{"id":67615,"date":"2015-08-05T09:20:22","date_gmt":"2015-08-05T14:20:22","guid":{"rendered":"http:\/\/thesocietypages.org\/socimages\/?p=67615"},"modified":"2015-08-05T00:45:48","modified_gmt":"2015-08-05T05:45:48","slug":"margins-of-error-and-the-real-rank-of-the-republican-primary-candidates","status":"publish","type":"post","link":"https:\/\/thesocietypages.org\/socimages\/2015\/08\/05\/margins-of-error-and-the-real-rank-of-the-republican-primary-candidates\/","title":{"rendered":"Margins of error and the real rank of the Republican primary candidates"},"content":{"rendered":"

The margin of error is getting more attention than usual in the news. That\u2019s not saying much since it\u2019s usually a tiny footnote, like those rapidly muttered disclaimers in TV ads (\u201cOffer not good mumble mumble more than four hours mumble mumble and Canada\u201d). Recent headlines proclaim, \u201cTrump leads Bush…\u201d A paragraph or two in, the story will report that in the recent poll Trump got 18% and Bush 15%.\u00a0 That difference is well within the margin of error, but you have to listen closely to hear that. Most people usually don\u2019t want to know about uncertainty and ambiguity.<\/p>\n

What\u2019s bringing uncertainty out of the closest now is the upcoming Republican presidential debate. The Fox-CNN-GOP axis has decided to split the field of presidential candidates in two based on their showing in the polls. The top ten will be in the main event. All other candidates \u2013 currently Jindal, Santorum, Fiorina, et al. \u2013 will be relegated to the children\u2019s table, i.e., a second debate a month later and at the very unprime hour of 5 p.m.<\/p>\n

But is\u00a0Rick Perry\u2019s 4% in a recent poll (419 likely GOP voters) really in a different class than Bobby Jindal\u2019s 25? The margin of error that CNN announced in that survey was a confidence interval of\u00a0 +\/- 5.\u00a0 Here\u2019s the box score.<\/p>\n

\"2\"<\/a>
\nJindal might argue that, with a margin of error of 5 points, his 2% might actually be as high as 7%, which would put him in the top tier.He might argue that, but he shouldn\u2019t.\u00a0 Downplaying the margin of error makes a poll result seem more precise than it really is, but using that one-interval-fits-all number of five points understates the precision. That\u2019s because the margin of error depends on the percent that a candidate gets. The confidence interval is larger for proportions near 50%, smaller for proportions at the extreme.<\/p>\n

Just in case you haven\u2019t taken the basic statistics course, here is the formula.<\/p>\n

\"4\"<\/a>
\nThe\u00a0p\u0302<\/b>\u00a0 (pronounced \u201cpee hat\u201d) is the proportion of the sample who preferred each candidate. For the candidate who polled 50%, the numerator of the fraction under the square root sign will be 0.5 (1-0.5) = .25.\u00a0 That’s much larger than the numerator for the 2% candidate:\u00a0 0.02 (1-0.02) = .0196.*Multiplying by the 1.96, the 50% candidate\u2019s margin of error with a sample of 419 is +\/- 4.8. That\u2019s the figure that CNN reported. But plug in Jindal\u2019s 2%, and the result is much less: +\/- 1.3.\u00a0 So, there\u2019s a less than one in twenty chance that Jindal\u2019s true proportion of support is more than 3.3%.<\/p>\n

Polls usually report their margin of error based on the 50% maximum. The media reporting the results then use the one-margin-fits-all assumption \u2013\u00a0even NPR<\/a>. Here is their story from May 29 with the headline \u201cThe Math Problem Behind Ranking The Top 10 GOP Candidates\u201d:<\/p>\n

There\u2019s a big problem with winnowing down the field this way: the lowest-rated people included in the debate might not deserve to be there.<\/p>\n

The latest GOP presidential poll, from Quinnipiac, shows just how messy polling can be in a field this big.\u00a0We\u2019ve put together a chart showing how the candidates stack up against each other among Republican and Republican-leaning voters \u2014 and how much their margins of error overlap.<\/span><\/p><\/blockquote>\n

\"14\"<\/a><\/p>\n

 <\/p>\n

The NPR writer, Danielle Kurtzleben, does mention that \u201cmargins might be a little smaller at the low end of the spectrum,\u201d but she creates a graph that ignores that reality.The misinterpretation of presidential polls is nothing new.\u00a0 But this time that ignorance will determine whether a candidate plays to a larger or smaller TV audience.<\/p>\n

—————————–<\/p>\n

* There are slightly different formulas for calculating the margin of error for very low percentages.\u00a0 The Agresti-Coull formula gives a confidence interval even if there are zero Yes responses. (HT: Andrew Gelman)<\/p>\n

Originally posted at Montclair SocioBlog<\/a>.<\/em><\/p>\n Jay Livingston is the chair of the Sociology Department at Montclair State University<\/a>. You can follow him at Montclair SocioBlog<\/a> or on Twitter<\/a>.<\/span>","protected":false},"excerpt":{"rendered":"

The margin of error is getting more attention than usual in the news. That\u2019s not saying much since it\u2019s usually a tiny footnote, like those rapidly muttered disclaimers in TV ads (\u201cOffer not good mumble mumble more than four hours mumble mumble and Canada\u201d). Recent headlines proclaim, \u201cTrump leads Bush…\u201d A paragraph or two in, […]<\/p>\n","protected":false},"author":258,"featured_media":67620,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[129,274,85,20068],"class_list":["post-67615","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized","tag-media","tag-methodsuse-of-data","tag-politics","tag-politics-election-2016"],"jetpack_featured_media_url":"https:\/\/thesocietypages.org\/socimages\/files\/2015\/08\/141.png","_links":{"self":[{"href":"https:\/\/thesocietypages.org\/socimages\/wp-json\/wp\/v2\/posts\/67615","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thesocietypages.org\/socimages\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thesocietypages.org\/socimages\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thesocietypages.org\/socimages\/wp-json\/wp\/v2\/users\/258"}],"replies":[{"embeddable":true,"href":"https:\/\/thesocietypages.org\/socimages\/wp-json\/wp\/v2\/comments?post=67615"}],"version-history":[{"count":6,"href":"https:\/\/thesocietypages.org\/socimages\/wp-json\/wp\/v2\/posts\/67615\/revisions"}],"predecessor-version":[{"id":67626,"href":"https:\/\/thesocietypages.org\/socimages\/wp-json\/wp\/v2\/posts\/67615\/revisions\/67626"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/thesocietypages.org\/socimages\/wp-json\/wp\/v2\/media\/67620"}],"wp:attachment":[{"href":"https:\/\/thesocietypages.org\/socimages\/wp-json\/wp\/v2\/media?parent=67615"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thesocietypages.org\/socimages\/wp-json\/wp\/v2\/categories?post=67615"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thesocietypages.org\/socimages\/wp-json\/wp\/v2\/tags?post=67615"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}