A SEMI-CLINICAL APPROACH

This method has the important limitation that IT DOES NOT TAKE INTO ACCOUNT the number of replicates for each condition. Therefore, it may underestimate the significance of the differences (type 2 error) and its use should be justified. MY SUGGESTIONS: its use does make sense if every experiment represents a specific case. In other words, with an example: the same cellular line extracted in different subjects/animals. In such a case, despite the replicates, we may think that the inter-variability is higher than intra-variability (e.g. the difference among subjects is higher than the variability of replicates). Furthermore, the number of experiments should be quite high, at least higher than the number of conditions. I suggest a number of experiments/subjects >= 10-15. I will show you the limitations with few experiments, considering our data.

THE PROCEDURE: we may use both normalized and not-normalized data. We calculate the mean value for each condition for each experiment. With not normalized and normalized data (example of the previous comments) and with this method we don’t use the SD arising from replicates:



Being each experiment a specific condition, we need a repeated measures test. In our case, we have 5 conditions and we need REPEATED MEASURES ANOVA. Note that after normalization the SD of controls is 0 and therefore an independent ANOVA cannot be performed. Let’s do it with SPSS. To visualize all the passages and to have a complete explanation of all, see the great work of Andy Field (http://www.statisticshell.com/docs/repeatedmeasures.pdf) Data will be inserted as follows:



To do Repeated Measures ANOVA: Analyze => Generalized Linear Model => Repeated Measures… we define factor1 with 5 levels, and then ADD…Once added, we can proceed with DEFINE. We select the variables C-C4 and move them in right panel. We have however the limitation that POST-HOC tests are not selectable, although there is a way to do them. IN SPSS, HOWEVER, A POST-HOC TEST WHICH COMPARES ALL THE CONDITION OF EXPOSURE WITH CONTROL, LIKE DUNNETT’S TEST, IS NOT SELECTABLE. I will show you a way to by-pass this limitation. Anyway, to do a full factorial post-hoc test, we click on OPTIONS. We select factor1 and move it in the VISUALIZE MEANS FOR. Now, we click on COMPARE MAIN EFFECTS and we select a test (i.e. Bonferroni, the most classical one). Then Continue and OK. From the OUTPUT, it appears quite evident that there are some concerns about data due to the low sample size (n=3 points per condition). Mauchly’s sfericity cannot be calculated, although the program performs ANOVA with the following result:



Despite the Sphericity, the test is anyway significant. However, with Bonferroni’s post hoc test we have bad news: the differences between pairs are in most cases not significant (except C3 vs C4, p=0.038 with not normalized data and C3 vs C5, p=0.035 with normalized data). We can be less conservative and compare C1-C2-C3-C4 with C performing only 4 comparisons (always Bonferroni). How to do that? We perform single paired sample t-test, but the significance would be p=0.05/4=0.0125 for each test (SPSS: Analyze => Compare Means =>Paired Samples T Test… and
select the pair of variables). Results:



Only C-C4 is at the limit of significance (Not normalized data). Why this result, despite the fact that differences among conditions appear evident? N=3 experiments are a little number with a very low statistical power. This is the reason why I suggest at least 10-15 experiments/subjects/animals. There is another order of problems. The Normalization of Data changes the results, and it may be critical when we are near 0.05. It should be noted that the normalization we have done should make the inter-experiment variability at the background concentration NULL, it is not an OVERALL normalization of the results. Therefore, the method we applied finds the differences between the conditions APART FROM such a variability, while the analysis on non-normalized data does not. The results are therefore different. The normalization which contains also this variability is very simple. You take the three not normalized control values (62, 72.6, 83.6), calculate the mean (72.733) and divide all the column for this value, obtaining the following results:



The results with normalized data 2 are the same of not-normalized data. Therefore, the choice of type of normalization is very critical and should be always chosen and justified.

To sum up:
1) NORMALIZATION OF EVERY SINGLE EXPERIMENT TO 1 ELIMINATES THE BACKROUND VARIABILITY OF CONTROL AND THE RELATIVE EFFECT OF EXPOSURE CONDITIONS MAY BE EVALUATED.

2) NO NORMALIZATION OR NORMALIZATION OF MEAN OF CONTROLS TO 1 TAKES INTO ACCOUNT ALL THE EXPERIMENTAL VARIABILITY.

We will consider the differences in the results, if present, case by case. Note that case 2 has the possibility to use independent measures ANOVA if there is no reason to think that exposure conditions are influenced by the number of the experiment (e.g. no differences in susceptibility are expected).

A BRIEF NOTE: "Repeated measures" means that with in vitro models each cell line arises from a different subject/animal. It is not applicable  to a traditional in vivo experiment, unless the same subject/animal testes all the proposed conditions. Generally, in vivo approach is different: we have only one experiment with n animals/subjects per condition. Therefore, we have to use a classical independent ANOVA (the number of ways may vary depending on the study) and not a repeated measures ANOVA.