Shapiro-Wilk and Lilliefors, reported together. How to read them, why the p value works backwards from what you expect, and why a significant result is much less alarming than it looks.
Quanta runs Shapiro-Wilk and Lilliefors together and reports both, so you are not relying on a single test's quirks.
The p value works backwards from most tests you use. The null hypothesis here is that the data is normal. A large p value is therefore the reassuring outcome: it means no significant departure was detected. A small p means a departure was found.
This inversion catches people constantly. Seeing p < .001 on a normality test and concluding the data is definitely normal is a common and consequential misreading.
Quanta states the verdict in words next to each statistic rather than leaving you to remember the direction, and it says what the result implies for your next step.
Normality tests are tests of statistical significance, so their power rises with sample size. At n = 30 they detect only gross departures. At n = 250 they detect departures far too small to affect anything. At n = 5,000 almost any real dataset fails.
So a significant result answers "is this distribution detectably non-normal", which is not the question you care about. The question you care about is whether the departure is large enough to distort the analysis you are about to run, and these tests do not answer that.
Look at the distribution rather than only the test. The stem-and-leaf display and the mean-versus-median comparison in descriptives tell you the shape, and shape is what matters.
Most parametric tests are robust to moderate departures at reasonable sample sizes. A flag is a prompt to look, not an instruction to abandon the analysis.
Small samples. Under about 30 cases the central limit theorem is not doing much work for you, and a real departure matters.
Ordinal items. A single five-point Likert item cannot be normal: it has five possible values. Shapiro-Wilk will flag it every time, correctly and uninformatively. Here a rank-based test genuinely is the better choice, and not because the test flagged, but because the measurement is ordinal.
Heavy skew or real outliers. Where the departure comes from a long tail or a handful of extreme values, the mean itself is a poor summary and the test is pointing at something substantive.
Check the right thing. For a paired t test, the assumption concerns the differences, not the two sets of scores. For regression, it concerns the residuals, not the raw variables. Testing the wrong quantity is a common error that a passing result will not save you from.
Open Descriptives & Explore and select the field you want checked. The Normality card reports Shapiro-Wilk and Lilliefors with their statistics, p values, and a plain-language verdict.
Read the verdict, then look at the shape. The card sits next to the stem-and-leaf display for exactly that reason.
Note the sample size in the verdict. Quanta states it alongside the finding, which is the context that makes a significant result interpretable.
Use the action bar to add the result to a report, copy the table, or copy the APA text.
Report the statistic, the sample size, and p, and say what you did about it.
Shapiro-Wilk indicated a significant departure from normality, W = 0.905, p < .001 (n = 250). Given the ordinal response format, rank-based tests were used for the primary analyses.
Give a reason for your choice that is about the data, not about the test result. "The normality test was significant so we used a nonparametric test" is weaker than naming the ordinal measurement or the visible skew that actually justified it.
Do not report a normality test as evidence that your data is normal. Failing to reject is not confirmation, particularly at small samples where the test has little power.
Where you proceeded with a parametric test despite a flag, say so and say why. Robustness at your sample size is a legitimate reason and stating it is more credible than omitting the test.
Every result carries a ReliCheck Intelligence card with one action: explain this result in plain language. It runs entirely on your Mac with Apple Intelligence. No upload, no API key, nothing to configure. The model only explains the result Quanta has already computed and validated. It never computes a statistic, and it never applies a decision on your behalf.
From the action bar you can add the result to a report, copy the table, or copy the APA text. Exported reports carry the APA table, its note, and a caution specific to that analysis beneath it.
Quanta's engine is pure Swift on Apple's Accelerate framework, with no R or Python at runtime. Every engine is checked against an independent reference rather than internal consistency alone, and the automated suite exceeds 500 checks. Full record on the validation page.
Descriptives & Explore is part of every Quanta subscription, $9.99 a month or $79.99 a year after the 30-day trial. One price for everyone. See pricing.
The analysis, the report builder, and the on-device explanations all work with the network off. Your dataset is never uploaded.
Descriptive statistics mean against median as a shape check · Stem-and-leaf seeing the distribution rather than testing it · Mann-Whitney U the rank-based alternative · the complete list on the analyses page.