The nature of correlation perception in scatterplots

For scatterplots with gaussian distributions of dots, the perception of Pearson correlation r can be described by two simple laws: a linear one for discrimination, and a logarithmic one for perceived magnitude (Rensink & Baldridge, 2010). The underlying perceptual mechanisms, however, remain poorly understood. To cast light on these, four different distributions of datapoints were examined. The first had 100 points with equal variance in both dimensions. Consistent with earlier results, just noticeable difference (JND) was a linear function of the distance away from r = 1, and the magnitude of perceived correlation a logarithmic function of this quantity. In addition, these laws were linked, with the intercept of the JND line being the inverse of the bias in perceived magnitude. Three other conditions were also examined: a dot cloud with 25 points, a horizontal compression of the cloud, and a cloud with a uniform distribution of dots. Performance was found to be similar in all conditions. The generality and form of these laws suggest that what underlies correlation perception is not a geometric structure such as the shape of the dot cloud, but the shape of the probability distribution of the dots, likely inferred via a form of ensemble coding. It is suggested that this reflects the ability of observers to perceive the information entropy in an image, with this quantity used as a proxy for Pearson correlation

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

Scatterplots are the most common way for statisticians, scientists, and the public to visually detect relationships between measured variables. At the same time, and despite widely publicized controversy, P-values remain the most commonly used measure to statistically justify relationships identified between variables. Here we measure the ability to detect statistically significant relationships from scatterplots in a randomized trial of 2,039 students in a statistics massive open online course (MOOC). Each subject was shown a random set of scatterplots and asked to visually determine if the underlying relationships were statistically significant at the P < 0.05 level. Subjects correctly classified only 47.4% (95% CI: 45.1%-49.7%) of statistically significant relationships, and 74.6% (95% CI: 72.5%-76.6%) of non-significant relationships. Adding visual aids such as a best fit line or scatterplot smooth increased the probability a relationship was called significant, regardless of whether the relationship was actually significant. Classification of statistically significant relationships improved on repeat attempts of the survey, although classification of non-significant relationships did not. Our results suggest: (1) that evidence-based data analysis can be used to identify weaknesses in theoretical procedures in the hands of average users, (2) data analysts can be trained to improve detection of statistically significant results with practice, but (3) data analysts have incorrect intuition about what statistically significant relationships look like, particularly for small effects. We have built a web tool for people to compare scatterplots with their corresponding p-values which is available here: http://glimmer.rstudio.com/afisher/EDA/.Comment: 7 pages, including 2 figures and 1 tabl

Norm-based coding of voice identity in human auditory cortex

Listeners exploit small interindividual variations around a generic acoustical structure to discriminate and identify individuals from their voice—a key requirement for social interactions. The human brain contains temporal voice areas (TVA) [1] involved in an acoustic-based representation of voice identity [2, 3, 4, 5 and 6], but the underlying coding mechanisms remain unknown. Indirect evidence suggests that identity representation in these areas could rely on a norm-based coding mechanism [4, 7, 8, 9, 10 and 11]. Here, we show by using fMRI that voice identity is coded in the TVA as a function of acoustical distance to two internal voice prototypes (one male, one female)—approximated here by averaging a large number of same-gender voices by using morphing [12]. Voices more distant from their prototype are perceived as more distinctive and elicit greater neuronal activity in voice-sensitive cortex than closer voices—a phenomenon not merely explained by neuronal adaptation [13 and 14]. Moreover, explicit manipulations of distance-to-mean by morphing voices toward (or away from) their prototype elicit reduced (or enhanced) neuronal activity. These results indicate that voice-sensitive cortex integrates relevant acoustical features into a complex representation referenced to idealized male and female voice prototypes. More generally, they shed light on remarkable similarities in cerebral representations of facial and vocal identity

Visual and interactive exploration of point data

Point data, such as Unit Postcodes (UPC), can provide very detailed information at fine scales of resolution. For instance, socio-economic attributes are commonly assigned to UPC. Hence, they can be represented as points and observable at the postcode level. Using UPC as a common field allows the concatenation of variables from disparate data sources that can potentially support sophisticated spatial analysis. However, visualising UPC in urban areas has at least three limitations. First, at small scales UPC occurrences can be very dense making their visualisation as points difficult. On the other hand, patterns in the associated attribute values are often hardly recognisable at large scales. Secondly, UPC can be used as a common field to allow the concatenation of highly multivariate data sets with an associated postcode. Finally, socio-economic variables assigned to UPC (such as the ones used here) can be non-Normal in their distributions as a result of a large presence of zero values and high variances which constrain their analysis using traditional statistics. This paper discusses a Point Visualisation Tool (PVT), a proof-of-concept system developed to visually explore point data. Various well-known visualisation techniques were implemented to enable their interactive and dynamic interrogation. PVT provides multiple representations of point data to facilitate the understanding of the relations between attributes or variables as well as their spatial characteristics. Brushing between alternative views is used to link several representations of a single attribute, as well as to simultaneously explore more than one variable. PVT’s functionality shows how the use of visual techniques embedded in an interactive environment enable the exploration of large amounts of multivariate point data