TL;DR
- Two groups only → a single t-test (Welch's if you are unsure about equal variances). No correction needed.
- 3+ groups, all pairwise comparisons → one-way ANOVA, then Tukey's HSD post-hoc.
- 3+ groups vs. one control → one-way ANOVA, then Dunnett's test.
- Small n (< 8 per group) → you can't reliably test normality, so judge by the data type and a Q–Q plot. For right-skewed concentrations, a log transform + t-test is often the most powerful valid choice; Mann–Whitney / Kruskal–Wallis is a fine fallback (but is also low-powered at tiny n).
- Paired samples → always use a paired test (paired t-test or Wilcoxon signed-rank).
- Non-normal data confirmed (and a transform doesn't fix it) → Mann–Whitney U (2 groups) or Kruskal–Wallis (3+ groups) → non-parametric tests.
Introduction
You have just finished running your ELISA plate. The data is exported and now comes the question that trips up even experienced researchers: which statistical test actually applies here?
With small samples you can't reliably test for normality: a normality test has too little power to detect real departures. So lean on what you know about the data type (raw OD is often roughly normal; percent inhibition and concentrations are often skewed) and a Q–Q plot, rather than defaulting to a rank test by reflex. A log transform often keeps the more powerful parametric test in play → checking assumptions.
What type of data do you have?
ELISA experiments produce three common output types, and the right test depends on which you are working with.
Raw OD values
Unitless absorbance readings directly from the plate reader. Often approximately normally distributed but sensitive to assay variation.
Calculated concentrations
Values interpolated from a standard curve using a 4PL or 5PL fit. Distribution depends on curve linearity and sample spread.
Percent inhibition
Ratio-transformed values bounded between 0 and 100. These are frequently non-normal.
Check normality
Before choosing a test, verify whether your data is normally distributed.
| Method | Best for | Limitation |
|---|---|---|
| Shapiro–Wilk test | n < 50 per group | Low power at very small n |
| Q-Q plot | Visual check any n | Subjective interpretation |
| CV check | Quick screen | Indirect indicator only |
Choose your test
Comparing two groups
| Condition | Recommended test | Notes |
|---|---|---|
| Normal distribution, equal variances | Student's t-test | Most common case |
| Normal distribution, unequal variances | Welch's t-test | Safer default in most ELISA contexts |
| Non-normal distribution | Mann–Whitney U | Use when n is small or data is skewed |
| Paired samples | Paired t-test or Wilcoxon | Always pair when the design calls for it |
Comparing three or more groups
| Condition | Recommended test | Follow-up |
|---|---|---|
| Normal distribution | One-way ANOVA | Tukey HSD or Dunnett post-hoc |
| Non-normal | Kruskal–Wallis | Dunn test with Bonferroni correction |
| Repeated measures | Repeated-measures ANOVA | Friedman test if non-normal |
ANOVA tells you something is different. Post-hoc tests tell you what. Always follow a significant ANOVA result with a post-hoc test.
Worked example
Here is a realistic scenario: an IL-6 ELISA comparing treated versus untreated cells, n = 6 per group.
IL-6 ELISA, n = 6 per group. The treated median (142 pg/mL) is well above the control median (61 pg/mL), but each group is right-skewed by one high well, so compare medians with a Mann–Whitney test rather than means. Hover any point for its concentration.
IL-6 concentrations like these are typically right-skewed, so the natural first move is a log transform, after which a Welch's t-test on the log values is valid and powerful (and tests the ratio of geometric means, a sensible quantity for a concentration). If skew or an outlier persists after transforming, fall back to Mann–Whitney U and report the median with interquartile range, the U statistic, and the p-value. Either way, don't decide between them on a Shapiro–Wilk p-value alone. At n = 6 it has too little power to be the arbiter.