Histogram

A histogram is the standard display for the distribution of a single continuous variable. Its most common failure is arbitrary bin-width selection: too few bins hide structure, too many bins create noise. Licklider applies automatic bin-width optimization and discloses the method used, eliminating one of the most common sources of misleading histograms.

STEP 1 —When to Use

Use a histogram when: you need to show the distribution shape of a single continuous variable; you want to visually assess normality, skewness, or bimodality; n >= 30 (below this, individual data or a dot histogram is more honest); you are comparing frequency distributions across two groups (overlapping semi-transparent histograms).

Do not use a histogram when: n < 20 (use a strip plot instead); you are comparing many groups (use violin plots); the primary message is the summary statistic, not the distribution shape.

[Image placeholder: Three histograms of the same dataset (n=80, right-skewed). Left: too few bins (5) —appears symmetric. Center: optimal bins (Sturges rule: 12) —reveals right skew clearly. Right: too many bins (50) —looks noisy, right skew obscured. Demonstrates the impact of bin-width selection.]

Bin-width matters: 5 bins (left) hides skewness. Optimal 12 bins (center) reveals it. 50 bins (right) creates noise.

STEP 2 —Journal Requirement

Bin-width or bin count method must be stated in the legend: "Bin width selected by Freedman-Diaconis rule."
Y-axis label must specify frequency, count, or probability density —these are not interchangeable.
If a normal curve is overlaid, this must be labeled: "Normal distribution curve fitted to the data."
n (total observations in the histogram) must be stated.

STEP 3 —Licklider Implementation

Input

Continuous variable column
Optional: grouping variable (for overlapping group histograms)
Bin-width method: Freedman-Diaconis (default, robust to outliers), Sturges, Scott, or user-specified
Y-axis: count, frequency (proportion), or density

Output

Histogram with auto-optimized bin width
Bin method and bin count labeled in legend
Optional normality curve overlay (Shapiro-Wilk result auto-appended to legend)
Optional KDE curve overlay (bandwidth labeled)
For two groups: semi-transparent overlapping histograms with distinct fills
Normality test result (Shapiro-Wilk W and p) displayed as a text annotation if normality check is enabled

[Image placeholder: Licklider histogram (n=65, right-skewed data). Freedman-Diaconis bin width, frequency density on y-axis, normal curve overlay (shown as dashed line), Shapiro-Wilk annotation: "W=0.91, p=0.003 (non-normal)", n=65 labeled, bin method in legend.]

Licklider histogram: optimal bins (Freedman-Diaconis), normality curve overlay, and Shapiro-Wilk result annotated.

STEP 4 —Draft Output (Draft / Needs review)

Histogram of [variable] for n = 65 observations. Bin width was selected
using the Freedman-Diaconis rule (bin width = 2.3 units; 18 bins).
Y-axis shows probability density. A fitted normal distribution is overlaid
for reference (dashed line). Shapiro-Wilk normality test: W = 0.91,
p = 0.003, indicating significant departure from normality.