{"id":495,"date":"2009-11-11T02:46:06","date_gmt":"2009-11-11T07:46:06","guid":{"rendered":"http:\/\/vgable.com\/blog\/?p=495"},"modified":"2009-11-12T09:47:15","modified_gmt":"2009-11-12T14:47:15","slug":"just-look-at-it-man","status":"publish","type":"post","link":"https:\/\/vgable.com\/blog\/2009\/11\/11\/just-look-at-it-man\/","title":{"rendered":"Just Look at it, Man!"},"content":{"rendered":"

You’re looking at Anscombe’s quartet<\/a>: 4 datasets with identical simple statistical properties (mean, variance, correlation, linear regression); but obvious differences when graphed.
\n<\/p>\n

\"325px-Anscombe.svg.png\"<\/div>\n

<\/a>
\n(via Best of Wikipedia<\/a>)<\/p>\n

Graphs aren’t a substitute for numerical analysis. Graphs are not a panacea. But they’re excellent for discovering patterns, outliers, and getting intuition<\/em> about a dataset. If you never graph your data, then you’ve never really looked at it<\/em>.<\/p>\n

War Story<\/h3>\n

I was working on optimizing color correction, using SSE (high performance x86 instructions). One operation required division — an expensive operation for a computer. The hardware had a divide<\/code> instruction, but sometimes using the Newton-Raphson method<\/a> to do the division in software<\/a> is faster. You never know until you measure.<\/p>\n

While doing the measurement, I somehow got the crazy idea to try both: I’d already unrolled the inner loop so instead of repeating the divide<\/code> or Newton’s Method twice, I’d do a divide<\/code> and then use Newton’s Method for the next value. Strangely enough, this was faster on the hardware I was benchmarking than either method individually. Modern hardware is a complex and scary beast.<\/p>\n

I was fortunate enough to have a suite of very good unit tests to run against my optimized code. But there was a caveat to testing correctness. Because computers don’t have infinitely precise arithmetic<\/a>, two correct algorithms might give different answers — but if the numbers they gave were close enough<\/em> to the infinitely precise answer (say a couple ulps<\/a> apart) it was good enough. (We can only be exact within some Tolerance<\/a>!) The tests cleared my hybrid divide<\/code>\/Newton-Raphson function: but we couldn’t use it, because it was fundamentally broken<\/em>.<\/p>\n

Even though the error was acceptably small, it had a nasty<\/em> distribution. Using divide<\/code> gave color values that were a bit too light. Doing a divide in software gave values that were a bit too dark. Individually these errors were fine. Randomly spread over the image<\/a> they would have been fine. But processing every other pixel differently had the effect of adding alternating light\/dark stripes! We see contrast, not absolute color<\/a>, so the numerically insignificant error was quite visible. Worse still, bands of 1 pixel stripes combined to form a shimmering Moir\u00e9 pattern<\/a>. It was totally busted. Unusable.<\/p>\n

This was all immediately obvious when the results of the color correction were “graphed”. Actually looking<\/em> at the answer caught a subtle error that our suite of unit tests missed.<\/p>\n

To be clear, more subjective graphical analysis is not<\/em> a substitute for numerical analysis and data mining. But I believe in actually looking at your data<\/em> at least once. A graph is a kind of end-to-end<\/a> visualization of everything, and that has value. Graphs are a cheap sanity check — does everything look right? And sometimes, they can give you real insight into a problem.<\/p>\n","protected":false},"excerpt":{"rendered":"

You’re looking at Anscombe’s quartet: 4 datasets with identical simple statistical properties (mean, variance, correlation, linear regression); but obvious differences when graphed. (via Best of Wikipedia) Graphs aren’t a substitute for numerical analysis. Graphs are not a panacea. But they’re excellent for discovering patterns, outliers, and getting intuition about a dataset. If you never graph […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,4],"tags":[530,304,529,377,158,535,416,378,536,23],"class_list":["post-495","post","type-post","status-publish","format-standard","hentry","category-bug-bite","category-programming","tag-analysis","tag-color","tag-data","tag-graphing","tag-optimization","tag-sse","tag-statistics","tag-visualization","tag-war-story","tag-x86"],"_links":{"self":[{"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/posts\/495","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/comments?post=495"}],"version-history":[{"count":5,"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/posts\/495\/revisions"}],"predecessor-version":[{"id":500,"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/posts\/495\/revisions\/500"}],"wp:attachment":[{"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/media?parent=495"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/categories?post=495"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vgable.com\/blog\/wp-json\/wp\/v2\/tags?post=495"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}