Hi guysIn my statistics book there is an example. They say that we

[Niles]

Hi guys

In my statistics book there is an example. They say that we see 3 occurrences of type A, and theoretically expect 7. This is a difference of 4, since we know that the standard deviation is 1.65 (they calculate it), then the difference is 2.4 standard deviations. Looking at a table of the Gaussian, this is significant at the 1% level.

My question is regarding the significance at the 1% level. What is it they mean by that statement?

 

[CompuChip]

If indeed the theoretical expectation is 7 with standard deviation 1.65, then of course it is possible that you get only 3 occurrences in any real experiment.
If you calculate the theoretical probability of actually observing this, you will see that it is very small. So if something with such a small probability does happen, this can hardly be a coincidence, and it is a significant event.
The significance level is just a mathematically sound way of saying what the term very small in the previous paragraph means. For example, taking a significance level of 1%, you consider any probability below 1% as very small (and therefore, if you actually observe such an event when you only run the experiment once or twice, it is significant).

 

[Niles]

That does make sense, thank you. I was viewing the significance level (SL) in the light of the null hypothesis. I always understood SL as being the probability that the event happened by chance from the null hypothesis. But in this example, the 3 occurrences of type (our null hypothesis) cannot "accidentally" yield 7 occurrences. So does this mean that my interpretation is wrong?