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Scatterplots are the most common way for statisticians, scientists, and thepublic to visually detect relationships between measured variables. At the sametime, and despite widely publicized controversy, P-values remain the mostcommonly used measure to statistically justify relationships identified betweenvariables. Here we measure the ability to detect statistically significantrelationships from scatterplots in a randomized trial of 2,039 students in astatistics massive open online course (MOOC). Each subject was shown a randomset of scatterplots and asked to visually determine if the underlyingrelationships were statistically significant at the P < 0.05 level. Subjectscorrectly classified only 47.4% (95% CI: 45.1%-49.7%) of statisticallysignificant relationships, and 74.6% (95% CI: 72.5%-76.6%) of non-significantrelationships. Adding visual aids such as a best fit line or scatterplot smoothincreased the probability a relationship was called significant, regardless ofwhether the relationship was actually significant. Classification ofstatistically significant relationships improved on repeat attempts of thesurvey, although classification of non-significant relationships did not. Ourresults suggest: (1) that evidence-based data analysis can be used to identifyweaknesses in theoretical procedures in the hands of average users, (2) dataanalysts can be trained to improve detection of statistically significantresults with practice, but (3) data analysts have incorrect intuition aboutwhat statistically significant relationships look like, particularly for smalleffects. We have built a web tool for people to compare scatterplots with theircorresponding p-values which is available here:http://glimmer.rstudio.com/afisher/EDA/.

A randomized trial in a massive online open course shows people don't  know what a statistically significant relationship looks like, but they can  learn