To think of attributes and variables may be distracting here. You are talking about the differences between levels of measurement. This concept has received criticism but it makes clear what you are talking about. There are 4 levels of measurement: nominal, ordinal, interval and ratio. Nominal = names and is the type of data that cannot have any arithmetical functions performed upon it. For example, someones name is data and you are unable to analyse this numerically except in terms of the frequency of its occurrence. Ordinal data has an order and numbers can express this (as can alpha codes). However, there is not distance implied between the order points. For example, house numbers determine the ordering of buildings but say nothing about how far apart buildings. Obviously, with ordered data you can do a lot more sophisticated form of analyses but you are still dealing with non-parametric data as you were with nominal data because there are no metric intervals in the data. The next 2 levels, interval and ratio, are parametric and they both are dealing with precise and constant intervals between points. These measurements, as they are consistent can be compared to group data - there is inherent meaning in the measurement scaling. The differences between interval and ratio is often not that important as ratio measurements have a precise and meaningful zero whilst interval scales do not. An example of this would be the age of the earth if we were able to determine a precise point at which the earth came into existence. In this situation nothing could exist on the earth before zero moment and each year would progress from there. The Gregorian Calendar that we use in the West has a zero at an arbitrary point and 10AD (CE) is 10 years past this point but it is possible to have 10BC (BCE). That is, the data has not precise zero at which point the scale commences. With this in mind, it is possible to see how the type of research that you are able to conduct and the types of statements you are able to make about your results are very different between parametric and non-parametric studies.
Can anybody suggest me about the transformation of data? How do you know if you need to do log(x+1) transformation or square root transformation? Some of my response variable have lots of 0 but not negative, Can anybody please suggest something?
Hi Bishwo, What type of data are they? If your data are not symmetrical, try log transformation, that will make the data symmetrical before you analyse them statistically..
Nischal dai: They are behavioural data. I am doing log(x+1) transformation for some of the variable. The distribution has become much better after I did log transformation. Do you know what I need to look at if I couldn't reach normality even after transformation?
I tried several distributions like poisson (for count data), gamma (time to event), beta (proportional) for relevant variables. Let me know if you have any idea.