Normal distributions and non-normal distributions do happen. That is why we have parametric tests and non-parametric tests. We use the appropriate test according to the distribution of the data that we collected. I am wondering why we have to "transform" a non-normal distribution into a normal one when our "fact" is a non-normal distribution.  Suchira, I think you have to choose a statistical tool that suits the data that you have actually collected. Honestly, I do not think there is an alternative non-parametric or parametric tool to multiple linear regression because the latter is not a "test". By scatter plot you may be able to find out if your regression line is straight-linear, exponential or quadratic. Ed

Dear Suchira,

the information you provide is by far not enough to give you a good help.

What do you want to test? What is your null hypothesis, what is the alternative hypothesis? What kind of data is it, where is it from, how was it collected? Are there any covariables?

The data seems to be discrete, so there can not be any transformation that will make it look normal distributed. Further there seem to be "too many" values exactely 10.0, what is kind of strange. If there a detection limit? If so, you may consider using a hurdle model.

@Suchira

Please see the attached probability plot of your data. The X-axis is the number of sigma above and below the mean. Much of your data appear to follow a normal distribution, it plots as a straight line. The data below 15 do not follow a normal. As  Jochen noted you appear to have a detection limit or a lowest limit. This should be explained.

It is possible to make the data - Normal. But your information is not sufficient. Moreover variety of non-parametric tests are available. The choice of use is dependent on the posed problem.

@Rajiv: how will you make any discrete data "normal"? I do not see how this should work.

@Frank: just as a hint: aspecially for smaller sample sizes, a normal-quantile quantile plot as Jospeph prepared in Excel is considerably better than a histogram to check the distribution of the data (see link). Further, statistics should first of all match the objective, not the data. If the data was obtained in a well-designed experiment/study with the particular objective in mind, the data should actually be consistent/compatible with the required statistical analysis. I admit that this is not always possible and sometimes heuristics have to help. Nevertheless, in many cases I know thinking about the scientific question and the experiment and data generation is better than mindlessly producing some data and then start thinking how one could analyze it (that's different for explorative analysis of complex observational data, but this is a different strory at all).

http://en.wikipedia.org/wiki/Q%E2%80%93Q_plot

Frank, all fine - I did not want to critique you. My apologies if I was mistaken. I just wanted to add some thought, pointing to a common misconception many people have about "statistics".

I had a book in my office that have some suggestions for transforming the data... I don't remember it! you can try inverse, square root, cube and square meanwhile.

In regard to non-parametric methods, if you fail to transform the data, they are very useful (whatever you use: U-test is very popular: http://en.wikipedia.org/wiki/U-test). However, their limitation is that they require that the groups you are comparing have the same SHAPE in the histogram: so you must show the histogram of the groups your are comparing!

Interesting discussion!!!!!

I am not an expert in Statistics or  models. However, having a look at the plot attached by Joseph, data seem to follow a logistic function. Perhaps,  logistic regression through  may be useful (not knowing anything about what data represent). Good luck with your research Suchira!!

Normal distributions and non-normal distributions do happen. That is why we have parametric tests and non-parametric tests. We use the appropriate test according to the distribution of the data that we collected. I am wondering why we have to "transform" a non-normal distribution into a normal one when our "fact" is a non-normal distribution.  Suchira, I think you have to choose a statistical tool that suits the data that you have actually collected. Honestly, I do not think there is an alternative non-parametric or parametric tool to multiple linear regression because the latter is not a "test". By scatter plot you may be able to find out if your regression line is straight-linear, exponential or quadratic. Ed

Have you tried Box-Cox transformation? It always finds a solution to get it symmetric, though not always normal (let's not ask too much).

I have used it in Stata, but other sofwares may have this as well.

Good luck.

For non-parametric studies i advise you to analyse your data by PLS (Partial Least Square). As PLS has advantages over other techniques when analyzing small sample sizes or data with non-normal distributions.

I think your description is not sufficient. As suggested above, i think you should check and re-check about your case. I agree with @Eddie that Normal distributions and non-normal distributions do happen.

If you're sure that it doesn't follow normal distribution, Spline regression is a technique that can handle this problem. this technique is very applicable nowadays. I suggest you to learn it if you've never known before. Good luck.

Dear Friends,

Thank you very much for all of your valuable comments and kind words. It seems I have given insufficient information on the data set for you all to come to a conclusion. I am not good in statistics at all. However, I try to analyze my data last few days. Please see the attachment for some more information (Topic, specific objectives, part of the questionnaire, results of descriptive statistics and hypothetical tests in brief). Kindly let me know whether what I have done so far is correct OR do not violate key statistical principle. Can I use multiple linier regression (Please see the last 3 pages of the attached document) for this analysis? If cannot please suggest an appropriate statistical technique.

Please see the attachment.

Kindly help me to arrive in to a conclusion. Thank you all

Your data contain extreme values represented by 10 which caused a heavy tail in the left side of your data. In fact,Extreme values sometimes have a big effect on statistical operations so,your data seem followed the normal distribution which is heavy-tailed. Sometimes Winsorizing (Winsorization replaces extreme data values with less extreme values) or  Trimming (There is an alternative to winsorization, which is just throwing out the extreme values) are used. This URL may be helpful for you.

http://www.r-bloggers.com/winsorization/

Best Regards.

Suchira

I have looked at your study. I cannot tell which data you have plotted and what you have applied to the stated objectives.

What have you applied to 

1. To determine attitudes and opinions of the adults in Colombo city of Sri Lanka towards illegal abortion and abortion law.

Instead of fitting data to some model could you not make a table of results that address this objective?

2. To identify the factors affecting and associated with the attitudes of the adults in the Colombo city of Sri Lanka towards illegal abortion.

Same as above, if you are identifying factors why not list the results by order of importance?

Are these your actual objectives or are you attempting to conclude a necessary outcome?

I think it is the residual error of your estimates that is most important to be normal to have valid estimate in most of the regression methods. Looking for the normality of variables is a matter of knowing the characteristics of our data. Of course, some data behave irrationally, though it could be as a result of method of collection or whatever, but they are needed to be used. It is possible to log and still not find normality.

you may use this approach

Article TO DETERMINE SKEWNESS, MEAN AND DEVIATION WITH A NEW APPROAC...

Many Thanks for sharing this...............