An Approximated Method

This method is quite simple to perform, but it does not take into account the number of experiments and it is statistically discussable. It may be used in all the conditions and presents some similarities with the semi-clinical approach (see one of my previous posts).

If we have k experiments with n replicates (n is the same for all the experiments), we may think to calculate the best possible experiment giving to all the experiments the same weight:

-the mean is the mean of k experiments;

-the SD is the mean of SD of k experiments.

In this way, we extrapolate a sort of “mean experiment”, where the number of degree of freedoms (df) remains n-1 for each condition. This method is “dangerous” if we have a low number of replicates and several experiments, and statistically is discussable because it does not take into account all the possible df of our system and gives to all the experiments the same weight.

Let’s look at the data (crude values):

 

 

 The last line represents the values we have to compare, considering n=5 replicates for each conditions. In the statistical softwares, there aren’t general options to compare mean (SD) with ANOVA only knowing that values and n, but we can use some sites that perform such a calculation. See for example:

 

http://www.danielsoper.com/statcalc3/calc.aspx?id=43

In alternative, some softwares perform t-Student tests. We can assess the differences between pairs of conditions using t-Student tests, but we have to consider that we have to apply the Bonferroni’s correction to the p value (true significance is 0.05/m, where m is the number of performed multiple comparisons). The results:

 

To perform the comparisons between exposed conditions and control (software OPENSTAT available at http://www.statprograms4u.com/ or the previous site with pairs of column):

0 vs 1 – p=0.0253

0 vs 2 – p=0.0003

0 vs 3 – p<0.0001

0 vs 4 – p<0.0001

Considering a significant p=0.05/4=0.0125, the condition 1 is the unique not significant condition, and therefore the results are intermediate between A SIMPLE APPROACH with and without random factors (all significant) and the SEMI-CLINICAL approach (no significances). However, this method, although very simplified and discussable, controls fairly the beta error.