look at a table of the first several partition numbers: he was essentially looking at a graph on the logarithmic scale. [sent-2, score-2.008]
3 I discuss some modern-day statistical examples in this article for Significance magazine . [sent-3, score-0.171]
4 I had a lot of fun creating the “calculator font” for the above graph in R and then writing the article. [sent-4, score-0.315]
5 Also check out this short note by Marcin Kozak and Wojtek Krzanowski on effective presentation of data. [sent-8, score-0.337]
6 I wrote this blog entry a month ago and had it in storage. [sent-12, score-0.276]
7 As I was posting, I had a funny thought in the back of my mind: December 22 . [sent-15, score-0.091]
8 I guess I must have seen that somewhere and it stuck in my mind. [sent-21, score-0.194]
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same-blog 1 1.0 1078 andrew gelman stats-2011-12-22-Tables as graphs: The Ramanujan principle
Introduction: Tables are commonly read as crude graphs: what you notice in a table of numbers is (a) the minus signs, and thus which values are positive and which are negative, and (b) the length of each number, that is, its order of magnitude. The most famous example of such a read might be when the mathematician Srinivasa Ramanujan supposedly conjectured the asymptotic form of the partition function based on a look at a table of the first several partition numbers: he was essentially looking at a graph on the logarithmic scale. I discuss some modern-day statistical examples in this article for Significance magazine . I had a lot of fun creating the “calculator font” for the above graph in R and then writing the article. I hope you enjoy it too! P.S. Also check out this short note by Marcin Kozak and Wojtek Krzanowski on effective presentation of data. P.P.S. I wrote this blog entry a month ago and had it in storage. Then my issue of Significance came in the mail—with my
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Introduction: John Tukey wrote about semigraphic displays. I think his most famous effort in that area–the stem-and-leaf plot–is just horrible. But the general idea of viewing tables as graphs is good, and it’s been a success at least since the early 1900s, when Ramanujan famously intuited the behavior of the partition number by seeing a table of numbers and implicitly reading it as a graph on the logarithmic scale. To return to the present, Steve Roth sent me a link to these table/graphs that he made: Europe vs. US: Who’s Winning? and State Taxes and Prosperity, Revisited . He writes: I [Roth] find the layout with the red/black gives a simultaneous numeric and graphical representation of the situation, and condenses a lot of immediately apprehensible info into a small space. It also helps me avoid at least one axis of cherry-picking (periods), which I am as prone to as all humans are. Any thoughts welcome. In particular, do you think the average and count aggregates at the bot
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Introduction: After our recent discussion of semigraphic displays, Jay Ulfelder sent along a semigraphic table from his recent book. He notes, “When countries are the units of analysis, it’s nice that you can use three-letter codes, so all the proper names have the same visual weight.” Ultimately I think that graphs win over tables for display. However in our work we spend a lot of time looking at raw data, often simply to understand what data we have. This use of tables has, I think, been forgotten in the statistical graphics literature. So I’d like to refocus the eternal tables vs. graphs discussion. If the goal is to present information, comparisons, relationships, models, data, etc etc, graphs win. Forget about tables. But . . . when you’re looking at your data, it can often help to see the raw numbers. Once you’re looking at numbers, it makes sense to organize them. Even a displayed matrix in R is a form of table, after all. And once you’re making a table, it can be sensible to
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Introduction: I received an email from the Royal Statistical Society asking if I wanted to submit a 400-word discussion to the article, Vignettes and health systems responsiveness in cross-country comparative analyses by Nigel Rice, Silvana Robone and Peter C. Smith. My first thought was No, I can’t do it, I don’t know anything about health systems responsiveness etc. But then I thought, sure, I always have something to say. So I skimmed the article and was indeed motivated to write something. Here’s what I sent in: As a frequent user of survey data, I am happy to see this work on improving the reliability and validity of subjective responses. My only comment is to recommend that the statistical sophistication that is evident in the in the design and modeling in this study be applied to the summaries as well. I have three suggestions in particular. First, I believe Figure 1 could be better presented as a series of line plots. As it is, the heights of the purple and blue bars dominat
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Introduction: I was at a talk awhile ago where the speaker presented tables with 4, 5, 6, even 8 significant digits even though, as is usual, only the first or second digit of each number conveyed any useful information. A graph would be better, but even if you’re too lazy to make a plot, a bit of rounding would seem to be required. I mentioned this to a colleague, who responded: I don’t know how to stop this practice. Logic doesn’t work. Maybe ridicule? Best hope is the departure from field who do it. (Theories don’t die, but the people who follow those theories retire.) Another possibility, I think, is helpful software defaults. If we can get to the people who write the software, maybe we could have some impact. Once the software is written, however, it’s probably too late. I’m not far from the center of the R universe, but I don’t know if I’ll ever succeed in my goals of increasing the default number of histogram bars or reducing the default number of decimal places in regression
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Introduction: Tables are commonly read as crude graphs: what you notice in a table of numbers is (a) the minus signs, and thus which values are positive and which are negative, and (b) the length of each number, that is, its order of magnitude. The most famous example of such a read might be when the mathematician Srinivasa Ramanujan supposedly conjectured the asymptotic form of the partition function based on a look at a table of the first several partition numbers: he was essentially looking at a graph on the logarithmic scale. I discuss some modern-day statistical examples in this article for Significance magazine . I had a lot of fun creating the “calculator font” for the above graph in R and then writing the article. I hope you enjoy it too! P.S. Also check out this short note by Marcin Kozak and Wojtek Krzanowski on effective presentation of data. P.P.S. I wrote this blog entry a month ago and had it in storage. Then my issue of Significance came in the mail—with my
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Introduction: Howard Friedman sent me a new book, The Measure of a Nation, subtitled How to Regain America’s Competitive Edge and Boost Our Global Standing. Without commenting on the substance of Friedman’s recommendations, I’d like to endorse his strategy of presentation, which is to display graph after graph after graph showing the same message over and over again, which is that the U.S. is outperformed by various other countries (mostly in Europe) on a variety of measures. These aren’t graphs I would ever make—they are scatterplots in which the x-axis conveys no information. But they have the advantage of repetition: once you figure out how to read one of the graphs, you can read the others easily. Here’s an example which I found from a quick Google: I can’t actually figure out what is happening on the x-axis, nor do I understand the “star, middle child, dog” thing. But I like the use of graphics. Lots more fun than bullet points. Seriously. P.S. Just to be clear: I am not trying
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Introduction: Under the subject line “Blog bait!”, Brendan Nyhan points me to this post at the Washington Post blog: For 2013, we asked some of the year’s most interesting, important and influential thinkers to name their favorite graph of the year — and why they chose it. Here’s Bill Gates’s. Infographic by Thomas Porostocky for WIRED. “I love this graph because it shows that while the number of people dying from communicable diseases is still far too high, those numbers continue to come down. . . .” As Brendan is aware, this is not my favorite sort of graph, it’s a bit of a puzzle to read and figure out where all the pieces fit in, also weird stuff going on like 3-D effects and the big space taken up by those yellow and green borders, as well as tricky things like understanding what some of those little blocks are, and perhaps the biggest question, what is the definition of an “untimely death.” But, as often is the case, the defects of the graph form a statistical perspective can
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Introduction: Details matter (at least, they do for me), but we don’t yet have a systematic way of going back and forth between the structure of a graph, its details, and the underlying questions that motivate our visualizations. (Cleveland, Wilkinson, and others have written a bit on how to formalize these connections, and I’ve thought about it too, but we have a ways to go.) I was thinking about this difficulty after reading an article on graphics by some computer scientists that was well-written but to me lacked a feeling for the linkages between substantive/statistical goals and graphical details. I have problems with these issues too, and my point here is not to criticize but to move the discussion forward. When thinking about visualization, how important are the details? Aleks pointed me to this article by Jeffrey Heer, Michael Bostock, and Vadim Ogievetsky, “A Tour through the Visualization Zoo: A survey of powerful visualization techniques, from the obvious to the obscure.” Th
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Introduction: Jeff writes: How far off is bglmer and can it handle ordered logit or multinom logit? My reply: bglmer is very close. No ordered logit but I was just talking about it with Sophia today. My guess is that the easiest way to fit a hierarchical ordered logit or multinom logit will be to use stan. For right now I’d recommend using glmer/bglmer to fit the ordered logits in order (e.g., 1 vs. 2,3,4, then 2 vs. 3,4, then 3 vs. 4). Or maybe there’s already a hierarchical multinomial logit in mcmcpack or somewhere?
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Introduction: Don Coffin writes: A colleague of mine and I are doing a presentation for new faculty on a number of topics related to teaching. Our charge is to identify interesting issues and to find research-based information for them about how to approach things. So, what I wondered is, do you know of any published research dealing with the sort of issues about structuring a course and final exam in the ways you talk about in this blog post ? Some poking around in the usual places hasn’t turned anything up yet. I don’t really know the psychometrics literature but I imagine that some good stuff has been written on principles of test design. There are probably some good papers from back in the 1920s. Can anyone supply some references?
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