Good question

The whole thing depends on what you want to do with your data, i.e the information you would like to obtain. First, you ran dilutions of your samples to obtain the colony forming units per gram. Typically, in microbiological analysis, what you see is the 10-fold dilution, so the log to base 10 transformation resolves the dilutions and enables a reproduction kinetics plot of your data, i.e the growth curve. Secondly, microbial growth or death occurs logarithmically, therefore the log transformation is most suitable for discussions involving microbial growth, productions or bio-conversions, decay, or die-away tests, inhibitions or susceptibility testing. Nevertheless, while discussing, you have to return data to real life situations where discuss actual numbers like 100, 000 cells present in 1 millilitre of milk sample at say time zero.

Good question

Hi,

CFU / gm or ml concentration is converted to log CFU/ gm or ml concentration for simply read and the statistical analysis processes

Dear Iolanda,

It seems that you have discovered the sort of problems which constantly face us in bench work!

Statistics is a means of summarising and differentiating between data sets, and the very best set of measurements would be for the entire population, no matter how many measurements that would involve. Instead, you have to make a pragmatic decision about how many measurements you are going to make, knowing full-well that the fewer you do, the less representative the sample mean and variance will be of the population mean and variance. Many simple statistical tests (e.g. t-tests) have modifications that compensate for low sample numbers, and many statistical software packages will warn you if the sample size becomes worryingly low and suggest that the P value is determined from tables rather than estimated.

If you get to the stage of very low sample sizes, sometimes it is best to move away from parametric tests (like the t-test) and adopt a less-robust non-parametric test (e.g. the Wilcoxon signed-rank test which is the non-parametric alternative to the t-test) which is less sensitive to low sample numbers (but not entirely - so you may still have that problem).

Ultimately, you should not do any quantitative measurements without the appropriate level of replication, as unless you can do some sort of statistical test, you will not be able to infer any differences or changes in your assays (!). I tend to go for n = 3 = 5 for practicality, but some assays are really affected by experimental errors, and for these we go for n = 8 ...

You question regarding log transformations is also interesting. If you want to use the robust parametric tests you need to show that some key assumptions are correct - usually that the data (or the residuals) are not skewed and are Normally distributed. You can test this using the Shapiro-Wilk test, but like every other statistical test it is sensitive to sample size ... there are other tests you could use (e.g. Levene's) but you cannot get away from the problem if you have very low sample sizes. If CFU data is not Normally distributed (S-W p < 0.05) then you could look at transforming the data using a log transformation, and continue doing this until the transformed data is Normally distributed (S-W p > 0.05). You could do some outlier analysis and remove those data that seem to be on the edges of the distribution, but you need to be aware that it is too easy to remove data and find that there is nothing left to analyse!

I am not too keen on the statement that log transformation are the most informative information when discussing microbial growth as bacterial replicating by fission should follow a x^2 relationship assuming that they are in perfect growth conditions allowing exponential growth. However, in reality, some cells may not divide or divide at different rates, and some cells will die. This means that the best log transformation may not be straightforward and may not relate easily to cell division.

If you are wondering why I have written such a long response it is because I have been locked up at home for the past six months avoiding Covid19!

Andrew

Hi, the transformation to logarithm is actually done to convert the exponential death or growth curves into a line. This means that your three points will fit better if you use logarithmic units and the calculation of the line allows you to interpolate data. The statistical tests are not influenced by the change to logarithms, the results simply give you in logarithms CFU / gr instead of in CFU / g and to obtain the CFU / g you will have to do the inverse (10x). On the other hand, three points for statistical tests are too few.