ExplanationCalculating and Using z Scores
The method of calculating a z score is very simple: subtract the sample mean from the value and divide what you get by the sample standard deviation.
It should be obvious to the reader that the resulting number (z) has the following properties:
In normally distributed data, 99.99% of the distribution falls below the point where z = 4, so z will rarely be greater than 4 or less than -4.
- z is positive when the value is greater than the mean
- z is negative when the value is less than the mean
- z is the number of standard deviations between the value and the mean.
- z is zero when the value equals the mean
- z has no theoretic upper or lower bound apart from that caused naturally by the range that values can take.
ExplorationThe formula for calculating a z score is given below.
It reads: z equals x minus the sample mean, all over the sample standard deviation, where x is the value for which a z score is required.
Hover over any part of the formula for an explanation of what it means.
ApplicationNow we turn to your own data. We will look at items correctly recalled in the 100 msecs sample. The mean of items correctly recalled in the 100 msecs sample is 13.9 and the standard deviation is 1.92.
Use the calculator to calculate z scores for the following values from your data. Give your answers to 2 decimal places.