jlhooter wrote: ↑Mon Jun 05, 2023 5:40 pm
Is the meaning of z-scores another way of saying all data is normalized to one another?
Yes. It represents how unusual a value is compared to the mean. For positioning, a z-score of 2 to 3 can be considered crowded.
Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score.
Yes. It represents how unusual a value is compared to the mean. For positioning, a z-score of 2 to 3 can be considered crowded.
I think that it should be said that an underlying assumption of these z-scores is that the data is Gaussian or normally distributed. This may or may not hold for each of the data shown. I don't know enough here specifically. Real-world datasets may often have non-normal components, e.g. skew or kurtosis. Or, they may often have fatter tails than normal distributions, e.g. see the Gumbel distribution.
The implications of this are that a z-score may imply that the likelihood of some even is really rare, say 3 or 4 z-score. However, if the tail is fatter truly than the normal distribution, then it's actually a more common event than expected.
