It's the same situation like any women has when she prepares herself to go out:
What dress to ware? What style? which clothes? Any data table with all values of Y can be expressed as log Y, or e expY, or 1/Y etc.
However the information of our data-table remains always the same. No new information at all, just a different presentation or a different look when you go out with another dress.
Then rises the question: why having different dresses or why expressing the same mathematical information in different ways? One answer: Just to present the given situation in the most understandable or most presentable (or sexy) way.
Any table of many values of x carry the identical information (not more and not less) than the data table of x or log x or x exp2 , or x exp (anything). You cannot increase the amount of information just by changing the outlook or the wrapping. Your friend remains the same person in an evening dress, bathing dress or necked......some presentations however may be more or less appealing. (no publication added)
Deepest thanks for that simplest explain, that's really helpful.
However, one point still unclear, since the different forms of transformation would yield a different sings, and usually significant, so what would be right??
Furthermore, In STATA for instance we should choose the best way to transform the variable based on the lower value of Chi-square, yet, do we shall use it even it's not significant or instead choose the lower significant Chi-square,,,
Thanks, Ajit Roy. I fully agree. Statistics is a great tool, however it does not replace additional experiments which will make the conclusions more safe or more doubtful. More experimental repetitions are fine for the statistics but new experiments, as different experiments, will increase you the impression to be on the right or wrong way.
(the problem of Dante in his: "Divina Commedia:" Nel mezzo del camin di nostra vita mi ritrovai in una selva scura perque la dirita via ho smarito......"