Power Analysis

Power can be defined as the probability of finding a real difference if it exists. 80% or 0.8 is considered an acceptable value for power. The Power Analysis is performed independently for each spot. Given the sample size, the variance of expression values and the difference we want to detect, we can calculate the power. Also, for a given power of 80% we can determine how many samples are required to ensure we find a difference if it actually exists. Within Progenesis Stats we do this as follows.

Power Calculation

For each spot we know the expression variance, the sample size and difference between the group means. Using this data, we calculate the power. This power tells us that if that difference between means was actually a true difference, then what is the probability of finding it to be significant. Clearly, we are more likely to find as significant those spots with a large difference between groups. Thus, these spots will have a high power. Also, these spots will have a lower p-value, as the greater the difference between spots (all other factors equal), then the lower the p-value.

Sample Size Calculation

For each spot we know the expression variance and difference between the group means. We choose a power level of 80%. Using this data, we calculate the sample size that would be required to find a significant difference between groups. There are some points to note. Clearly, if group means will be relatively close together, then a larger number of replicates will be required to find this difference significant. If group means are relatively far apart, then less replicates will be required to find this difference significant. Thus, spots with a high p value will need a high number of replicates to achieve an 80% power while spots with a low p-value will require far fewer replicates