Shruti Kulkarni
046

Definition of 'Z-Score'

• A Z-Score is a statistical measurement of a score's relationship to the mean in a group of scores. 
• A Z-score of 0 means the score is the same as the mean.
•  A Z-score can also be positive or negative, indicating whether it is above or below the mean and by how many standard deviations.
• In addition to showing a score's relationship to the mean, the Z-score shows statisticians whether a score is typical or atypical for a particular data set.
•  Z-scores also allow analysts to convert scores from different data sets into scores that can be accurately compared to each other. 
• One real-life application of z-scores occurs in usability testing.
• A z-score (also known as z-value, standard score, or normal score) is a measure of the divergence of an individual experimental result from the most probable result, the mean. 
• Z is expressed in terms of the number of standard deviations from the mean value.

 (6)

X = ExperimentalValue

μ = Mean

σ = StandardDeviation

• Z-scores assuming the sampling distribution of the test statistic (mean in most cases) is normal and transform the sampling distribution into a standard normal distribution. As explained above in the section on sampling distributions, the standard deviation of a sampling distribution depends on the number of samples. 

• Whenever using z-scores it is important to remember a few things:

1) Z-scores normalize the sampling distribution for meaningful comparison.
2) Z-scores require a large amount of data.
3) Z-scores require independent, random data.

 (7)

n = SampleNumber