Scatter Plot

The scatter plot is the fundamental visualization for the relationship between two continuous variables. Its most common error is the implied causal claim: a regression line drawn through a scatter plot, even without an equation, visually implies that X predicts or causes Y. Licklider's scatter plot requires explicit disclosure of whether the relationship is associative or causal.

STEP 1 —When to Use

Use a scatter plot when: you want to display the relationship between two continuous variables; you want to show the correlation coefficient with its confidence interval; you want to identify subgroup patterns within the bivariate relationship (color by group).

Overplotting guard: for n > 200, point transparency is required; for n > 500, a 2D density contour is recommended instead.

[Image placeholder: Scatter plot with n=45. Two variables, color by group (3 groups). Pearson r and 95% CI shown as text annotation in the plot. No regression line (correlation only). Each group shown with distinct point shapes. Points semi-transparent to show overlap.]

Scatter plot: correlation coefficient with 95% CI annotated. No regression line —correlation does not imply causation, and no line means no causal implication.

STEP 2 —Journal Requirement

Correlation coefficient type (Pearson or Spearman) must be stated with its 95% CI.
If a regression line is shown: Rﾂｲ, slope, and 95% CI for the slope must be stated.
Correlation vs. causation disclosure: the legend or methods must state whether the relationship is associative or causal, and what justifies the claim.
n must be stated. For multiple groups, n per group.

STEP 3 —Licklider Implementation

Input

Two continuous variables (x and y)
Optional: categorical grouping variable (color and shape)
Correlation method: Pearson (parametric, default executed) with Spearman (non-parametric, advisory when residual normality fails) always available in the Inspector
Regression line: optional (with causation disclosure trigger)

Output

Scatter points with optional transparency (auto-applied for n > 200)
Correlation coefficient r and 95% CI annotated on figure
p-value for correlation (with note if n is large and p is trivially small)
Optional smooth LOESS curve (non-parametric trend, non-causal)
Correlation vs. Causation guard: fires when regression line is requested —requires user to declare causation basis or label the line as "associative fit"

[Image placeholder: Licklider scatter plot with LOESS smooth (not linear regression). Annotation: "r = 0.54 (95% CI [0.31, 0.72]), Pearson, n = 48." Legend note: "LOESS smooth shown for visualization; relationship is associative, not causal." Colorblind-safe group colors.]

Licklider scatter with LOESS smooth: correlation annotated, causation disclosure in legend, colorblind-safe group colors.

STEP 4 —Draft Output (Draft / Needs review)

Scatter plot of [Y] versus [X] (n = 48). Pearson correlation: r = 0.54
(95% CI [0.31, 0.72], p < 0.001). A LOESS smooth is shown for
visualization purposes. The relationship between [X] and [Y] is
associative; no causal claim is made. Statistical independence of
observations was verified (Durbin-Watson = 1.94).