STATISTICS


Just because we can run a statistical test, doesn’t mean we should. Statistical assumptions, study design and data quality are central to us making the correct decision for what test to run, if at all!


One-tailed and two-tailed tests


Many t-test tools allow a choice between one-tailed and two-tailed tests. This choice should not be made casually. A two-tailed test asks whether there is


evidence of a difference in either direction. A one-tailed test asks whether there is evidence of a difference in one specified direction only. In most routine laboratory projects, a two-tailed approach is safer because an unexpected difference in the opposite direction may still mater. A one-tailed test should only be


used when the direction of interest was specified in advance and a difference in the opposite direction would not be interpreted in the same way. It should not be selected after seeing the data simply because it produces a smaller P-value.


ANOVA


ANOVA is used when comparing means across more than two groups. A one- way ANOVA asks whether the observed variation between group means is greater than would be expected from the variation within groups. The historical origin of ANOVA is also helpful. It was born out of the need to compare agricultural treatments while accounting for natural variation between plots. The same logic applies in laboratory setings: observed differences between groups must be interpreted against the background variability within those groups. ANOVA is therefore not simply a more complicated t-test; it is a way of comparing multiple group means in relation to within-group variation. A common misuse is to compare three


groups by performing three separate t-tests. For example, if turnaround time is compared between emergency department, ward, and outpatient samples, pairwise t-tests might compare emergency department versus ward, emergency department versus outpatient, and ward versus outpatient. Each test carries a risk of a false-positive finding. As the number of comparisons increases, the overall chance of at least one misleading ‘significant’ result also increases. ANOVA provides an overall test before any planned or post-hoc comparisons are


considered. A significant ANOVA result does not identify which groups differ. It only suggests that not all group means are compatible with being equal. If the overall comparison is important, follow- up comparisons should be planned and interpreted cautiously, especially when there are many groups. As with the t-test, there are


alternatives when assumptions are questionable. Welch ANOVA can be used when group variances are unequal. Repeated-measures ANOVA may be relevant when the same specimens, patients, or units are measured under several conditions, although more complex repeated-measures designs may require specialist statistical input.


Non-parametric alternatives


Non-parametric tests are often described as alternatives when data are not normally distributed. That is partly true, but incomplete. These tests usually work with ranks or signs rather than the raw values themselves. They may therefore answer a different question from a mean- based test. These alternatives are valuable,


especially for ordinal outcomes or clearly non-Gaussian continuous data where a rank-based comparison matches the laboratory question. However, they should not be used automatically. A small dataset does not automatically become reliable because a non-parametric test has been used. Small datasets remain uncertain, regardless of the method. The Mann–Whitney test is a


useful example. It is often described as comparing medians, but that interpretation is only straightforward under particular conditions, such as similarly shaped distributions. More generally, it assesses whether values in one group tend to be higher or lower than values in another group. If one group has a different spread or shape, the test may reflect more than a simple shift in central location.


Assumptions: what laboratory readers need to check Assumptions should not be treated as obscure statistical technicalities. They


describe the conditions under which the method gives a sensible answer. For routine laboratory projects, the most important considerations are usually practical. First, observations should be


independent unless the method explicitly accounts for pairing or repeated measurements. If several results come from the same specimen, patient, analyser run, day, operator, or batch, the data may not be fully independent. Ignoring this structure can give misleading confidence intervals and P-values. Second, paired data should be analysed


as paired data. In a split-aliquot storage study, the key information is not simply the mean result under each condition; it is the difference within each specimen. Treating the two sets of results as independent discards important design information. Third, normality should be considered


in relation to the relevant quantity. For a paired t-test, this means the distribution of the paired differences, not necessarily the raw values in each condition. For ANOVA, the assumption concerns the residual variation around group means, not perfect normality of every group. In practice, visual inspection and understanding of the measurement process are often more informative than a software normality test. Fourth, unequal variance maters. If


one group is much more variable than another, especially when group sizes are also unequal, classical equal-variance methods may perform poorly. Welch methods can help when the question remains a comparison of means but the equal-variance assumption is doubtful. Fifth, outliers and skewed data require judgement (see Article 1 in series – details below). An outlier may be a data entry error, a real but unusual specimen, a process failure, or a true feature of the population. Removing it simply because it changes the P-value is poor practice. The laboratory meaning of the observation should be considered. Finally, sample size maters. A very


small study may be too uncertain to support a strong conclusion, even if the selected test is technically appropriate. A non-significant result from a small study is not proof that the groups are equivalent.


Changing the test can change the question


Changing the statistical test is not merely a technical adjustment. It may change the question being answered. This maters because the laboratory conclusion should match the test. A rank-based test may provide evidence that one group tends to


June 2026 WWW.PATHOLOGYINPRACTICE.COM 19


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