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

In summary, the conversation discusses the significance level in statistics and its relation to probability and the null hypothesis. The example given shows a difference of 4 occurrences between the observed and expected values, which is significant at the 1% level. The significance level is a way of determining the probability of an event happening by chance and in this case, the small probability of the observed result makes it a significant event. The significance level should not be interpreted as the probability of an event happening by chance from the null hypothesis, but rather as a measure of how significant the observed result is.
  • #1
Niles
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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?
 
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  • #2


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).
 
  • #3


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?
 

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

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