There is no such thing as "nonparametric data". You may have data that is measured on some measurement scale which requires a nonparametric statistical analysis. Could you be more specific how the data look like? Do you have count data with several possible values? If what you have are data are appear to be non-normal, this is different from data that (say) take on values 1,2,3.

Indeed Prof. Raid, I may mistakenly called it non-parametric data. As you said, it's rather a parameter that does not follow a normal distribution. The parameter is calculated from measured variable, which all have numerical data.  The treatment is the width of foundation (15 levels). There are three blocking factors, (3, 3, and 9) levels, respectively. The total response data contain 540 values. I'm not aware what kind of DOE, I have suggested it is incomplete blocks (non square GLSD) design, I may be wrong. I'll appreciate your clarification professor about what kind of tests I can use in both cases parametric and non-parametric. Thanks a lot for your answer. 

For your convenience the data is attached herewith. Normal Distribution (Part-1)

Using 15 levels for the treatment factor is a rather large number of levels. You stated above that the three blocks have 3,3, and 9 levels, respectively. You also stated in the description of the problem that the three blocks have 3,3,and 15 levels. Then you stated that the number of treatments is 15.

Is it like this:

Factor has 15 levels (the treatments)

Blocking Factor 1: 3 levels

Blocking Factor 2: 3 levels

Blocking Factor 3: 9 levels

If you use a factorial experiment, do you have all possible combinations of factor levels covered?

Why did you use 15 factor levels? This is a very large number of treatments. 

Dear Professor Raid, 

Greetings, 

Thanks for your prompt response. That treatment reflects the sizes of foundations that may be used in the project. I believe yes all possible combination are covered, so can I use the factorial design or you suggest to reduce the level of treatments? 

Regards, 

You should consider using a fractional factorial experiment so that it becomes more manageable. I would also reduce the number of treatments.

Many thanks for your valuable recommendations.