PSYC 5016 - Week 8: Data Visualization and Bias

Vocabulary flashcards covering data visualization concepts, graph types, linear model assumptions, sources of bias, and robust remediation techniques from PSYC 5016 Week 8.

Anscombe's Quartet

A collection of four datasets (Anscombe, 1973) that share identical descriptive statistics (mean number of sessions = $9.0$, $SD = 3.3$; mean well-being = $7.5$, $SD = 2.0$; correlation $r = .82$) but reveal completely different distributions and relationships when plotted visually.

Interocular Effect

A visual property of a graphic described by Tukey (1990) where the data display has an immediate, striking, and unambiguous message that hits the viewer right between the eyes.

Tufte's Visualization Principles

A set of design guidelines (Tufte, 2001) stating that graphs should show the data, avoid distortion, induce thought about the data rather than the design, present many numbers with minimum ink, make large datasets coherent, and encourage comparisons.

Boxplot (Box-Whisker Diagram)

A graphical summary of data displaying the minimum (without outliers), first quartile ($Q1$, bottom $25\%$), median, third quartile ($Q3$, top $25\%$), the interquartile range ($\text{middle } 50\%$), maximum (without outliers), and individual outlier points.

Density Plot

A visualization that displays a smoothed representation of the continuous distribution and probability density of a variable across its range of values.

Jitter Plot (Strip Plot)

A visualization that plots individual data points along a categorical axis while adding small, random positional displacements (jitter) to prevent identical or overlapping points from obscuring one another.

Dot Plot

A statistical graph displaying individual observations as dots along an axis, often presented alongside summary statistics such as the mean and confidence intervals.

Violin Plot

A statistical graphic that combines features of a boxplot and a kernel density trace to show the mirrored probability density and distributional shape of data across groups.

Raincloud Plot

A composite visualization described by Allen et al. (2021) combining a smoothed density plot (the cloud), jittered raw data points (the rain), and summary statistics such as a boxplot to concurrently reveal individual observations, patterns/clustering, and overall distribution tendencies.

Slopegraph

A plot used to visualize change between two discrete time points or conditions (such as baseline and 6 months) by connecting paired observations with straight line segments.

Quantile-Quantile (Q-Q) Plot

A diagnostic graph plotting the quantiles of a sample variable against the theoretical quantiles of a specified distribution (often a normal distribution); values falling along the diagonal indicate concordance, while departures from the line signify skewness or kurtosis.

Hexagonal Binning (Hexbin) Plot

A two-dimensional density plot that tessellates the plotting surface into regular hexagons, shading each hexagon according to the count of overlapping data points to resolve severe overplotting in large datasets ($N > 40{,}000$).

Bubble Chart

A multi-variable graph extending a scatterplot by mapping an additional quantitative dimension to the area or size of the circular points (and optionally another dimension to point colour).

Estimation

The statistical procedure of calculating numerical estimates of unknown population model parameters using observed sample data (Flora, 2017).

Outlier

An observation or set of observations substantially distinct from the remaining data, capable of biasing parameter estimates (such as the mean), inflating the sum of squared errors, and distorting precision measures like standard deviations, standard errors, and confidence intervals.

Linearity

The linear model assumption that the outcome variable in the population shares a true, straight-line relationship with any predictor variables.

Additivity

The linear model assumption that when multiple predictors are included, their collective influence on the outcome variable is best represented by summing their individual effects together.

Expected Value of Errors is Zero

The assumption that prediction errors average to zero across all values of the model ($\sum (x - \bar{x}) = 0$), guaranteed mathematically by ordinary least squares (OLS) estimation so that overestimates and underestimates cancel each other out.

Homoscedasticity (Homogeneity of Variance)

The assumption that the variance of the outcome variable (or model residuals) is stable and relatively equal across all levels of a predictor variable, or across all experimental groups.

Heteroscedasticity

A violation of linear model assumptions where the variance of residuals changes systematically at different levels of a predictor, resulting in inaccurate standard errors, invalid confidence intervals, and compromised significance tests.

Independence of Errors

The spherical error assumption that residuals (prediction errors) are uncorrelated, meaning the error for one individual observation does not influence or predict the error for another observation.

Normality of Errors

The assumption in ordinary least squares (OLS) linear models that the unobservable errors of the model (manifested in the sample residuals) follow a normal distribution, regardless of the distribution of the raw observed variables.

Robust Test

A statistical analysis procedure or model (Wilcox, 2017) that remains accurate and maintains its validity even when standard parametric assumptions are broken.

Bootstrapping

A robust resampling technique that estimates the sampling distribution of a parameter by repeatedly drawing samples with replacement from the dataset ($n$ times over, e.g., $1{,}000$ iterations), computing the statistic for each sample, and deriving standard errors and confidence intervals from this empirical distribution.

Trimming the Data

A bias-reduction method that involves symmetrically deleting a fixed percentage of extreme observations (such as $5\%$, $10\%$, or $20\%$) from both tails of an ordered dataset.

Winsorizing (Windsorizing)

A robust data adjustment method wherein extreme outlier scores beyond a specified cut-off (e.g., top and bottom $5\%$, $10\%$, or $20\%$) are replaced by the most extreme remaining score that is not an outlier.

Data Transformation

The procedure of applying a mathematical function to all values of a variable to meet statistical assumptions; while it maintains ordinal relationships, it alters differences across variables and can hinder accuracy as often as it helps (Games & Lucas, 1966).