Question

when comparing gene expressions, what is an adjusted p-value?

Answer 1

The adjusted P value is the smallest familywise significance level at which a particular comparison will be declared statistically significant as part of the multiple comparison testing.

A separate adjusted P value is computed for each comparison in a family of comparisons. But the value of these adjusted P values depends on the entire family. The adjusted P value for one particular comparison would have a different value if there were a different number of comparisons or if the data in the other comparisons were changed. Each comparison will have a unique adjusted P value. But these P values are computed from all the comparisons, and really can't be interpreted for just one comparison.

Adjusted P values in Prism

Prism can compute multiplicity adjusted P values following Bonferroni, Holm, Tukey or Dunnett multiple comparison testing. Check the option in the third tab of the ANOVA dialog. This feature was introduced in Prism 6. Note a minor bug in Prism 6 and 7. With Dunnett's test, Prism can only compute adjusted P values that are greater than 0.0001. If the adjusted P value would be less than 0.0001, Prism reports 0.0001 but should report <0.0001.  

p-value means "probability value". It ranges between 0 and 1. But how to interpret the p-value entirely depends upon the test that is being used to calculate that p-value. Some tests (like fitting Langmuir's adsorption isotherm, or semi-log dose-response curves) examine how well a data set fits a hypothesized relationship. For those tests, a higher p-value is MORE significant (so 0.99 would mean "that data really fits my hypothesis", and a 0.01 would mean "that data really does not fit my hypothesis). However, it is far more common to see a test like a t-test or an ANOVA (Analysis of Variance) test- in which researchers do not propose a hypothesis, but instead, propose to test the hypothesis that there is NO effect. Thus, for t-tests and ANOVAs (and Pearson's correlations for example), a small p-value means there is a small chance that the observed results occurred by chance, and a big p-value means that the data could easily have occurred by chance.