I have data on weight of a group of people after and before a diet. I want to see if weight loss is distributed normally.
> weightloss <- dietA$Peso.inicial-dietA$Peso.final  7.48 3.71 4.30 5.47 3.80 6.31 7.76 4.07 3.70 4.11 4.96 4.63 5.18 5.68 4.76 1.87  7.80 3.29 7.23 6.67 3.96 0.72 4.36 0.10 2.30 7.15 5.61 7.20 5.27 7.86 4.81 6.08  5.90 5.16 1.60 5.50 6.16 5.99 6.36 0.91
I ran the Shapiro-Wilk test using R:
> shapiro.test(weightloss) Shapiro-Wilk normality test data: weightloss W = 0.95123, p-value = 0.08357
Now, if I assume the significance level at 0.05 then the p-value is larger than alpha (0.08357> 0.05) and I cannot reject the null hypothesis about the normal distribution, so can we accept the null hypothesis? I know that divergent views exist on this (see Interpretation of Shapiro-Wilk test, What is Hypothesis Testing? and When to use Fisher and Neyman-Pearson framework?), in addition the difference between values is short and with significance level at 0.1 we can reject the null hypothesis.
I try to see other way that gave me other element like QQPlot:
> qqnorm(weightloss) > qqline(weightloss)
As you can see the first points are rightmost and at the end we have one point rightmost too, so maybe I can conclude not normality of the data(see How to interpret a QQ plot). In order to see other points I create a histogram
So with this almost I can say that the sample hasn't a normal distribution or I can accept normality with uncertainty. I am not sure about this.