Dear Abdul,

I looked into your excel sheet. The next step you need to do is pool the data from each replication because to me it doesnt seem statistically different (but you need to check yourself to be sure). And then just run ANOVA where I believe your isolates are the main treatments. Then you can easily see that if the isolates differ or not in terms of resistance component which is determined looking at your pvalue.

I dont understand about the infection frequency but if we look into the literatures its actually the infection efficiency.

Also i advise you to plot the AUDPC but i am not sure for how many days did u collect the data.

regards

Shankar

Dear Abdul,

If I'm reading your data correctly, it looks like you have a block design with treatments (R1-R4) within isolates (blocks). Also, since your data are proportions you will need to model it using a binomial family of errors.

Here are a couple links that might be useful:

http://www3.imperial.ac.uk/pls/portallive/docs/1/1171926.PDF

http://www3.imperial.ac.uk/pls/portallive/docs/1/1171926.PDF

Then again, I might be interpreting your data incorrectly.

Cheers,

Clint

Dear Dr Kelly,

Yes i have a completely randomized block design, isolates are main treatments and R1-R4 are replications

Thanks for providing useful links

Actually my main aim is to study aggressiveness among isolates

Hi Abdul,

In addition to an ANOVA or, more appropriately a generalized model with an error distribution that is suitable for your data - as suggested by Clint Kelly - I would encourage you to explore your data using some multivariate methods that will help you see which variables are associated with particular differences among your isolates. I'd also encourage you to spend some time thinking about the sorts of differences among isolates which are BIOLOGICALLY as opposed to statistically significant. The different sizes of differences in the variables you measured will have biological significance and interpreting the results of your experiment properly will depend on you having a good feel for what size of difference matters in each case. A related issue to be aware of is that because the different variables will inherently have different levels of natural variation, your experiment has different power to detect true differences for the different variables (probably). This being the case, having a single blanket significance level for all of the variables is probably not a good idea.

well, thanks McRoberts for detailed and helpful explaination

Hi Dr. Wilhelm,

thanks for your suggestions. can you please tell me what are dependent and independent variables for multivariate analysis. again please consider my data, my aim is to test the aggressiveness of ten different strains of phytophthora infestans on potato leaves. aggressiveness parameters are infection effeciency, lesion expansion, latent period, LGR, and RAULEC. can you please specify what would be dependent and independent variables in this case. Thanks

Hi, if you mean me: I did not yet give any suggestions...

But as I understood the question ("what is the variability...between isolates?") you just need to estimate this variability from the data. There is no independent variable.

An independent variable would be used to predict the values of the dependent variable. But this is not your question (as I understood). Your isolate number is not systematically related to the aggressiveness parameters (APs); you assume that the different isolates acually should give the same values for the APs, but for unknown (i.e. random!) reasons the values obtained are not constant between isolates. You now just want to check how large this (random) variation between the isolates is. It is difficult to compare the size of variation between different APs (e.g. "Infection frequency varies more [or less] than the latency"). Numerically, the coefficients of variation (CV = standard deviation divided by the mean) can be used to compare the "relative" variation, but it is not clear how this relates to the biological relevance.

Practically, you should first average the values from the replicates. Then you can calculate (estimate) the variances for each AP. Note that the variance is nothing that is intimately related to the normal distribution - the variance is just the average squared difference to the mean. These values (or the derived CVs) may be compared, but - as I said - the biological relevance has to be interpreted!

You may calculate confidence intervals for the variances and translate the limits to the CVs to get an impression of how precisely the variances (or CVs) were determined from the sample.

Instead of the variance you may take any other measure of variability, too. For instance the median absolute deviation from the mean or median (MAD), or the interquartile range (IQR) or the interdecile range (IDR) or the total range or any other statistic for variability that comes into your mind. The range estimates (IQR, IDR, range) are no "sufficient statistics", that means they don't use all information of the data and therefore they might be less suitable. However, the choice of the best measure for variability should be guided by your biological expertise. For instance, when it is most important to focus on extraordinary high and low values, the range might be the best statistic to measure the *relevant* variability.

Thanks Doctor,

I think this is the most comprehensive explanation and answer to my question, thanks a lot

Abdul, what is R1, R2, R3,R4 in the file

Not the best strategy, ask why statistical analysis applied after taking the data, is like a surgery and ask later, that is sick?

Carlos, R1, R2, R3, R4 are replications

Different isolates are the main treatments and R1 - R4 are replications

Wich are isolates in the file

Hi Carlos,

isolates are 1,2,3,4,5,6,7,8,9 and 10 arranged in the firs column

Isolates are different?

Yes Dr. Carlos,

isolates differ in their aggressiveness behavior

Abdul, by what I see, its design should be turned by a ONEWAY, but the problem is the sample size, the number of replicas has impact at making the difference more evident when the sample is small.

Thanks Carlos,

I am trying to apply one way anova