You're a third‑year PhD candidate in clinical psychology, your supervisor wants the quantitative chapter by Friday, and the Shapiro‑Wilk test on your pre‑intervention scores gave a p‑value below .05, flagging non‑normality and throwing your planned ANOVA into doubt. You’ve already tried a few transformations with little improvement, and the thought of rewriting the hypothesis section feels overwhelming.
What does “normality” actually mean for my doctoral prospectus?
When the module guide lists “assumption of normality” it’s not asking you to prove a perfect bell curve; it’s checking whether the residuals of your model are roughly symmetric and free of extreme outliers. The rubric typically circles the terms Shapiro‑Wilk, skewness, kurtosis, and the phrase “distributional assumptions”. Graders expect you to report the test statistic, the p‑value, and a brief interpretation that connects the result to your analytic choice.
In practice, the SPSS output shows the W statistic (e.g., W = 0.78) and the p‑value. If p < .05, the null hypothesis of normality is rejected. That doesn’t automatically invalidate every parametric test, but it does raise a red flag that the Type I error rate could be inflated, especially with small sample sizes common in clinical trials.
Consider a concrete scenario: you have 28 participants, each with a pre‑intervention depression score. The Shapiro‑Wilk yields W = 0.71, p = .02, and the histogram shows a right‑skewed tail. The rubric will look for you to note the sample size, the test result, and the visual evidence (histogram or Q‑Q plot). If you simply write “data are non‑normal” without justification, the committee may deduct points for incomplete reporting.
Actionable takeaway: list the exact statistics the rubric demands, attach a histogram or Q‑Q plot, and explain why the deviation matters for an ANOVA.
Why does the Shapiro‑Wilk result break my ANOVA plan?
The technical dead end stems from the ANOVA’s reliance on the normality of residuals, not the raw scores. SPSS assumes that each group’s errors are normally distributed. When the pre‑intervention scores are skewed, the residuals in a mixed‑design ANOVA can inherit that skew, leading to inaccurate F‑ratios.
Three common failure modes appear in the output:
- Significant Shapiro‑Wilk p‑value for a group, yet the ANOVA table still reports a “significant” main effect—this mismatch can be flagged by reviewers.
- Levene’s test for homogeneity of variance may also turn significant, compounding the problem.
- Box’s M test (if you run a MANOVA) often flags non‑sphericity when normality is violated.
One practical fix is to switch to a robust ANOVA method, such as the Welch correction, which SPSS can compute by selecting “Options → Welch” in the GLM dialog. Another route is a non‑parametric alternative like the Friedman test for repeated measures, which sidesteps the normality assumption entirely.
Transformation attempts (log, square‑root, inverse) sometimes succeed when the skewness originates from a single outlier. If the histogram still shows a heavy tail after transformation, the data are likely intrinsically non‑normal—perhaps due to a floor effect in your clinical measure.
Key warning: don’t force a transformation that makes the data look normal but distorts the clinical meaning. A log‑transformed depression score is harder to interpret for your audience and may raise questions about construct validity.
Will my supervisor flag the non‑normal data as a methodological flaw?
Integrity fear often revolves around how the prospectus will be judged for methodological rigor. The committee’s primary concern is whether you’ve acknowledged the assumption violation and chosen an appropriate analytic path. If you simply ignore the Shapiro‑Wilk result, the reviewer may note “failure to address normality assumptions” and deduct points.
To keep the integrity flag low, follow these steps:
- Document the Shapiro‑Wilk statistic, p‑value, skewness, and kurtosis in a concise table.
- Include the histogram and Q‑Q plot as supplemental figures.
- State explicitly whether you will (a) proceed with a robust ANOVA, (b) adopt a non‑parametric test, or (c) report the violation and discuss its impact.
- Justify the choice with a brief citation of standard practice (e.g., “When normality is violated and sample size < 30, non‑parametric tests are recommended”).
When you write the hypothesis section, re‑frame the language to match the analytic decision. Instead of “We expect a significant difference in mean scores,” you might say “We expect a difference in median scores, assessed with the Friedman test.” This shows you’ve aligned your hypotheses with the statistical method, which reviewers appreciate.
One common mistake is to leave the original ANOVA in the draft while tacking on a footnote about the violation. That creates confusion and suggests you’re not confident in the analysis. Choose one path and follow through consistently.
Takeaway: transparent reporting of the violation and a justified alternative analysis will satisfy the committee more than a forced parametric test.
How can I salvage the chapter in two days?
Time is tight, but a focused plan can get you a polished chapter by Friday. Below is a checklist you can start tonight, followed by a decision matrix that helps you pick the quickest viable analysis.
Two‑day action checklist
- Re‑run Shapiro‑Wilk for each group and copy the exact W and p values into a new SPSS output window.
- Generate histograms and Q‑Q plots for raw and log‑transformed scores; save as .sav files for easy insertion.
- Choose an analysis route:
- If transformation yields p > .05 for all groups, proceed with the original ANOVA.
- If not, run the Welch ANOVA (GLM → Options → Welch) and note the adjusted F and p.
- If Welch still shows violation, switch to the Friedman test (Analyze → Nonparametric Tests → Related Samples).
- Copy the output tables into your Word document, replace the default SPSS headings with APA‑style labels (e.g., “Table 1. Shapiro‑Wilk Tests of Normality”).
- Update the hypothesis paragraph to reflect the chosen test (mean vs. median, parametric vs. non‑parametric).
- Write a brief “Assumption Checks” subsection: one paragraph describing the Shapiro‑Wilk result, the visual checks, and the decision you made.
- Proofread for APA 7 formatting: italicize statistical symbols, round p‑values to three decimals, and include effect size (e.g., η² or Kendall’s W).
- Send the draft to your supervisor by Wednesday evening for a quick sanity check; incorporate any feedback by Thursday night.
Decision matrix for the next 48 hours
| Condition | Analysis option | Key output | Interpretive note |
|---|---|---|---|
| All groups p > .05 after log transformation | Standard repeated‑measures ANOVA | F, p, η² | Report means, note transformation in methods. |
| Any group p ≤ .05 even after transformation | Welch’s ANOVA (robust) | F_welch, p, ω² | State that Welch correction addresses heterogeneity. |
| Welch still violates assumptions or N < 30 | Friedman test (non‑parametric) | χ², p, Kendall’s W | Interpret medians; discuss clinical relevance. |
The matrix lets you see at a glance which analysis fits the data you have tonight. If you can get a p > .05 after a simple log, you’ll stay with the original ANOVA and only need to add a transformation note. If not, the Welch option adds only a few clicks in SPSS and yields an APA‑ready table. The Friedman test is a bit more work (ranking each participant), but it’s the safest fallback if assumptions remain broken.
Final tip: keep the narrative tight. Start the results section with the assumption check, then present the chosen test’s table, and finish with a brief interpretation that ties back to your research question. That flow satisfies the rubric’s demand for logical progression.
Good luck—you’ve got the data, the software, and a clear plan. Stick to the checklist, let the matrix guide your analysis choice, and you’ll have a solid quantitative chapter ready for Friday.