z scores are assumed to have come from a normal population with mean zero and standard deviation one. So the farther a z score deviates from the mean of zero the more significant, or unusual, it must be taken to be.
The measure of 'how significant' is the probability of getting a bigger z score.
For example, the probability of getting a z score bigger than 1.96 is about 0.025, the probability of getting one bigger that 3.5 about 0.000233.
Now the obvious problem is, how small is small? For a lot of scientific work either 0.05 is considered 'small enough'. Sometimes 0.01 is demanded. I notice that for recent Higg's boson work scientists have only accepted results associated with even smaller probabilities for some reason.
When you need to calculate probabilities such as these you can use published tables, or there are various kinds of software for desktop use. I have just used wolframalpha.com on the web with the following kind of input:
P[X<3.5] for X~normal with mean 0 standard deviation 1
(You will notice the z score of 3.5 in this expression.)
Chat with our AI personalities
It shows us by telling us how far away it is from the mean.
The Z-score is just the score. The Z-test uses the Z-score to compare to the critical value. That is then used to establish if the null hypothesis is refused.
what is the z score for 0.75
Yes a Z score can be 5.
Assume the z-score is relative to zero score. In simple terms, assume that we have 0 < z < z0, where z0 is the arbitrary value. Then, a negative z-score can be greater than a positive z-score (yes). How? Determine the probability of P(-2 < z < 0) and P(0 < z < 1). Then, by checking the z-value table, you should get: P(-2 < z < 0) ≈ 0.47725 P(0 < z < 1) ≈ 0.341345