Is this a correct statement regarding a normal distribution?

#1
Note: this is not homework.

I am trying to make sure I understand the differences between percentiles and z-score. Please tell me if the following compare/contrast statements are correct.

Thanks,

Mike

1. The 95th percentile is the value such that 95% of all observations are below. In other words it gives the top 5% of values, regardless of how closely the data actually fits the normal distribution.

2. Values with a z-score >= 1.64 are values at least 1.64 standard deviations greater than the mean. This corresponds to the 5% significance level for a 1-tailed test.

3. In perfectly normally distributed data the 95th percentile and values with a z-score >= 1.64 will be the same (if not then really close).

4. Percentiles will always give a cutoff which includes some of the data. Z-scores may give a cutoff which includes none of the data if the distribution of that data is actually not so normally distributed.
 

CB

Super Moderator
#3
1. The 95th percentile is the value such that 95% of all observations are below.
Yes

2. Values with a z-score >= 1.64 are values at least 1.64 standard deviations greater than the mean.
Yes

This corresponds to the 5% significance level for a 1-tailed test.
Yes, though "z-tests" aren't used that often in actual applied significance testing.

3. In perfectly normally distributed data the 95th percentile and values with a z-score >= 1.64 will be the same (if not then really close).
Yes

4. Percentiles will always give a cutoff which includes some of the data. Z-scores may give a cutoff which includes none of the data if the distribution of that data is actually not so normally distributed.
Erm, I suppose so. Unusual question.

HTH.
 
#4
I thought, perhaps wrongly, that z-scores corresponded to percentiles, i.e. 0 is the 50th centile. Or, is this only true when the data is normally distributed?
 

CB

Super Moderator
#5
I thought, perhaps wrongly, that z-scores corresponded to percentiles, i.e. 0 is the 50th centile. Or, is this only true when the data is normally distributed?
It will be true when the variable is normally distributed, but will not necessarily be true if it is not.

Cheers,
CB