Work out norm referenced score instantly with clear inputs, formula shown and shareable results.
A norm-referenced score expresses performance relative to a reference group. A raw score of 68 against a mean of 55 and standard deviation of 9 is 1.44 standard deviations above the mean - the 92.6th percentile, a T score of 64.4 and a standard score of 121.7. All four express the same position on different scales.
z score
z = (raw score - norm mean) / norm standard deviation
Score scales
T = 50 + 10z; standard score = 100 + 15z
Whatever the test manual specifies, since norms are published on a particular scale. Reporting the percentile alongside makes it interpretable to non-specialists.
Converting z to a percentile does. If the norm distribution is skewed, empirical percentile tables from the norming sample are more accurate.