# Is my data normal graphical vs. analytical test

I am trying to determine if my data is normal. I am using R.

I run the jarque bera test that has a NULL hypothesis of Normality

jarque.bera.test(dat)
Jarque Bera Test

data:  dat
X-squared = 4.6747, df = 2, p-value = 0.09658


since the pvalue is > .05 I cannot reject he null so the data IS normal

I also run the shapiro wilk test with a null of NORMALITY

shapiro.test(dat) #Ho is normal

Shapiro-Wilk normality test

data:  dat
W = 0.9149, p-value = 0.001375


so I reject the Null and the data is not NORMAL

THEN when I look at a QQnorm I see

and that does not look normal.

So 2 of 3 tests say the data is not normal is that enough to say it is not normal? What do you think?

• Why are you testing normality? – Glen_b -Reinstate Monica Mar 28 '15 at 2:09
• Even if we have to repeat it infinitely: a high p value does not imply a true null. So you will never be able to show normality using these tests. – Michael M Mar 28 '15 at 9:50
• hi Glen and Michael - I am testing for normality because I wan to see if I can use a t test to test if the differences between means and normality is required. MIchael - I am not sure what you mean. The p value is lowest level of significance at which you can accept the null so if pvalue is .00001 and i use a .05 significnace then I cannot accept null. DO you agree? – joesyc Mar 29 '15 at 17:01

First your qq-plot deviates quite a bit from the line. Moreover, going by the Shapiro-Wilk test -- it's not even close -- your p-value is $\approx .001$. That's very significant. If it was 0.04, that would be more of a subjective call...