You have just run a one-way ANOVA comparing pain scores across four treatment groups — placebo, low dose, medium dose, and high dose — and the F-test returns p = 0.0003. Your supervisor says: "Good. Now which groups actually differ?" This is the question ANOVA deliberately does not answer. The F-test is a doorbell: it tells you that something is happening inside the house, but you still need to open every room to find out what. Post hoc tests are the keys to those rooms. The challenge is that you have six rooms to check (six pairwise comparisons among four groups), and each time you check, you risk a false alarm. The two most widely used methods for controlling that risk in medical research — Tukey's HSD and the Bonferroni correction — solve the same problem by different strategies, with real consequences for statistical power and which findings survive.
Why Post Hoc Testing Is Required After ANOVA
The one-way ANOVA F-test answers one specific question: "Is there at least one difference among the group means?" If the F-test is significant, you know that the null hypothesis of equal means is false — but you have no information about which groups differ, by how much, or in which direction. This is why the ANOVA F-test is called an omnibus test: it evaluates all groups simultaneously and returns a single p-value for the overall pattern.
To identify the specific pairs of groups that differ — the clinically actionable information — you need to follow up with pairwise comparisons. But here lies the fundamental problem that post hoc methods are designed to solve.
The Multiple Comparisons Problem
With k groups, there are k(k−1)/2 distinct pairwise comparisons. If you compare each pair using a standard t-test at α = 0.05, the probability of at least one false positive — declaring a difference significant when none exists — rises sharply with the number of comparisons. This is the family-wise error rate (FWER):
FWER = 1 − (1 − α)ᵇ ≈ mα (for small α)
Alpha Inflation: How Type I Error Rises With Comparisons
At m=6 (4 groups), uncorrected testing has a 26.5% chance of at least one false positive — 5.3× the nominal α = 5%. Both Tukey and Bonferroni constrain this back to 5%.
Post hoc tests are specifically designed to keep the FWER at or below the nominal α level (typically 0.05) while still providing meaningful statistical power to detect true differences. They differ in how they achieve this control, which is why the choice between methods matters.
The Bonferroni Correction
The Bonferroni correction is the simplest and most general method for controlling the FWER. Named after Italian mathematician Carlo Emilio Bonferroni, it adjusts the significance threshold for each individual comparison by dividing the desired α by the total number of comparisons m:
The logic is straightforward: if each test uses a threshold of α/m, the sum of individual error rates is at most α, guaranteeing the FWER is controlled. For example, with 6 pairwise comparisons among 4 groups, the Bonferroni threshold is 0.05/6 = 0.0083 per test. A comparison must have a raw p-value below 0.0083 to be declared significant.
Strengths and Limitations of Bonferroni
Strengths: Bonferroni is universally applicable — it works for any number of m tests of any type, not just pairwise group comparisons. It is simple to explain, easy to compute by hand, and accepted across all scientific disciplines without question. It is also the most conservative approach available, which means it has the lowest Type I error rate of any post hoc method.
Limitations: Because Bonferroni treats every test as independent, it is overly conservative when comparisons are correlated (as pairwise comparisons always are — the groups share the same error variance). When the number of comparisons m is large (m ≥ 5–6), Bonferroni sacrifices substantial statistical power, increasing the Type II error rate (missing real differences). For a study comparing 5 treatment groups (m = 10 pairwise comparisons), the Bonferroni threshold of α/10 = 0.005 makes it very difficult to detect moderate true effects.
Tukey's HSD (Honestly Significant Difference)
Tukey's HSD, introduced by statistician John Tukey in 1949, was designed specifically for the problem of comparing all possible pairs of means following ANOVA. Instead of adjusting the individual significance threshold, Tukey's method uses the Studentized range distribution (q-distribution) to compute the minimum mean difference that must be exceeded for significance:
Two group means are declared significantly different at the α level if their mean difference exceeds the HSD. Importantly, Tukey's method accounts for the correlation among pairwise comparisons — because the comparisons share common group means and a common error term, they are not independent, and treating them as such (as Bonferroni does) is unnecessarily conservative.
Strengths and Limitations of Tukey's HSD
Strengths: Tukey's HSD is more powerful than Bonferroni for complete pairwise comparisons (all pairs tested) because it correctly exploits the correlation structure of pairwise contrasts. As the number of groups increases, the power advantage over Bonferroni grows substantially. Tukey's method is the gold standard for all-pairwise comparisons in ANOVA, recommended by most statistical guidelines for medical research when the equal variance assumption holds.
Limitations: Tukey's HSD is specifically designed for all pairwise comparisons. If you are conducting only a planned subset of comparisons, or comparing groups against a single control (where Dunnett's test is appropriate), Tukey's method is not optimal. Tukey also assumes equal group variances (homoscedasticity) and equal (or approximately equal) sample sizes for the exact formulation; the Tukey-Kramer extension handles unequal sample sizes, but when variances differ significantly (Levene's test p < 0.05), the Games-Howell procedure should be used instead.
Tukey vs Bonferroni: Direct Comparison
The choice between Tukey and Bonferroni is not arbitrary — it follows from the specific comparison structure your study requires. The following table compares both methods alongside other common post hoc tests to assist in method selection:
| Method |
Best for |
Variance assumption |
Power (vs Bonferroni) |
Software |
| Tukey's HSD |
ALL pairwise comparisons among k groups |
Equal variances required |
Higher power when m ≥ 4 |
SPSS, R, SAS, Prism |
| Bonferroni |
Any set of m comparisons (pairwise or planned contrasts); preferred when m is small |
No specific assumption |
Lower power as m grows; competitive at m ≤ 3 |
All software + by hand |
| Games-Howell |
All pairwise comparisons when variances are unequal (Levene p < 0.05) |
No equal-variance assumption |
Similar to Tukey HSD |
SPSS, R |
| Dunnett's test |
Comparing all groups vs ONE control group only |
Equal variances required |
Highest power for control comparisons |
SPSS, R, SAS |
| Scheffé |
Complex contrasts (linear combinations, not just pairwise) |
Equal variances required |
Most conservative; lowest power of all |
SPSS, R, SAS |
| Holm-Bonferroni |
Any set of m tests — more powerful sequential variant of Bonferroni |
No specific assumption |
Always ≥ Bonferroni power |
R, SAS |
The bottom line: When all pairwise comparisons are planned and equal variances are confirmed (Levene's test p ≥ 0.05), use Tukey's HSD. When you have a pre-specified small subset of comparisons, or when comparing across different outcomes (not just group pairs), use Bonferroni. When variances are unequal, use Games-Howell for pairwise tests or Welch's ANOVA + Games-Howell for the full analysis.
Decision Guide: Which Post Hoc Test to Choose
1
Is the ANOVA F-test significant (p < 0.05)?
YES — proceed to post hoc testing | NO — do not proceed (Type I error protection; conclude no group differences)
2
Does Levene's test of homogeneity of variances return p < 0.05?
YES (variances unequal) — use Welch's ANOVA + Games-Howell for all pairwise comparisons | NO (variances equal) — continue to step 3
3
Are you comparing ALL possible group pairs?
YES — use Tukey's HSD (more powerful for all pairwise) | NO — proceed to step 4
4
Are you comparing all groups against a single control group only?
YES — use Dunnett's test (optimised for control comparisons) | NO — use Bonferroni (flexible for any planned subset of m comparisons)
Clinical Examples
1
Analgesic Dose-Response: Four-Group Drug Trial
A randomised controlled trial evaluates three doses of a new analgesic (50 mg, 100 mg, 200 mg) against placebo in 60 patients with chronic low back pain (n = 15 per group). The primary outcome is pain score on a 0–10 NRS at 4 weeks. One-way ANOVA is significant. Which dose groups differ?
7.1
Placebo mean ± SD (1.4)
4.7
100 mg mean ± SD (1.5)
3.4
200 mg mean ± SD (1.3)
ANOVA Result
F(3, 56) = 14.82, p < 0.001, η² = 0.443 (large effect)
MSE = 2.14, df_error = 56
Levene's test: F(3, 56) = 0.72, p = 0.547 → equal variances, Tukey appropriate
Tukey HSD Calculation
q(0.05, k=4, df=56) ≈ 3.74 (from Studentized range table)
HSD = 3.74 × √(2.14 / 15) = 3.74 × 0.378 = 1.41
Mean difference ≥ 1.41 NRS points → statistically significant
| Comparison | Mean Diff | Exceeds HSD? | Tukey p-adj | Result |
|---|
| Placebo vs 50 mg | 1.30 | No (1.30 < 1.41) | 0.142 | n.s. |
| Placebo vs 100 mg | 2.40 | Yes | 0.001 | p < 0.05 |
| Placebo vs 200 mg | 3.70 | Yes | <0.001 | p < 0.001 |
| 50 mg vs 100 mg | 1.10 | No | 0.418 | n.s. |
| 50 mg vs 200 mg | 2.40 | Yes | 0.001 | p < 0.05 |
| 100 mg vs 200 mg | 1.30 | No | 0.142 | n.s. |
Tukey HSD: 100 mg and 200 mg doses both significantly reduced pain vs placebo. Adjacent doses (50–100 mg and 100–200 mg) do not differ significantly from each other.
Clinical interpretation: The minimum effective dose is 100 mg. The 50 mg dose fails to separate from placebo (p = 0.142), while 100 mg and 200 mg both achieve meaningful reductions. The 100 mg vs 200 mg comparison is non-significant (p = 0.142), suggesting the additional efficacy of doubling the dose does not justify the increased side-effect burden — a clinically important finding that guides dose selection for the Phase III programme. Note: Had Bonferroni been used here (threshold 0.05/6 = 0.0083), both the 100 mg vs placebo and 50 mg vs 200 mg comparisons would have required p < 0.0083. At these borderline p-values (0.001 and 0.001), both remain significant, but in a study with smaller n, Tukey's greater power would matter more.
2
Surgical Technique Comparison: Five Hospitals
A multicentre study compares operative time (minutes) for laparoscopic cholecystectomy across five hospitals using different team protocols (A through E), with n = 20 patients per hospital (N = 100). The ANOVA F-test is significant. The research question is whether any hospital outperforms the others — requiring all 10 pairwise comparisons. Here we demonstrate why Tukey dominates Bonferroni as the number of comparisons grows.
10
Pairwise comparisons (m)
0.005
Bonferroni threshold (0.05/10)
≅3.86
Tukey q critical (k=5, df=95)
≅4.42
Bonferroni t critical (df=95, α=0.005)
ANOVA Result
F(4, 95) = 6.14, p < 0.001, η² = 0.205 (large effect)
Hospital means: A=68, B=74, C=63, D=81, E=71 minutes | MSE=82.4
Levene's test: F(4, 95) = 1.38, p = 0.248 → equal variances confirmed
Minimum Detectable Difference at α = 0.05
Tukey HSD: q(0.05,5,95) × √(82.4/20) = 3.86 × 2.03 = 7.84 min
Bonferroni: t(0.005,95) × √(82.4/20 × 2) = 2.88 × 2.87 = 8.27 min
Tukey detects differences ≥ 7.84 min; Bonferroni requires ≥ 8.27 min
A difference of 8.1 min: Tukey detects it, Bonferroni misses it
For 5 groups (10 comparisons), Tukey's HSD is 5.2% more sensitive than Bonferroni — the gap grows further with more groups
Why this matters: Hospital D (81 min) vs Hospital C (63 min) shows an 18-minute difference — easily detected by both methods. But Hospital D vs Hospital A (13 min difference) sits between the two thresholds: detected by Tukey (13 > 7.84), missed by Bonferroni only if the difference lands near the boundary. In a real clinical performance evaluation, misclassifying one hospital as "equivalent" when it actually takes 13 minutes longer per procedure matters for staffing, resource allocation, and patient throughput. This example illustrates a practical rule: with 5 or more groups requiring all pairwise comparisons, Tukey should be the default choice.
3
HbA1c Across Glycaemic Categories: Unequal Group Sizes
An endocrinology clinic measures HbA1c (%) in three patient groups: normoglycaemic controls (n = 35), prediabetic (n = 28), and type 2 diabetic (n = 42). ANOVA is significant. Group sizes are unequal, so the Tukey-Kramer extension is needed. Levene's test returns p = 0.018 — variances are heterogeneous — triggering a switch to Games-Howell.
5.3%
Normal (n=35, SD=0.3)
6.1%
Prediabetic (n=28, SD=0.5)
8.4%
Diabetic (n=42, SD=1.2)
0.018
Levene's p (heterogeneous)
Welch's ANOVA (replacing standard ANOVA due to unequal variances)
Welch F(2, 52.7) = 98.4, p < 0.001 (robust to variance heterogeneity)
Games-Howell Post Hoc (replacing Tukey due to Levene p < 0.05)
Normal vs Prediabetic: Δ = 0.8%, p < 0.001, 95% CI [0.62, 0.98]
Normal vs Diabetic: Δ = 3.1%, p < 0.001, 95% CI [2.68, 3.52]
Prediabetic vs Diabetic: Δ = 2.3%, p < 0.001, 95% CI [1.84, 2.76]
All three pairs significantly differ (all p < 0.001). Games-Howell correctly handles heterogeneous variances and unequal group sizes where Tukey would be invalid.
Clinical and methodological insight: The diabetic group's SD (1.2%) is four times that of the normoglycaemic group (0.3%), reflecting the wide variability in glycaemic control among diabetic patients. Using standard Tukey's HSD in this setting would be statistically inappropriate — it assumes equal variance across groups and would produce incorrect critical values and p-values. Levene's test is always the gatekeeper: run it before selecting your post hoc method, and switch to Games-Howell if it is significant. In SPSS, both tests are available in the same dialog: Options → Homogeneity of Variance Test; Post Hoc → Games-Howell.
Thesis Writing Recommendations
Methods Section
State clearly: (1) the statistical package and version used (SPSS 28, R 4.3.1, GraphPad Prism 10); (2) that you first assessed homogeneity of variances with Levene's test; (3) the post hoc method selected and the explicit reason — "Tukey's HSD was used for all pairwise comparisons as Levene's test confirmed homogeneity of variances (p = 0.547)" or "Games-Howell was used as Levene's test indicated heterogeneous variances (p = 0.018)"; (4) the family-wise error rate maintained at α = 0.05.
If Bonferroni was chosen for a specific subset of planned comparisons, justify why those specific pairs were pre-specified: "Three planned comparisons were specified a priori based on clinical hypotheses (dose 1 vs dose 3, dose 1 vs placebo, and dose 3 vs placebo). Bonferroni correction was applied (corrected α = 0.05/3 = 0.017)."
Results Section
Model Reporting Sentence — Tukey HSD
"One-way ANOVA revealed a significant effect of analgesic dose on pain score [F(3, 56) = 14.82, p < 0.001, η² = 0.44]. Levene's test confirmed homogeneity of variances [F(3, 56) = 0.72, p = 0.547]. Post hoc analysis using Tukey's HSD indicated that pain scores were significantly lower in the 100 mg group (mean = 4.7 ± 1.5) compared to placebo (mean = 7.1 ± 1.4; mean difference = −2.4, 95% CI: −3.8 to −1.0, p = 0.001) and in the 200 mg group compared to placebo (mean difference = −3.7, 95% CI: −5.1 to −2.3, p < 0.001). No significant difference was observed between the 50 mg group and placebo (p = 0.142) or between adjacent dose groups."
Model Reporting Sentence — Bonferroni
"Post hoc pairwise comparisons were conducted using Bonferroni correction (corrected α = 0.05/6 = 0.0083 for six comparisons). Pain scores in the 200 mg group were significantly lower than placebo (pₐᵤʲ < 0.001) and than the 50 mg group (pₐᵤʲ = 0.006). The 100 mg vs placebo comparison approached but did not reach the Bonferroni-corrected threshold (pᵣᵚᵛ = 0.009, pₐᵤʲ = 0.054). No other comparisons were significant after correction."
Always present a complete pairwise comparison table in the results (not just a list of significant pairs). Include mean differences, 95% CIs, and adjusted p-values for every comparison — non-significant comparisons are part of the result and must be reported. Include effect size (η² or ω²) for the overall ANOVA.
Common Mistakes Researchers Make
Mistake 1: Running Post Hoc Tests After a Non-Significant ANOVA
The ANOVA F-test is a gatekeeper. Running post hoc pairwise comparisons when the overall F is not significant (p ≥ 0.05) inflates the Type I error rate — the ANOVA's protection against false positives only works when you obey its decision. Finding a "significant" pair after a non-significant F-test is a spurious result that reviewers will correctly reject.
Fix: Only proceed to post hoc testing when the overall F-test is significant. If you had strong a priori hypotheses about specific pairs, these should have been pre-specified as planned contrasts (not post hoc tests) before data collection, with Bonferroni correction applied regardless of the overall F.
Mistake 2: Skipping the Levene's Test
Tukey's HSD and Bonferroni both assume homogeneity of variances. When group variances are heterogeneous (Levene's test p < 0.05), applying Tukey produces incorrect p-values — typically too liberal, detecting differences that do not exist at the stated α level. This error is common when one group has much wider spread than others (e.g., a diabetic group with high intra-group variability).
Fix: Always run Levene's test before selecting your post hoc method. In SPSS: Analyze → Compare Means → One-Way ANOVA → Options → check "Homogeneity of variance test." If Levene's p < 0.05, use Welch's ANOVA + Games-Howell.
Mistake 3: Running Multiple t-Tests as "Post Hoc" Analysis
Substituting multiple pairwise t-tests at α = 0.05 for a proper post hoc method is statistically equivalent to using no correction at all. With 4 groups (6 tests), the FWER reaches 26.5%. This error frequently appears in papers from clinical disciplines where the researcher is more comfortable with the t-test than with ANOVA post hoc procedures.
Fix: Use a dedicated post hoc method. If software is not available, manually apply Bonferroni correction by dividing α by the number of comparisons and using the corrected threshold for each t-test. Report the correction explicitly.
Mistake 4: Choosing Scheffé When All Pairwise Comparisons Are Planned
Scheffé's test is the most conservative post hoc method available — it is designed for exploratory comparisons involving complex contrasts (linear combinations of means), not simple pairwise differences. Using Scheffé when you only need pairwise comparisons wastes statistical power unnecessarily. Many researchers choose it because it appears "safer," but this false conservatism increases Type II error.
Fix: Use Tukey for all pairwise comparisons. Reserve Scheffé only for complex contrasts (e.g., comparing the mean of groups A and B combined against the mean of groups C and D combined).
Mistake 5: Reporting Only Significant Pairs
Selectively reporting only the group pairs that reached significance after post hoc testing, while omitting non-significant comparisons, is a form of outcome reporting bias. It prevents readers from assessing the full pattern of findings and violates CONSORT and APA reporting guidelines.
Fix: Report all pairwise comparisons in a table, whether significant or not. Include mean differences, 95% CIs, and adjusted p-values for every pair. Label non-significant comparisons as "n.s." or report their exact adjusted p-value.
Mistake 6: Applying Bonferroni Correction Across Unrelated Outcomes
Some researchers apply Bonferroni correction across all statistical tests in a paper, including tests for completely different outcomes (blood pressure, lipids, and glucose treated as a single "family" of 15 tests). This conflation of the "family" concept is incorrect and excessively conservative. Bonferroni correction applies to a defined family of related tests — comparisons within the same outcome from the same ANOVA, not all tests in a study.
Fix: Define the "family" as the set of pairwise comparisons within a single ANOVA outcome. A study with multiple outcomes should apply post hoc correction separately within each outcome's ANOVA results. Cross-outcome correction is a separate decision (typically handled by pre-specifying a single primary endpoint).
Practical Guidance for Medical Researchers
Always Pre-Specify Your Post Hoc Method
State in your study protocol and ethics submission which post hoc method you will use and why. Selecting the method after seeing the ANOVA result ("whichever one gives p < 0.05") is a form of analysis flexibility that invalidates the Type I error guarantees of any correction method. Pre-registration on ClinicalTrials.gov or OSF eliminates this concern entirely.
Use Letter Notation in Figures
When presenting means in bar charts or box plots with post hoc results, use compact letter notation: groups sharing a letter do not differ significantly. "a, ab, b, c" communicates the entire post hoc pattern at a glance and avoids cluttered significance brackets on figures with many groups. Most journals accept this convention; state "groups not sharing a letter differ significantly at p < 0.05 (Tukey's HSD)" in the figure legend.
Report Adjusted p-Values, Not Just *
Reporting "*p < 0.05, **p < 0.01" in figure legends is insufficient. Modern journals require explicit adjusted p-values (pₐᵤʲ = 0.003, pₐᵤʲ = 0.041) or the corrected threshold used (Bonferroni αₐᵤʲ = 0.0083). Exact values allow readers to assess the magnitude of evidence, not just the binary decision.
Consider Statistical Power Before Collecting Data
Post hoc correction reduces power. A study powered at 80% for the overall ANOVA F-test may have only 65–70% power for individual post hoc comparisons. When designing a multi-group study, use the expected pairwise comparison effect size (Cohen's d) and the chosen post hoc method to calculate the sample size needed to detect pairwise differences with adequate power.
Always Report the Effect Size for the Overall ANOVA
The ANOVA F-test and post hoc significance results tell you about statistical significance. Eta-squared (η²) or omega-squared (ω²) tells you about practical significance — the proportion of variance in the outcome explained by group membership. Include η² or ω² for the overall ANOVA alongside the F-statistic. Small η² with significant F in a large sample may represent a clinically trivial difference.
Include 95% CIs for All Pairwise Differences
A confidence interval around the mean difference is more informative than the p-value alone. For Tukey's HSD, the 95% CI for a pairwise difference is: (x̄ᵢ − x̄ⱼ) ± HSD. Report these intervals alongside adjusted p-values. A CI that just misses zero at Bonferroni level is a very different result from one that stops far short of zero — the CI communicates this distinction; the p-value alone does not.
Frequently Asked Questions
Why do I need a post hoc test after a significant ANOVA? +
A significant ANOVA F-test tells you that at least one group mean differs from the others, but it does not identify which groups differ. The F-test is an omnibus test — it evaluates all groups simultaneously. Post hoc tests follow up with pairwise comparisons while correcting for the family-wise error rate (the risk of false positives from multiple testing). Without post hoc correction, running all pairwise t-tests at α = 0.05 for 4 groups inflates the Type I error to 26.5%.
What is the family-wise error rate? +
The family-wise error rate (FWER) is the probability of making at least one Type I error (false positive) across a set of related tests. If you conduct m comparisons at individual α = 0.05, FWER = 1 − (1 − 0.05)^m. For m = 6 comparisons: FWER = 26.5% — far above the nominal 5%. Both Tukey and Bonferroni control the FWER at or below the nominal α = 0.05, ensuring the overall false-positive probability stays at 5% regardless of how many pairs are tested.
When should I use Tukey instead of Bonferroni? +
Use Tukey's HSD when you plan to test all possible pairwise comparisons among your groups and variances are equal (Levene p ≥ 0.05). Tukey is based on the Studentized range distribution, which is specifically designed for this scenario and is more powerful than Bonferroni when m ≥ 4–5 comparisons. For 4 or more groups with all pairs tested, Tukey is almost always the preferred choice.
When should I use Bonferroni instead of Tukey? +
Use Bonferroni when: (1) you have a pre-specified subset of comparisons (not all pairs); (2) very few comparisons (m ≤ 3) where the correction is minimal; (3) you are correcting across different types of tests (not just pairwise group comparisons); or (4) simplicity and universal recognisability matter (cross-disciplinary journals, non-statistical audiences). Bonferroni is the more general tool; Tukey is the more powerful tool for the specific all-pairwise-comparisons use case.
What post hoc test should I use when variances are unequal? +
When Levene's test for homogeneity of variances is significant (p < 0.05), use the Games-Howell post hoc test, which does not assume equal variances or equal sample sizes. For the overall ANOVA, use Welch's ANOVA (robust to variance heterogeneity) instead of the standard F-test. Both are available in SPSS under the One-Way ANOVA dialog: Welch under Options, Games-Howell under Post Hoc.
Can I run post hoc tests after a non-significant ANOVA? +
Traditional practice says no — post hoc tests after a non-significant F-test violate the protected LSD approach and inflate Type I error. If comparisons were pre-specified a priori (specified before data collection as part of the study protocol), they can be conducted with Bonferroni correction regardless of the overall F — but this must be stated in the Methods before analysis. Post-hoc specification of comparisons after a non-significant F to find "significant" pairs is not statistically valid.
What is the Bonferroni-corrected significance threshold for 6 comparisons? +
For 6 pairwise comparisons at α = 0.05: corrected threshold = 0.05 / 6 = 0.0083. Each individual comparison must have a raw p-value below 0.0083 to be declared significant. Equivalently, multiply raw p-values by 6 (Bonferroni-adjusted p-value) and compare to 0.05. SPSS automatically computes Bonferroni-adjusted p-values when you select Bonferroni under Post Hoc tests.
Is Tukey's test available in SPSS? +
Yes. In SPSS, go to: Analyze → Compare Means → One-Way ANOVA → Post Hoc → check Tukey. This produces the Tukey HSD post hoc table with mean differences, standard errors, significance values (already adjusted for multiple comparisons), and 95% confidence intervals for each pair. Also check "Homogeneity of variance test" under Options and "Welch" under Options to test assumptions. SPSS also offers Games-Howell in the same Post Hoc dialog.
How do I report post hoc results in a thesis? +
Report: (1) the post hoc method and justification; (2) all pairwise comparisons in a table with mean differences, 95% CIs, and adjusted p-values; (3) a figure with letter notation or significance brackets. Model sentence: "Tukey's HSD identified significantly lower pain in the 100 mg group vs placebo (mean difference = −2.4, 95% CI: −3.8 to −1.0, p = 0.001). No significant difference was found between the 50 mg group and placebo (p = 0.142)." Always report non-significant pairs too.
Is it acceptable to say "p < 0.05 after Bonferroni correction" without specifying the corrected threshold? +
No. This phrasing is ambiguous — readers cannot reproduce your analysis without knowing how many comparisons were corrected for. Always state the corrected threshold explicitly: "Bonferroni-corrected α = 0.0083 for six pairwise comparisons," or report adjusted p-values directly. The APA Manual (7th ed.) and CONSORT guidelines both require the explicit correction threshold and adjusted p-values, not just the binary significant/non-significant classification.
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