Some software give a p-value that is extremely close to zero just as "0" (zero). It is a good practice to report very small p-values just as "p < 0.001", as it simply indicates that your observed data is extremely unlikely under the used and restricted model. Thus, a "highly significant p-value" and a p-value of zero mean pretty much the same thing.

In general, the p-value depends on the everything, in particular on the data, the amount of data, the model and the restriction in the model, and on the particular evaluation of the likelihood of the data including underlying probability models. You stated that you calculated a p-value for untransformed and for transformed data. So you change the data, and therefore it is not unexpected* to get different results. Noteably, the underlying probability model won't be adequate for both versions (transformed and untransformed data), so if the test is ok for one version it might actually be inappropriate for the other version. It can happen that one of the p-values is rather large and the other is rather small what might even lead to contrary conclusions.

You should actually first decide if you want to analyze the untransformed or the transformed data, then you should identify a sensible probability model for the parameter you like to test, then you need to find or construct the appropriate test. What makes no sense is to perform significance testst on several versions of your data (or to use different tests or models on the same data).

* with following exception: the test is about an order statistic ("non-parametric") and the transformation is order-invariant (monotone).

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you'll find a nice discussion here :

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4120293/

(see section 3.2)

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Thank you, Fabrice, for the nice discussion you refer, which illustrates the problems caused by data transformations.

Anyway, significant differences - e.g., in the mean - in the transformed data are very difficult to interpret in the original scale of non-transformed data.

To Benzaman, how can you expect that the p values does not change by a transformation when you apply the same model for analysing the data. A non-linear transformation changes a model and it changes the basic behaviour of data. Thus, it is the rule - not the exception - that the p values change.

The article referred to by Fabrice underlines the necessity of more general models to analyse the data. More general models that are more flexible with respect to distributional assumptions.

I agree that transformation does change the model, but in contrast to the authors of the paper cited by Fabrice I do not think that the "linear scale" is "more natural" or "correct" than the "log scale". The argumentation in the paper is a bit religious, as if there is something special about an "original scale" that must not be transformed. I think the actually relevant question is if the changes one wants to analyze are independent of the magnitude of the measurments. If they were independent, looking at (mean) differences would be appropriate. However, in biological (and bio/chemical) systems this is almost never the case, and differences can be really misleading when judging the relevance of the results. In these cases it would be better to look at relative changes, i,e, on ratios rather than differences. And just here, logarithms enable us to use the tools developed for the analysis of differences to analyse ratios (the log of a ratio is the difference of the logs).

Hi Everyone, Thanks for your suggestions.

If the overall nature of DV or IV leads to transformation of values, from a result relevancy point of view, should the final model fit statistical parameters being taken under consideration alone ? Frankly I am aware that all estimation changes when the model structure changes, however lets say a variable highly significant in one model (before transformation) changes in a such a high degree after transformation that it looses it significance. When the explanation needs to given, should it be a comparative? That was my query.

Regarding p value - yes the softwares do behave that way, however, for my analysis I am getting any standard errors or t-statistics. I am not sure, whether it is safe to assume, their value is no minuscule that the column is left blank.

When you change the model or the kind of data (e,g, by transformation) then the tests refer to entirely different hypotheses, It is not that the p-value for the test of some hypothesis is changing - these are two different p-values about two different hypotheses in different models / with different data. There is no reason why an apple should look like a peach. These are just different things. The major problem seems to be that people are usually not aware of the fact that these are different things and/or that they have no concrete idea what statistical hypothesis they are actually testing.

@ Benzaman, « however, for my analysis I am [not ?] getting any standard errors or t-statistics. »

May seem a stupid remark, but are you sure you do not have 0/

Emmanuel, so for transformed case, the std.error value in some case is zero, corresponding t value and p value are given as " - " in the result and not as zero. Now this is just a simple case " not even a log transformation".

You cannot have a SD of 0. You have a problem in your data. Or you can't do anything with your variable. No variation = no possible statistics.

So, first thing to do, investigate why you have a 0 SD... Are you sure you're dealing with quantitative variables, not numerically coded qualitative variables?

Considering the fact that s.e & s.d are not the same thing, the s.e of the estimated parameter of "intercepts", I got s.e as 0. 

Ok, sorry, I misunderstood the result you gave. Your question did not specified you were speaking of linear-model (or similar) coefficients estimations, so seeing the mention of Student I wrongly deduced you were in a classical Student test case. Apologies for the misunderstanding.

Without further information on e, q and q1, I would say that you have an overspecified model or some major colinearity problem or a (quasi) separation problem. It's very difficult to diagnostic without knowing what exactly you are doing...

if you transform your data and apply this transformation aright, the statistical significance status of the model cannot change from what it was before since the models are logically equivalent. However it seems you have a misconception about the connection between high statistical significance and a zero p-value because a zero p-value indicates high statistical significance.