If I have data that appears normally distributed, but it contains a lot of zeros, are there issues with assuming a normal distribution? Suppose I have the following data where the data looks normal but contains a lot of zeros. For example, I generated half of the data as standard normal and half as zeros. Does this cause us to run into any issues when considering things like hypothesis tests, etc?
mydata <- c(rnorm(500),rep(0,500))



There's no sense in which I'd be tempted to claim that this "appears normally distributed" per the title - it is clearly really far from normally distributed; it looks like what it is --  a mixture of a spike and a continuous distribution.

As for how much it matters, that very much depends on the situation. For example, if you were testing equality of variances, I wouldn't suggest you try assuming normality. On the other hand, a test relating to the upper tail of the distribution might not be all that much impacted by the spike.
