Question

Walk us through the process of how you would calculate your t-stat for the above study and how you would draw a conclusion using a repeated measures t-test.

In addition to repeated-measures t-tests, this week you also got an introduction to analysis of variance (or, ANOVA) using the f-statistic. Before I have you come up with a study that would use the f-statistic (a study that require an ANOVA) first explain the major difference between a study that would use t and a study that would use f. Compare and contrast the two.

Answer 1

Dear student, please comment in the case of any doubt and I would love to clarify it.  

Here, I can not see the above study and conduct T or Anova test, let me explain the difference between these 2 with examples.

The t-test is a method that determines whether two populations are statistically different from each other, whereas ANOVA determines whether three or more populations are statistically different from each other. Both of them look at the difference in means and the spread of the distributions (i.e., variance) across groups; however, the ways that they determine the statistical significance are different.

These tests are performed when 1) the samples are independent of each other and 2) have (approximately) normal distributions or when the sample number is high (e.g., > 30 per group). More samples are better, but the tests can be performed with as little as 3 samples per condition.

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.

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

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 a 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.

ANOVA Test

ANOVA can determine whether there is a difference between the groups, but cannot determine which group contributes to the difference. For a single variable test, ANOVA can be used first. To account for the multiple comparisons, the ANOVA data should be analyzed with another test (e.g., Duncan, Newman-Keuls) where the alpha can be set at 0.05.

It is also important to mention the sample size. You mentioned that you had three populations of cells. A minimum of 3 biological replicates should be used to conduct initial statistical comparisons to understand the effect size (signal) and variance (noise). This information will determine the sample size that you’ll need to ensure that the power is no less than 0.80. Notably, more accurate information will be obtained with a larger sample set in the pilot study. Sometimes, the signal and noise are known a priori; in this case, a pilot study may not be needed.