The data table example posted by OP looks like functional overrepresentation analysis data- not line-by-line gene expression data. I soldier on with the same interpretation as other posters.

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.

In old-school data analysis, only one or a few outcomes are being measured. Say for instance I want to see how fast mice can solve a maze- I measure their speed (in seconds). I test 10 young mice and 10 old mice. I find that young mice solve the maze in an average of 10 seconds plus or minus 2 seconds of standard deviation, that old mice are twice as slow and solve the maze in an average of 20 seconds plus or minus 2 seconds of standard deviation. All of these values I've just reported values ARE statistics- the average, the standard deviation, and, yes, even the fold change. All of them describe facets of the observations in question, none of them report all of the information, and all of them dimensionally flatten the data in some way. One could have decided to use the median rather than the average, the confidence interval instead of the standard deviation, the difference in averages rather than the fold change.

But none of these descriptive statistics, by themselves, can tell you the likelihood that such a finding could have arisen by chance. To find that out, you have to do a statistical test. Unfortunately, neither the statistical test nor the descriptive statistics can tell you whether something is biologically meaningful. They can be used to flag a finding that appears significant in an observational study, or they can be used to help evaluate whether a finding is significant in an experiment designed to intervene in a biologically meaningful way. So it's the experimental design, not the descriptive statistics or statistical tests, that are the heart of determining biological meaning.

Now consider that you are looking at transcriptional data instead of maze results. Instead of one set of measures (maze latencies), you have 10,000 measures (one set for each gene- with 10 young and 10 aged observations). Let's say you were doing a t-test on gene expression for the 10 young vs the 10 aged. If you have 10,000 genes to test, and you test them with a p-value cutoff of 0.01 (meaning you are at least 99% sure that such results did not arise by chance), then you can also predict that 1% of the time, they would arise by chance. Since you are testing 10,000 genes, then 1% of the time means 10,000 x 1%. Therefore, you should expect 10,000 x 0.01 = 100 genes to be significant in your data set even if nothing is going on.

This is called "multiple testing error" and different methods that have been proposed to try and control for it. Bonferroni offered the most severe correction- divide your p-value cutoff (in this case, we're saying 0.01) by the number of tests (10,000). So... 0.01/10,000 = 1E-6, and therefore you would only consider results that had p < 0.000001 as significant- effectively, at that significance level, you would also be saying "there is only a 5% chance that any gene in my current list is there by chance".

However, there is a trade off- while you increase confidence that results exceeding the criterion are true positives, you also increase the likelihood that you will exclude results that were also true positives (you would have a high false negative rate). Several other methods more charitable than Bonferroni (Tukeys, Holm-Sidak, Neuman-Keuls, various step-down methods etc) have been proposed. But Benjamini and Hochberg's False Discovery Rate (FDR) correction, particularly the modified version described by Storey (that produces q- values) has become invaluable in transcriptional profiling, and large-scale bioinformatics analysis in general.

At its simplest level, the FDR takes a list of p-values, and sorts them in order from smallest to largest. Identify your list size- in our example, our list is 10,000 genes long. Now, on each row, the number of genes with a p-value at or less than the p-value for the gene on that row are counted. So in row 1, you have your smallest p-value, there are no genes with smaller p-values, so the result here is '1' (that is the number observed). Then, multiply that smallest p-value (the one in row 1) by the total list size (10,000)- that tells you the number of genes you would expect to find at that p-value by chance (say here that you would 'expect' 0.1' gene by chance- this is the number expected). Then, divide the number expected (0.1) by the number found (1), and that gives you the false discovery rate (0.1). According to the original method, then, you run all those calculations for each row, then go the the bottom of the list, and start scrolling up. The first time you see an FDR that is below your criterion (say < 0.05), then every gene with a p-value smaller than the one with the acceptable FDR is retained as significant. The Storey modification improves the estimate of the significance of the list, but that is a 'Storey' (: for another day.

So, the FDR is a modification of the p-value. The p-value for a single gene (in its standard presentation- this does not hold for LIMA or EdgeR or other analysis approaches that use Bayesian estimates, but does hold for conventional analyses) is independent of the other p-values in the profile, while the FDR takes those other tests into account (both are useful - the FDR can be a great indicator of the strength of a study- the p-value can be more useful for statistical power analyses in future studies). Fold change by itself is intuitive, and does not require replication, but cannot test for chance likelihood on its own, does not incorporate estimates of variance, assumes a central tendency, and is vulnerable to very small measures.

However, p-values (and FDRs) have their own problems- at small p-values, they can be 'twitchy' from study to study, and show big swings (e.g, 0.05 in one study, 1E-6 in another), while fold changes, particularly for well-annotated genes with reliable signal intensity/ counts, can be much more stable across studies. So generally, an amalgam of fold change and p-value, especially the 'volcano plot', can be used to identify reliable, strong expression changes.

Dear Aziz,

Usually, people use a threshold of 0.05 on the p-value to define a significant hit/change.

In your case, it appears that you may have done multiple tests (one per line in your table). Therefore, it is common to adjust the raw pvalues to account for the fact that each time there is a 5% chance your finding is obtained by chance.

False Discovery rate correction (FDR) is one method to account for multiple hypothesis testing.

Hope this help,

Kevin

I will try to offer a practical answer, because I'm sure you can find the theoretical definitions elsewhere. To make a long story short, FDR is an adjusted p-value to trim false positive results. Briefly, when you are working with hundreds and thousands of genes you are going to get false positives just by chance, this is inherent to the definition of p-value. So, FDR offers more confidence than just p-value. Usually, results below 0.05 are considered real. However, this statistic is just telling you if the differences observed are due to chance or not, i.e. if they are real and can be trusted. If your intention is to select the most affected genes you should look at the fold change ratio as well as the FDR.

However, from your snapshot I suppose that you are looking at a functional enrichment analysis of some kind because you have an input list of genes and you are comparing them to some background. In this case you are getting an FDR value to know if that functional category is enriched in a significant manner in your set of genes.

one can use TRANSMODIS is a probabilistic model for predicting direct targets from binding motif, sequence data, expression data and ChIP-chip experiments. The probabilistic framework removes arbitrary cutoffs in target selection procedures and allows integration of data coming from various sources. Compared with other criteria for identifying targets, TRANSMODIS is usually more stringent by requiring consistent and significant expression fold changes across all experiments.

Well, in my opinion you won't get the most affected genes by looking only at p-values or FDR. Those values indicate that genes are differentially expressed (DE) at a statistical point of view, and are useful to choose which genes are DE compared to the experimental noise or biological variation between samples. As said before, many authors choose a DE cutoff of FDR < 0.05. Now, the statistical tools used to identify DE genes in RNA-seq experiment usually give an indication of fold-change (FC) between your test and control conditions. The probable most meaning DE genes at a biological point of view are probably the ones with the greatest fold changes, both up- and down-regulated. If you want to take both the statistical and biological parameters into account, a rapid and easy way to decide which genes might be of interest is to draw a so-called volcano plot, where you plot log10(FDR) versus log2(FC) for your comparison. Genes in both upper left and upper right parts of the graph are the most statistically significant DE genes with the greatest fold changes.

The data table example posted by OP looks like functional overrepresentation analysis data- not line-by-line gene expression data. I soldier on with the same interpretation as other posters.

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.

In old-school data analysis, only one or a few outcomes are being measured. Say for instance I want to see how fast mice can solve a maze- I measure their speed (in seconds). I test 10 young mice and 10 old mice. I find that young mice solve the maze in an average of 10 seconds plus or minus 2 seconds of standard deviation, that old mice are twice as slow and solve the maze in an average of 20 seconds plus or minus 2 seconds of standard deviation. All of these values I've just reported values ARE statistics- the average, the standard deviation, and, yes, even the fold change. All of them describe facets of the observations in question, none of them report all of the information, and all of them dimensionally flatten the data in some way. One could have decided to use the median rather than the average, the confidence interval instead of the standard deviation, the difference in averages rather than the fold change.

But none of these descriptive statistics, by themselves, can tell you the likelihood that such a finding could have arisen by chance. To find that out, you have to do a statistical test. Unfortunately, neither the statistical test nor the descriptive statistics can tell you whether something is biologically meaningful. They can be used to flag a finding that appears significant in an observational study, or they can be used to help evaluate whether a finding is significant in an experiment designed to intervene in a biologically meaningful way. So it's the experimental design, not the descriptive statistics or statistical tests, that are the heart of determining biological meaning.

Now consider that you are looking at transcriptional data instead of maze results. Instead of one set of measures (maze latencies), you have 10,000 measures (one set for each gene- with 10 young and 10 aged observations). Let's say you were doing a t-test on gene expression for the 10 young vs the 10 aged. If you have 10,000 genes to test, and you test them with a p-value cutoff of 0.01 (meaning you are at least 99% sure that such results did not arise by chance), then you can also predict that 1% of the time, they would arise by chance. Since you are testing 10,000 genes, then 1% of the time means 10,000 x 1%. Therefore, you should expect 10,000 x 0.01 = 100 genes to be significant in your data set even if nothing is going on.

This is called "multiple testing error" and different methods that have been proposed to try and control for it. Bonferroni offered the most severe correction- divide your p-value cutoff (in this case, we're saying 0.01) by the number of tests (10,000). So... 0.01/10,000 = 1E-6, and therefore you would only consider results that had p < 0.000001 as significant- effectively, at that significance level, you would also be saying "there is only a 5% chance that any gene in my current list is there by chance".

However, there is a trade off- while you increase confidence that results exceeding the criterion are true positives, you also increase the likelihood that you will exclude results that were also true positives (you would have a high false negative rate). Several other methods more charitable than Bonferroni (Tukeys, Holm-Sidak, Neuman-Keuls, various step-down methods etc) have been proposed. But Benjamini and Hochberg's False Discovery Rate (FDR) correction, particularly the modified version described by Storey (that produces q- values) has become invaluable in transcriptional profiling, and large-scale bioinformatics analysis in general.

At its simplest level, the FDR takes a list of p-values, and sorts them in order from smallest to largest. Identify your list size- in our example, our list is 10,000 genes long. Now, on each row, the number of genes with a p-value at or less than the p-value for the gene on that row are counted. So in row 1, you have your smallest p-value, there are no genes with smaller p-values, so the result here is '1' (that is the number observed). Then, multiply that smallest p-value (the one in row 1) by the total list size (10,000)- that tells you the number of genes you would expect to find at that p-value by chance (say here that you would 'expect' 0.1' gene by chance- this is the number expected). Then, divide the number expected (0.1) by the number found (1), and that gives you the false discovery rate (0.1). According to the original method, then, you run all those calculations for each row, then go the the bottom of the list, and start scrolling up. The first time you see an FDR that is below your criterion (say < 0.05), then every gene with a p-value smaller than the one with the acceptable FDR is retained as significant. The Storey modification improves the estimate of the significance of the list, but that is a 'Storey' (: for another day.

So, the FDR is a modification of the p-value. The p-value for a single gene (in its standard presentation- this does not hold for LIMA or EdgeR or other analysis approaches that use Bayesian estimates, but does hold for conventional analyses) is independent of the other p-values in the profile, while the FDR takes those other tests into account (both are useful - the FDR can be a great indicator of the strength of a study- the p-value can be more useful for statistical power analyses in future studies). Fold change by itself is intuitive, and does not require replication, but cannot test for chance likelihood on its own, does not incorporate estimates of variance, assumes a central tendency, and is vulnerable to very small measures.

However, p-values (and FDRs) have their own problems- at small p-values, they can be 'twitchy' from study to study, and show big swings (e.g, 0.05 in one study, 1E-6 in another), while fold changes, particularly for well-annotated genes with reliable signal intensity/ counts, can be much more stable across studies. So generally, an amalgam of fold change and p-value, especially the 'volcano plot', can be used to identify reliable, strong expression changes.

Thank you all for your valuable answers and suggestions. It really helped.

Dear Aziz,

I hope by now you would have obtained the answer, as I read most of the competent people have answered probably more specifically. The p-value that I have used previously was to check the significance of the associated factors, applying the t-test, 0.05 was considered as significant, and factors having 0.00 and 0.05 were considered in association. But my supervisor at KMU also considered those variables with p-values of 0.13 having liner by liner association 0.05. In my opinion you can select column # 3,4 and 7,8,9.

Thanks.

Dear Mazhar Khan, thanks for sharing your suggestion.

Just to add to the above answers, one thing you also want to consider is the number of reads generating those p/FDR values. eg if your control has 100 reads in a certain region, while your disease has 0/1, this will create distorting p values. you can remedy this by setting cutoff based on your overall read depths.