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.