PSYC 5016 - Week 8: Data Visualization and Bias

Vocabulary flashcards covering data visualization methods, graphic formats, model assumptions, outlier bias, and corrective techniques from Week 8 of PSYC 5016.

Exploration vs. Presentation

The two primary complementary purposes of visualizing data: discovery and analysis of patterns, outliers, and assumptions (exploration) versus clearly communicating findings and statistical inferences to an audience (presentation).

Anscombe's Quartet

Four distinct datasets developed by F. J. Anscombe (1973) that share identical summary statistics—mean of $x = 9.0$, $SD_x = 3.3$, mean of $y = 7.5$, $SD_y = 2.0$, and correlation $r = .82$—yet reveal completely different underlying relationships and distributions when visualized.

Interocular Effect

A visual data display principle described by Tukey (1990) wherein a graph presents an immediate, clear message that hits the viewer right between the eyes.

Tufte's Visualization Principles

Guidelines established by Edward Tufte (2001) stating that graphs should show the data, avoid distorting it, present many numbers with minimum ink, make large datasets coherent, encourage visual comparisons, and induce the reader to think about the data rather than graphic design elements.

Bar Chart

A common chart type that displays summary statistics (such as means) using vertical or horizontal bars, often criticized for using excessive ink and obscuring underlying sample distributions unless combined with individual data points.

Boxplot (Box-Whisker Diagram)

A standardized visual display of a distribution that depicts the median, the interquartile range (IQR, encompassing the middle $50\%$ of data between quartiles Q1 and Q3), whiskers representing the minimum and maximum values without outliers, and individual points denoting extreme outliers.

Histogram

A graph that organizes continuous scores into adjacent discrete bins and uses the height of bars to represent the frequency or count of observations falling within each interval.

Density Plot

A smoothed continuous representation of the distribution of data points over a numeric variable, created via kernel density estimation as an alternative to a histogram.

Jitter Plot (Strip Plot)

A visualization of raw observations where a small amount of random horizontal displacement (jitter) is added to identical or closely positioned values along a discrete axis to reduce overplotting.

Dot Plot

A visual display representing individual observations or statistical estimates (such as means and confidence intervals) as distinct circular markers along an axis.

Violin Plot

A visualization that shows data distributions by mirroring a continuous kernel density curve on both sides of a central axis, providing an intuitive depiction of distribution shape and multimodality.

Raincloud Plot

A hybrid visualization combining raw individual observations (jitter plot), statistical summaries (boxplot), and a half-density smoothed distribution estimate to fully display central tendency, dispersion, clustering, and modality (Allen et al., 2021).

Slopegraph

A graph that visualizes changes in scores between paired or repeated conditions (such as baseline versus a follow-up assessment) by connecting data points for each participant or observation with a straight line.

Quantile-Quantile (Q-Q) Plot

A diagnostic graph plotting the quantiles of sample data against the theoretical quantiles of a specified distribution (often the normal distribution); observations falling along the diagonal line confirm conformance to the theoretical distribution.

Hexagonal Binning (Hexbin) Plot

A two-dimensional density plot used for large sample sizes (e.g., $N > 40{,}000$) that partitions the coordinate plane into regular hexagonal bins and shades each hexagon according to the frequency of observations within it (LaPlume, 2022).

Multidimensional Bubble Plot

A complex scatterplot variant that presents several variables simultaneously by varying marker coordinates (x and y variables), marker size, marker colour, panel facets, and animation frames across time (LaPlume, 2022).

Estimation

The formal statistical process of computing numerical estimates of population model parameters (such as regression intercepts and slopes) from sample data (Flora, 2017).

Outlier

An observation or set of observations markedly different from the rest of the sample data that can substantially bias parameter estimates (such as the mean), inflate error metrics (like sum of squared errors), and distort confidence intervals and standard errors.

Linearity Assumption

The linear modeling assumption that the true relationship between the outcome variable and each predictor variable in the population is linear; violation invalidates the model.

Additivity Assumption

The multivariable modeling assumption that the combined effect of several predictors on an outcome variable is accurately described by adding their separate individual effects together.

Expected Value of Errors is Zero

An assumption of linear regression stating that unobservable model errors have a mean of zero in the population ($\sum(x - \bar{x}) = 0$), which ordinary least squares (OLS) estimation mathematically guarantees so overestimates and underestimates cancel out.

Homoscedasticity (Homogeneity of Variance)

The spherical errors assumption that the variance of the outcome variable (or model residuals) remains stable and constant across all levels of a predictor variable or across distinct testing groups.

Heteroscedasticity

A condition in linear models where the variance associated with prediction errors systematically differs across values of the predictor, leading to inaccurate standard errors, confidence intervals, and significance tests.

Independent Errors Assumption

The assumption that model residuals (prediction errors) are uncorrelated and do not influence one another, meaning the prediction error for one participant provides no information about that of another.

Normality of Errors Assumption

The ordinary least squares (OLS) assumption that the unobservable errors of the model (manifested in the model residuals) are normally distributed, rather than requiring the observed raw data themselves to be normal.

Robust Test

A statistical procedure or model designed to maintain mathematical accuracy and validity even when standard parametric assumptions are broken (Wilcox, 2017).

Bootstrapping

A non-parametric resampling procedure that treats the sample as a pseudo-population and repeatedly draws samples with replacement (often $1000$ times) to estimate the empirical sampling distribution, standard error, and confidence intervals of a statistic.

Trimming

A bias-reduction technique that removes a fixed percentage of extreme values (such as $5\%$, $10\%$, or $20\%$) from both the upper and lower ends of an ordered dataset prior to statistical computation.

Windsorizing (Winsorization)

A method for handling outliers by replacing extreme scores with the nearest acceptable value in the distribution that is not classified as an outlier.

Data Transformation

The application of a consistent mathematical function to every raw score to help satisfy statistical assumptions, altering scale differences while preserving monotonic relationships between variables (Games & Lucas, 1966).