t-test & ANOVA (Analysis of Variance)

Figure 4. Overlapping histogram plots for concentrations of protein 4 in different populations.

t-test Example

We want to determine whether the concentration of Proteins 1 – 4 in serum are significantly different between healthy and diseased patients. A t-test is performed, which can be visually explained by plotting the protein concentration on the X-axis and the frequency along the Y-axis of the two proteins on the same graph (Figures 1 - 4).

Proteins 1 & 2 have the same difference in protein concentration means but different group variances. Alternatively, Proteins 3 & 4 have similar variances but Protein 4 has a larger difference in protein concentration means between the patient groups.

A t-test assigns a "t" test statistic value to each biomarker. A good differential biomarker, represented by little to no overlap of the distributions and a large difference in means, would have a high "t" value.

Which is a better biomarker of disease: Protein 1 or Protein 2?

Protein 1

Which is a better biomarker of disease: Protein 3 or Protein 4?

Protein 4

What type of statistical value do I get? The t-test and ANOVA produce a test statistic value ("t" or "F", respectively), which is converted into a "p-value." A p-value is the probability that the null hypothesis – that both (or all) populations are the same – is true. In other words, a lower p-value reflects a value that is more significantly different across populations. Biomarkers with significant differences between sample populations have p-values ≤ 0.05.