How to find if a difference is statistically significant? I have a web crawler that scrapes items on an hourly basis and expect to get 375 items every time. In the past 10 runs, I have scraped the following number of items:
[360, 361, 363, 364, 368, 372, 375, 375, 375, 375]

On the 11th run, I only scrape 300. I want to determine whether or not this difference in item count on the 11th run is statistically significant as compared to the mean? That is, I want the to know if the subsequent run is significantly lower than the mean.
 A: If you're identifying the "300" by looking at the data (i.e. not based on characteristics that would pick it out before you saw it was 300), then you can't simply test for a difference from the rest.
For calculations of consistency to be meaningful, you must take account of the fact that you picked out the most-discrepant-looking observation to test.
There are a variety of ways to simulate this under the null, depending on exactly what you want to achieve, but unless you have a substantially larger sample, you'd probably need to make some parametric assumption.
A: You also bring up testing difference from the mean, but your first question is about difference from 375 as "expected" (careful: in statistics and economics, "expectation" has a specific meaning that may not be what you think). You do a statistical test to see if a given sample conforms to a hypothesis about a population - so if you expect the "population" mean to be 375, then you can test whether your sample of 10 has a mean of 375. You don't do a statistical test to see if a given value is different from 375 - of course 300 is different than 375. If you want to know if 300 is a big enough outlier to consider sufficiently different, then you can calculate sample statistics like mean, standard error of the mean, confidence intervals around the mean, etc. Or if your distribution is not Normal, then there are other parameters you could be after - for instance, if it is count data and it is skewed (so a normal approximation isn't appropriate), you could be looking at a Poisson distribution, which would give you different statistics 
This could also get more complicated than you want it to, but most statistical tests assume independent observations. It may be that there is serial dependence in your observations, meaning the scrape now is dependent on the prior scrape. If that's the case, you've got a time series and that is an entirely different set of analyses to consider.
