distributionsnormal distributionskew-normal-distributionskewness
I have this question: What do you think the distribution of time spent per day on YouTube looks like?
My answer is that it is probably normally distributed and highly left skewed. I expect there is one mode where most users spend around some average time and then a long right tail since some users are overwhelming power users.
Is that a fair answer? Is there a better word for that distribution?
If the distributions are similar (in particular have the same variance) and the group sizes are identical (balanced design), you probably have no reason to worry. Formally, the normality assumption is violated and it can matter but it is less important than the equality of variance assumption and simulation studies have shown ANOVA to be quite robust to such violations as long as the sample size and the variance are the same across all cells of the design. If you combine several violations (say non-normality and heteroscedasticity) or have an unbalanced design, you cannot trust the F test anymore.
That said, the distribution will also have an impact on the error variance and even if the nominal error level is preserved, non-normal data can severely reduce the power to detect a given difference. Also, when you are looking at skewed distributions, a few large values can have a big influence on the mean. Consequently, it's possible that two groups really have different means (in the sample and in the population) but that most of the observations (i.e. most of the test runs in your case) are in fact very similar. The mean therefore might not be what you are interested in (or at least not be all you are interested in).
In a nutshell, you could probably still use ANOVA as inference will not necessarily be threatened but you might also want to consider alternatives to increase power or learn more about your data.
Also note that strictly speaking the normality assumption applies to the distribution of the residuals, you should therefore look at residual plots or at least at the distribution in each cell, not at the whole data set at once.
For youtube I think the distribution depends on the distribution of video length. Most videos are about 8 to 10 minutes (this is the average span of the people attention). One might watch 0, 1, 2, or any other number of videos. A Poison distribution might be a good candidate to model the number of visits to a website or the number of videos watched per day. If the distribution of the time of a single video would be $P_V(t)$ then the distribution of total time would be something like $$P_{Total}(t)=\sum_{i}^{} P_p(N=i)P_{Vi}(t)$$ where $i$ is the number of visits, $P_p(N=i)$ is the Poisson distribution and $P_{Vi}$ is distribution of total time of $i$ videos which can be obtained by performing convolution on $P_v$. If $P_v(t)$ is approximately Gaussian then the distribution would be a mixture of Gaussians. Something that looks like the following picture. (I only guessed the distribution, not to scale)
For facebook there might be something similar to a video length. For example the time required to look at one page.
Best Answer
A fraction per day is certainly not negative. This rules out the normal distribution, which has probability mass over the entire real axis - in particular over the negative half.
Power law distributions are often used to model things like income distributions, sizes of cities etc. They are nonnegative and typically highly skewed. These would be the first I would try in modeling time spent watching YouTube. (Or monitoring CrossValidated questions.)
More information on power laws can be found here or here, or in our power-law tag.