{"id":886,"date":"2023-03-16T14:06:37","date_gmt":"2023-03-16T14:06:37","guid":{"rendered":"https:\/\/www.allendowney.com\/blog\/?p=886"},"modified":"2023-03-16T14:15:22","modified_gmt":"2023-03-16T14:15:22","slug":"what-does-skew-mean","status":"publish","type":"post","link":"https:\/\/www.allendowney.com\/blog\/2023\/03\/16\/what-does-skew-mean\/","title":{"rendered":"What does skew mean?"},"content":{"rendered":"\n

My audience skews left; that is, the people who read my blog are more liberal, on average, than the general population. For example, if I surveyed my readers and asked where they place themselves on a scale from liberal to conservative, the results might look like this:<\/p>\n\n\n\n

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To be clear, I have not done a survey and this is fake data, but if it were real, we would conclude that my audience is more liberal, on average, than the general population. So in the normal use of the word skew, we might say that this distribution “skews to the left”.<\/p>\n\n\n\n

But according to statisticians, that would be wrong, because within the field of statistics, skew has been given a technical meaning that is contrary to its normal use. Here’s how Wikipedia explains the technical definition:<\/p>\n\n\n\n

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positive skew<\/em>: The right tail is longer; the mass of the distribution is concentrated on the left of the figure. The distribution is said to be right-skewed<\/em>, right-tailed<\/em>, or skewed to the right<\/em>, despite the fact that the curve itself appears to be skewed or leaning to the left; right<\/em> instead refers to the right tail being drawn out and, often, the mean being skewed to the right of a typical center of the data. A right-skewed distribution usually appears as a left-leaning<\/em> curve.<\/p>\nhttps:\/\/en.wikipedia.org\/wiki\/Skewness<\/cite><\/blockquote>\n\n\n\n

By this definition, we would say that the distribution of political alignment in my audience is “skewed to the right”. It is regrettable that the term was defined this way, because it’s very confusing.<\/p>\n\n\n\n

Recently I ran a Twitter poll<\/a> to see what people think skew means. Here are the results:<\/p>\n\n\n\n

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Interpreting these results is almost paradoxical: the first two responses are almost equally common, which proves that the third response is correct. If the statistically-literate people who follow me on Twitter don’t agree about what skew means, we have to treat it as ambiguous unless specified.<\/p>\n\n\n\n

The comments suggest I’m not the only one who thinks the technical definition is contrary to intuition.<\/p>\n\n\n\n