Summative Likert scale score of questions or items (measured on 5-point scale (Strongly agree to strongly disagree)) will be treated as ordinal or interval? If interval or ordinal, please you may provide justification and references.
(2) Can we use a rule of thumb that says a variable is reasonably close to normal if its skewness and kurtosis have values between –1.0 and +1.0, while statistical tests of normality are significant?. Sample size is 650.
Strictly speaking, a Likert style scale is an ordinal one – there is no definite gradation in between each of the categories.. one person’s disagree may be the same of another person’s ‘strongly disagree’. … To be safe, you could take the view to analyse using non parametric statistics. But other researchers have advised me that it is quite usual to assume that the scale is reasonably ‘continuous’ and that you can take it be near enough to ‘interval’.. I’ve not hunted for any references, but I suggest that you do a search using Likert scale and take a look at the method of statistical analysis.. I am sure you will find plenty where the mean is used in conjunction with a t test. You can cite these as evidence to support your approach… or you can play safe and use non parametric if you like. With a sample size of 650 – which is quite large, this is further support to allow it to be used as an interval scale.
I agree with the others that it is not uncommon to treat a Likert scale as continuous. You often find this in survey research in sociology and political science alike.
On the second issue: tests for normality strike me as superior to separate tests for skewness and kurtosis. However, there are many tests for normality and some of them are quite sensitive in the sense of quickly rejecting the null of normality.