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I believe there are many ways to determine if data is normal or not:

  • histogram shape

  • QQ plot

  • skewness

  • kurtosis

  • shapiro test.

Which of the above is the best way to determine if data is normal and one can proceed with parametric tests?

Edit:

After going through this thread (Is normality testing 'essentially useless'?) as suggested in comments by @Luca, I am inclined to conclude that:

  1. Formal tests can be misleading (may show non-normal distribution in large sample sizes, even if data is largely normal); hence can be avoided.

  2. Non-parametric tests should be used for small samples. They are reasonably good even for normal data.

  3. Parametric tests should be for large samples. They are reasonably good even for non-normal large data.

  4. qqnorm(vect) & hist(vect) (R commands) plots may be best for graphic / visual assessment.

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    $\begingroup$ Many answers on this thread can help you: stats.stackexchange.com/questions/2492/… $\endgroup$
    – Luca
    Oct 24 '14 at 16:44
  • $\begingroup$ There are, generally speaking, no ways to determine if data is normal. There are sometimes ways to determine data isn't normal, but formal hypothesis tests are not generally useful for deciding whether to use parametric tests; they answer the wrong question. QQ plots give you some idea of in what way data might be non-normal data and how badly -- this may be helpful in assessing the likely form of and extent of its impact on whatever inference you're interested in, if you know how sensitive the procedure is to particular forms of deviation from assumptions at the given sample size or sizes $\endgroup$
    – Glen_b
    Oct 25 '14 at 6:43
  • $\begingroup$ Thanks for explaining. Please see the edit in my question above and comment on the conclusions. $\endgroup$
    – rnso
    Oct 25 '14 at 7:24
  • $\begingroup$ See the answer to a similar question here $\endgroup$
    – Aksakal
    Dec 31 '14 at 18:46