A SIMPLE APPROACH

Looking at in vitro models, this approach is very simple to apply and does not require any particular statistical knowledge. In my opinion the conditions to use it are:

1)      The same cellular line for each experiment. No differences due to the cell source or origin (i.e. a commercially available cell line).

2)      Each experiment is exactly the same as the others in all the experimental details.

The number of experiments may be also low (n=2-3).

Under these assumptions, each replicate inside each experiment is a cell sample made of n cells, and there is no reason to not consider the total number of replicates – 1 as the total number of degrees of freedom, as there is no reason why the experiments are different. In this view, also a different number of replicates per experiment may be used.

This may have some consequences that we will see, but as a first step we may think to consider the replicates all together as the experiment was one. It may be applied with each type of normalization. Therefore, to compare the effects of a toxicant we have to use One-Way ANOVA for independent measures, as reported in the figure with not normalized (crude) and normalized 1 (norm1) data. Note that the grouping variable has the following meaning: 0=control; 1=C1; 2=C2; 3=C3; 4=C4. Only 0-1 are reported for spatial reasons.

Let’s go with SPSS. There are two ways to perform one-way ANOVA with SPSS; I will show you one method, as it will be further used for more complicated models.

Go to Analyze…=> Generalized Linear Model… => Univariate…. And select the variable group as fixed factor and crude/norm1 as dependent variable.

Then go on post-hoc… and paste the variable group in the post-hoc test for… window. Note that there are several possible post-hoc tests, whose use depends on several factors, among which heteroscedasticity (e.g. difference variance among groups tested by Levene’s test during analysis, different n groups, etc). To simplify the analysis, we will use the Dunnett’s test to compare only the exposed groups with control (the reference group is the first).

The most important results:

ANOVA is highly significant: F=58.99, p<0.001 (crude) – F=42.38, p<0.001 (norm1) and all the groups are significantly higher than control, independently on the type of normalization. Note that in this case, the normalized variable HAS a SD due to the fact that it is calculated on the replicates.

 

Therefore THE RESULT is COMPLETELY DIFFERENT FROM THE SEMI-CLINICAL APPROACH… and in this case it makes sense!

There are two important limitations: (1) the result may be very sensitive to outlier experiment or replicate, therefore AN EXPERIMENT DIFFERENT FROM THE OTHERS MAY ALTER THE RESULTS and cause some problems of normality. (2) A reader may think that performing different experiments is completely useless. Why not only one experiment with more replicates? In reality, the use of more than one experiment has the aim to verify the inter-experiment variability, which may be an important factor in determining the repeatability of the results. Therefore, THE USE OF >1 EXPERIMENT IS DESIDERABLE.  We are apparently in contradiction: This approach cannot distinguish an experiment with several replicates and more experiments with few replicates. But it is not impossible to take into account of it, as we will see the next time.

NOTE: Normalization 1 should be cautiously made in this case, because a normalization experiment per experiment is not completely in agreement with the assumptions made and is not completely justifiable, as we do not expect a different susceptibility in different experiments.