Q-Q Plot

Figure purpose

This page is a guidance-only interpretation page for how Q-Q plots are commonly read in assumption review. It is not a claim that the current product exposes a dedicated Q-Q plotting renderer.

A Q-Q plot compares observed sample quantiles with the quantiles you would expect under an ideal reference distribution, often a normal distribution. When the points stay roughly on a straight line, the sample may be more consistent with that reference shape.

What this page gives you today is reading guidance: what a Q-Q plot is, what patterns usually matter, and how to avoid over-interpreting it. It should not be read as a promise that the current public figure surface will generate this plot on demand.

When to use or avoid

Use Q-Q plot as a supporting visual check when distribution shape matters for later interpretation. It is most useful when read together with sample size, outlier context, and other distribution views.

Avoid reading "the Q-Q plot looks fine" as "the analysis is safe." That jump is too strong, especially with small samples, mixed populations, or influential outliers.

Use it when the main question is whether the sample looks broadly compatible with a reference distribution. Avoid using it as a standalone pass/fail gate for model validity.

How to read a Q-Q plot

The common reading patterns are:

• Points close to a straight line: the sample is more compatible with the reference distribution in the plotted range.
• Systematic S-shape curvature: the sample may differ in skew or tail behavior from the reference distribution.
• Tail points bending away from the line: the tails may be heavier or lighter than the reference distribution, or a few extreme points may be influential.
• Isolated points far from the line: possible outliers or a small number of influential observations.

These are visual cues, not formal decisions. Similar-looking deviations can arise from different causes, including skew, mixtures of subpopulations, discretization, ceiling effects, or a few extreme rows.

Required columns

• Conceptually, Q-Q plot needs one numeric variable.
• In the current docs set, this page should be read as interpretation guidance rather than as a confirmed dedicated figure contract.

Because this page is guidance-only, the "required columns" section is conceptual rather than a promise about a current UI contract.

Related statistics or disclosure

Q-Q plot and Histogram can complement each other. Histogram helps you inspect overall shape and bin-based concentration, while Q-Q plot helps you compare the sample against an ideal reference line.

Neither view should be treated as a final yes-or-no certification step on its own. For assumption-sensitive contexts, read this page together with Normality and Homoscedasticity Checks.

Licklider does not automatically determine from a Q-Q plot alone whether an apparent deviation is practically important, whether it is driven by outliers, or whether a parametric method would still be robust enough for the sample size and design. That is why this page positions Q-Q reading as supporting evidence rather than as an automatic decision system.

Design rationale and references

Licklider keeps this page in guidance-only mode because the important user need right now is interpretive literacy: many researchers see Q-Q plots in textbooks, software, and review comments, but may not know how to read them without over-claiming what they prove.

The page also frames Q-Q plots as supporting diagnostics rather than as standalone arbiters of validity because graphical normality checks work best when combined with sample-size context, outlier review, and formal assumption checks [1, 2]. A visually straight pattern can still coexist with a poor design choice, and a visibly imperfect pattern does not automatically invalidate every parametric analysis.

Methodological foundations

1. Fox, J. (2016). Applied Regression Analysis and Generalized Linear Models (3rd ed.). SAGE Publications. -> Practical reference for using Q-Q plots as graphical diagnostics rather than as binary proof of model adequacy.

2. Thode, H. C. (2002). Testing for Normality. CRC Press. -> Standard reference on formal and graphical normality assessment, including the complementary role of Q-Q plots.

Current support boundary

• This page is an interpretation guide, not a confirmed dedicated figure contract for the current public product.
• Licklider does not claim here that a standalone Q-Q renderer is available just because the concept is documented.
• Licklider does not automatically determine from a Q-Q plot whether non-normality is severe enough to require a different model or test.
• Licklider does not automatically identify the cause of deviation from the reference line; outliers, skew, mixtures, truncation, and discretization can look similar in a Q-Q view.
• Use this page to understand how to read Q-Q-style evidence, then pair that interpretation with Histogram and Normality and Homoscedasticity Checks.

Alternative figures

• Use Histogram for a more direct view of skew, spread, and multimodality.
• Use Residual Plot only as a conceptual next step when model-specific diagnostics matter, since that page is also still conservative in its current support level.

TODO (Phase02+)

• If a dedicated Q-Q renderer is added later, update this page from guidance-only interpretation notes to an implementation-backed figure page.