Date:         Tue, 27 Jul 1999 10:52:38 -0500
Reply-To:     Tim Dunsworth <Tim.Dunsworth@METROSTATE.EDU>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Tim Dunsworth <Tim.Dunsworth@METROSTATE.EDU>
Subject:      Re: Level of departure from normality
Content-Type: text/plain; charset=US-ASCII

Others have already responded about the issues of using alternatives to parametric tests when the data are non-normal, but I would like to address the data itself. The sum of five 1-5 scale items should be in the range 5-25, so an observed range of sums from 3 to 14 suggests the presence of missing data. If true, this would make a sum a poor choice for a combined measure, and it might be better to use something like:
COMPUTE combo = MEAN.2(Score 1 TO Score5).
with your selected threshold number in place of the 2 (that is, cases with less than that minimum acceptable number of non-missing values would get a missing value for the combined score). It is even quite possible that the missing data accounts for some of the skewness you are seeing, if most cases answered three items, say, and smaller numbers answered four or all five items. Compute a mean score and see how it comes out on the normality tests (also, you might want to use a Kolmogorov-Smirnov test for an overall assessment of normality, then use skewness and kurtosis for further describing the nature of any departure from normality). If the mean score is still non-normal, then start considering the use of transformations or non-parametric test alternatives.

>>> Sylvain Labrie <labries@GLOBETROTTER.NET> 07/24 4:16 PM >>>
I would need some advice in how to assess the level of departure from
normality of a distribution. The data I am using was obtained from a
sample of 54 people using five items that constitute a scale. Each
item uses a five point scale where 1 = never and 5 = very often and I
have computed a total score from those items. The descriptive data is
the following for the total score distribution:

n cases:  54
mean:  5.66
std dev:  2.42
min:  3      max:  14
skew:  .9731
se skew:  .3246
z score for skewness (skewness divided by se skew):  2.9978
Kurt:  1.0736
se kurt:  .6389
z score for kurtosis (kurtosis divided by se kurt):  1.6803

 From the obtained z scores, I know that the skewness is significantly
different from 0 since z for skewness = 2.9978 is greater than 2.576
(from z table at alpha level .01). Therefore, I know that the
distribution for this data in non normal (positively skewed).
Tabachnick and Fidell suggest to assess the level of departure from
normality but they don't really address this issue. From this
example, what can we consider severe departure from normality as
opposed to moderate and tolerable departure from normality? How does
one take position in this kind of situation? What could be juged as
an adequate guideline?

Thank you very much for your time. Any help will be greatly appreciated.

Best regards, Sylvain.
||Sylvain Labrie*Universite de Montreal*labries@magellan.umontreal.ca||