STATISTICS
Practical statistics: hypothesis testing – t-tests, ANOVA, and others
In this second article in his new series, Stephen MacDonald moves on to hypothesis testing. Here, he looks at statistical assumptions, study design and data quality, which are central to arriving at the correct decision about what test to run, if at all.
Clinical laboratories generate and compare things constantly. Has a change in sample transport reduced turnaround time? Do specimens stored at room temperature and 4°C give meaningfully different results after 24 hours? Are three request locations associated with different processing times? Do two methods/lots of reagent perform the same? Has a change in workflow reduced the time between sample receipt and authorisation? There are also research- based projects where often the first question is… what statistical test do I need to do? These are practical laboratory questions that affect all aspects of laboratory work. Yet the statistical method is often selected late in the project, sometimes only after the data have been collected. A project may be designed informally, data may be extracted because they are convenient, a test may be selected from a software menu, and the final conclusion may rest almost entirely on whether a P-value crosses 0.05.
Question
Two independent groups Two paired measurements
More than two independent groups More than two paired conditions
That is far from ideal. The statistical method must be considered at the design stage, not bolted on at the end. Poor test selection can lead to false reassurance, unnecessary process changes, or overconfident conclusions from limited data. Proper statistical thinking can make even a modest laboratory project more defensible by clarifying the question, the comparison being made, the assumptions involved, the size of the observed effect, and the uncertainty around it. The t-test, analysis of variance
(ANOVA), and their common alternatives are among the most familiar statistical methods we consider. They are also among the most casually misused. A P-value may be reported without the size of the observed difference. Paired data may be analysed as if they were independent (Table 1). Multiple t-tests may be performed where a single overall comparison would be more appropriate. Non-parametric tests may be used automatically when data ‘look non-normal’, without enough
Data structure Different samples/patients/runs Typical method Welch t-test or Student t-test if justified
Same sample before/after or split aliquots Paired t-test Three or more groups
Same units under several conditions Table 1. Which comparison are you making? 16
WWW.PATHOLOGYINPRACTICE.COM June 2026 ANOVA/Welch ANOVA Repeated-measures ANOVA/Friedman
thought about what those tests actually compare. This article discusses how we should approach common comparative questions. The key point is that the statistical
test must match the design. A paired t-test is not chosen because there are ‘two columns of data’; it is chosen because each value in one condition has a direct partner in the other condition (Table 1). ANOVA is not used because it sounds more advanced; it is used because more than two group means are being compared, and repeated t-tests would inflate the chance of false-positive findings.
Why these methods are often misunderstood or under-taught The t-test and ANOVA are often taught as procedures rather than as tools for answering specific questions. This encourages a menu-driven approach: open the software, choose a test, obtain a P-value, and decide whether the result is ‘significant’. That workflow is backwards.
Common mistake Using paired test
Treating as independent Multiple t-tests
Ignoring repeated structure
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56
