Justify the use of parametric tests on non normally distributed data

#1
Hello there.
I have 5 Likert scale questionnaires that have been answered by the same people who have been randomly selected (N=24) and i have the following problem:

I first test the data distribution of each scale in order to determine what statistical analysis tests should i employ (parametric or non parametric).

The first two scales (let call them A and B) have approximately normally distributed data based on visual, numerical and normality tests.

The next three scales (C,D and E) however have some anomalies and normality cannot be assumed.
These anomalies rely on 1 outlier in scale C and D and E is just weirdly distributed.
Trying to transform data using LG10 or SQRT functions doesnt really work. Therefore, everyone seem to suggest that i should use non-parametric test on these scales.

My question is:
Can i proceed with the use of Parametric tests (means and sd's and correlations) on these scales and justify it by assuming normality based on the fact that the sample has been randomly selected and on the normality tests of the previews scales (A and B)? If yes, is there any reference to support this?

For example:

"Leave your data non-normal, and conduct the parametric tests that rely upon the assumptions of normality. Just because your data are non-normal, does not instantly invalidate the parametric tests. Normality (versus non-normality) is a matter of degrees, not a strict cut-off point. Slight deviations from normality may render the parametric tests only slightly inaccurate. The issue is the degree to which the data are non-normal."
From: http://www.psychwiki.com/wiki/How_do...n-normality?

OR

"However, it is not actually necessary for sample data to follow a normal distribution in order to subject the data to parametric statistical analysis (which is often the case with the smaller sample sizes described in clinical studies). Rather, it is necessary for the sample data to be compatible with having been drawn from a population, which is normally distributed."
From:
http://ceaccp.oxfordjournals.org/content/7/4/127.full

Thanks.
 
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#2
I think the first step is to determine if you can remove the outliers. The second step depends on what test you're using. repeated measures ANOVA only requires that your data be approximately normal and some deviations from normality should be ok. If you use mixed models, these are even more robust with data that's not completely normal. Non-parametric tests are avoided because they have much less power and normality of the distribution alone is not an automatic justification for using these tests.

I am not an expert and am learning statistics myself, but you will find this guide helpful: http://www.graphpad.com/guides/prism/6/statistics/index.htm?stat_the_power_of_nonparametric_tes.htm

Make sure to read the other articles in the same section.
 
#3
Hi Excelsius and thanks for your reply.
I am more interested in descriptive statistics and correlation testings.
The outlier can be removed but again this wont sort the problem completely.
 
#4
of course transformations don't eliminate outliers, but rather just move them

what's the study question you're trying to answer?
you have 5 measures on 24 people and ... what?
 
#5
Thanks for your reply ted00
I would like to come up with descriptive statistics and correlation tests as i said before.
The problem is i prefer to do means and sd's rather than medians as it is the best practice for non normal data.
Again my question is if i can assume normality on a distribution that is not normal based on the fact that i know sample is drawn randomly and its normally distributed in the first 2 scales.


For example:
"Leave your data non-normal, and conduct the parametric tests that rely upon the assumptions of normality. Just because your data are non-normal, does not instantly invalidate the parametric tests. Normality (versus non-normality) is a matter of degrees, not a strict cut-off point. Slight deviations from normality may render the parametric tests only slightly inaccurate. The issue is the degree to which the data are non-normal."
From: http://www.psychwiki.com/wiki/How_do_I_deal_with_non-normality?

OR

"However, it is not actually necessary for sample data to follow a normal distribution in order to subject the data to parametric statistical analysis (which is often the case with the smaller sample sizes described in clinical studies). Rather, it is necessary for the sample data to be compatible with having been drawn from a population, which is normally distributed."
From:
http://ceaccp.oxfordjournals.org/content/7/4/127.full


of course transformations don't eliminate outliers, but rather just move them

what's the study question you're trying to answer?
you have 5 measures on 24 people and ... what?