I want to know if average time people spending on their favourite social media are statistically different. I consider here five groups, and the total number of participant is 700 persons.
I have already performed the Shapiro-Wilk normality test, on each group (Facebook, Twitter ...) to see if the time people spend on social media follows a normal distribution, according to the test, the null hypothesis fails so the time isn't normally distributed. Though, I decided to consider the time as a normal distributed parameter, because the average time is approximately normally distributed as $n=700$ is large enough.
Next, I carry out the 'Test of homogeneity of Variances', according to the the results the equality of variances is ruled out.
Meanwhile, I looked at the 'Robust test of equality of means' or 'Welch and Brown-Forsythe', both tests results in p-value $0,000$.
Now, I want to know if I can trust the results of Post hoc? Or I frequently violated the rules? If so how I can eventually compare means?
I have a very few experience in data analyses, so I apologise here for carelessness of my argument.