Why do examiners’ comments on the statistics chapter look so similar from one thesis to the next? Because the same fifteen statistical mistakes recur, and they recur for understandable reasons: SPSS computes whatever it is given, textbooks spend more pages on running tests than on preparing data, and most students report their first analysis under time pressure. The good news is that almost every item on this list is cheap to fix once it has a name. The statistical mistakes below are grouped by stage, from preparing the data to interpreting the results, and each entry gives the reason it matters, the fix, and a one-line example.
This article is part of our guide How to Write a Master’s Thesis by the Mastermind PhD team and relates to our Statistical Analysis service. Sources last checked: November 2026.
What is a statistical mistake in a thesis? An error in preparing the data, choosing or running a test, reporting a result or interpreting it that leads the reader to a conclusion the data do not support. Few statistical mistakes are computational. They are decisions: testing the wrong unit, skipping an assumption check, dropping a non-significant hypothesis, or describing a p value as if it measured importance. An experienced examiner spots most of them in minutes, which is why they attract comments out of proportion to the effort needed to avoid them.
Statistical mistakes in preparing the data
1. Negatively worded items were not reversed. Scale scores and reliability are distorted: alpha falls or turns negative, and group means drift toward the midpoint. Fix: reverse every negatively worded item before computing reliability or scale scores, and check the Item-Total Statistics table for negative correlations. Example: one satisfaction subscale returned α = .62 before item 7 was reversed and α = .84 afterwards.
2. Single Likert items were tested instead of scale scores. A single item is ordinal and unreliable, and testing 28 items across three groups means 84 tests, several of which will be significant by chance. Fix: compute the subscale scores the instrument was designed to yield (parametric tests on summed or averaged scales are defensible; Norman, 2010), test those, and describe items only where the research question requires it. Example: replace 28 one-way ANOVAs with four, one per subscale, and adjust alpha if several tests serve one hypothesis.
3. Missing data and outliers were handled silently. Listwise deletion changes the sample from table to table (N = 312 in Table 1, 287 in Table 6) with no explanation, and a few extreme cases pull means and regression lines. Fix: report missing values per variable, the rule applied (for example, cases with more than 20% of items missing excluded; scale scores computed with at least 75% of items), the outlier check (boxplots; standardized scores beyond ±3.29) and the decision. Example: “Six cases with more than 20% of items missing were excluded; all analyses are based on N = 383 unless stated.”
4. The sample size was asserted rather than justified, and tiny subgroups were compared. A table value such as 384 says nothing about the power of your comparisons, and a group of 9 principals compared with 280 teachers cannot support a conclusion. Fix: run an a priori power analysis for the main tests, and merge or exclude sparse categories before testing, saying so. Example: “A sample of 128 (64 per group) was required to detect d = 0.50 with 80% power at α = .05; 300 valid responses were obtained.”
Statistical mistakes in choosing and running the test
5. Several t tests were run where one ANOVA was needed. This is one of the most frequent statistical mistakes in group comparisons. Three groups compared with three t tests inflate the family-wise Type I error rate from 5% to about 14%. Fix: one-way ANOVA followed by a post hoc test (Tukey HSD, or Games-Howell when variances differ). Example: “F(2, 147) = 4.21, p = .017, η² = .054; Tukey HSD showed that only the third group differed from the first.”
6. Assumptions were not checked, or Levene’s test was misread. Normality is checked for the whole sample instead of within groups, and the “Equal variances assumed” row is read even when Levene’s test is significant. Fix: report the assumption checks in a short paragraph before the test, read the Welch row when variances differ, and switch to a non-parametric alternative for small non-normal groups. Example: “Levene’s test was significant, F(1, 298) = 4.22, p = .041, so Welch’s t test is reported: t(274.8) = 3.35, p = .001.”
7. Pearson’s r was used for ordinal or non-linear data, and the result was described as causal. Pearson’s coefficient assumes interval measurement and a linear relationship, and no correlation identifies the direction of influence. Fix: use Spearman’s rho for ranks and single items, inspect a scatterplot, and write “associated with”. Example: “Satisfaction was positively associated with commitment, r(310) = .42, p < .001″, not “satisfaction increased commitment”.
8. Regression was reported without diagnostics. Collinear predictors, dependent residuals and influential cases make coefficients unstable, and a three-category nominal variable entered as a number is treated as a quantity. Fix: report VIF values (below 5, preferably below 3), residual plots, influential cases, and dummy-code categorical predictors. Example: “All VIF values were below 2.1, residuals were approximately normal, and no case exceeded a Cook’s distance of 1.”
9. The test did not match the data type or the design. Chi-square with expected counts below 5 in more than 20% of cells, an independent samples t test on pre-test and post-test scores from the same students, or a parametric test on a two-point scale. Fix: match the test to the level of measurement and the design with a decision table; use Fisher’s exact test or merge categories, and use the paired t test or Wilcoxon for repeated measurements. Example: “Because three of six cells had expected counts below 5, categories were merged: χ²(1, N = 120) = 5.84, p = .016.”
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Statistical mistakes in reporting
10. p = 0.000, stray zeros and shifting decimals. SPSS rounds to three decimals; a probability is never zero, and statistics bounded by 1 take no leading zero. Fix: p < .001; p = .003, r = .42, α = .84 without a leading zero; d = 0.39 and SD = 0.71 with one; the same number of decimals in every row of a column. Example: “p = 0.000″ becomes “p < .001″.
11. Effect sizes and confidence intervals were omitted. A p value depends on sample size; it does not say how large a difference is, and APA 7 and the Journal Article Reporting Standards require an effect size for every test. Fix: d for t tests, η² for ANOVA, r or R² for associations, Cramér’s V for chi-square, with confidence intervals where available. Example: “t(298) = 2.05, p = .041″ becomes “t(298) = 2.05, p = .041, d = 0.24, 95% CI [0.01, 0.47]”.
12. SPSS output was pasted as the thesis table, and tables were not referred to. Gridlines, English column labels, six decimals, and a paragraph that says “the table below shows”. Fix: rebuild each table in APA format (number and title above, horizontal lines only, a note below), one table per research question, referred to by number before it appears. Example: “the table below shows” becomes “Table 6 shows”.
13. Results were reported selectively or changed after the fact. A non-significant hypothesis disappears from the chapter, a two-tailed test becomes one-tailed after p = .08 appears, or cases are removed until significance is reached. Fix: report every pre-stated hypothesis with the same completeness, fix the number of tails in the methodology chapter, and document every exclusion. Example: “H4 was not supported, t(298) = 1.13, p = .260, d = 0.13″ stays in the chapter.
Statistical mistakes in interpretation
14. p above .05 was read as “no effect” and p below .05 as “important”. A non-significant result in a small sample is absence of evidence, not evidence of absence, and statistical significance says nothing about practical magnitude (Wasserstein & Lazar, 2016). Fix: interpret effect sizes and their confidence intervals, write “no significant difference was detected”, and discuss power in the limitations. Example: “d = 0.12 was statistically significant in a sample of 600 but corresponds to a negligible difference in practice.”
15. Causal and general claims were drawn from a cross-sectional convenience sample. The design cannot support them, and examiners count such sentences among the most serious statistical mistakes because they read them as a misunderstanding of the method. Fix: align the strength of each claim with the design, hedge appropriately, and state the sampling limitation. Example: “The results demonstrate that leadership causes satisfaction” becomes “In this cross-sectional sample, leadership was positively associated with satisfaction.”
Worked example: one results sentence, before and after
Before: “There was a highly significant difference between males and females in burnout (t = 3.35, p = 0.000), proving that gender affects burnout.”
This sentence contains statistical mistakes 10, 11, 14 and 15, and it also omits the degrees of freedom, the group descriptives and the variance check behind the test.
After: “Levene’s test indicated unequal variances, F(1, 298) = 4.22, p = .041, so Welch’s t test is reported. Women (M = 3.49, SD = 0.64) reported higher burnout than men (M = 3.21, SD = 0.78), t(274.8) = 3.35, p = .001, d = 0.39, 95% CI of the difference [0.12, 0.44], a small-to-medium effect.”
The second version is longer by one line, removes all four statistical mistakes, and answers every question an examiner would otherwise ask: which test, why that version, how large the difference is, and in which direction.
How do you audit your results chapter before submission?
Each row of the table targets one or more of the statistical mistakes above, so work through it row by row before you submit.
| Check | Where to look | Pass criterion |
|---|---|---|
| Reversed items | Reliability output, Inter-Item Correlation Matrix | No negative correlations; α reported per subscale with item count |
| Unit of analysis | Hypothesis tests | Scale scores, not single items, unless the question concerns an item |
| Sample consistency | Every table | The same N, or a stated reason for each change |
| Power | Methodology chapter | A priori calculation for the main tests, or a stated limitation |
| Assumptions | Paragraph before each test | Normality per group, homogeneity of variance, and the consequence drawn |
| Test choice | Methodology and results | Each test matched to the level of measurement and the design |
| Number format | All text and tables | p < .001, no leading zeros on bounded statistics, consistent decimals |
| Effect sizes | Every inferential sentence | An effect size and, where available, a confidence interval |
| Tables | Results chapter | APA format, referred to by number, one per question |
| Hypotheses | Summary table | Every hypothesis stated in Chapter 1 has a decision |
| Language | Discussion | Associations, not causes; claims limited to the sample and design |
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Frequently asked questions
Is it a mistake to report non-significant results?
No. It is a mistake to hide them. A non-significant result reported with its test statistic, exact p value and effect size is a finding; a thesis that reports only what reached significance invites questions about what was left out.
Do I always need a Bonferroni correction?
Only when several tests address the same hypothesis or family of comparisons. State in the methodology chapter whether you adjusted the alpha level and how; if you did not, explain why the tests are treated as separate questions.
Can I use parametric tests with Likert data?
On scores formed from several Likert items, yes, with the usual checks; Norman (2010) reviews the evidence. On a single item, treat the data as ordinal and use the median, percentages and non-parametric tests.
What if my sample is too small for the planned test?
Report the power you had, use the appropriate non-parametric alternative where distributions are doubtful, and interpret cautiously. Do not remove cases, change tails or drop hypotheses to reach significance; those are statistical mistakes in their own right.
Should assumption checks appear in the thesis?
Yes, briefly: a paragraph or a small table before the inferential results, with the full output in an appendix if your department expects it. Examiners look for the check and for the decision that followed from it.
Sources
- Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). SAGE.
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum.
- American Psychological Association. (2020). Publication Manual of the American Psychological Association (7th ed.); Journal Article Reporting Standards: Quantitative. https://apastyle.apa.org/jars/quantitative
- Wasserstein, R. L., & Lazar, N. A. (2016). The ASA statement on p-values: Context, process, and purpose. The American Statistician, 70(2), 129–133. https://doi.org/10.1080/00031305.2016.1154108
- Norman, G. (2010). Likert scales, levels of measurement and the “laws” of statistics. Advances in Health Sciences Education, 15(5), 625–632.
- Delacre, M., Lakens, D., & Leys, C. (2017). Why psychologists should by default use Welch’s t-test instead of Student’s t-test. International Review of Social Psychology, 30(1), 92–101. https://doi.org/10.5334/irsp.82
- Pallant, J. (2020). SPSS Survival Manual (7th ed.). Open University Press.
Sources last checked: November 2026. This article is general educational guidance and does not replace your university regulations or your supervisor’s instructions. How we prepare our content.