Z Score- Group 1 Arti Chandavarkar

Z-SCORE

In statistics, the standard score also called the z- score is the number of standard deviations an observation or datum is above the mean. Thus, a positive standard score represents a datum above the mean, while a negative standard score represents a datum below the mean. It is a dimensionless quantity obtained by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. This conversion process is called standardizing or normalizing.

The standard score of a raw score x is

where:

μ is the mean of the population;

σ is the standard deviation of the population.

Values of Z-scores:

   Has a value of 0, it is equal to the group mean.

    Is positive, it is above the group mean.

    Is negative, it is below the group mean.

    Is equal to +1, it is 1 Standard Deviation above the mean.

    Is equal to +2, it is 2 Standard Deviations above the mean.

    Is equal to -1, it is 1 Standard Deviation below the mean.

    Is equal to -2, it is 2 Standard Deviations below the mean.

    Is equal to +3, it is 3 Standard Deviations above the mean.

    Is equal to -3 it is 3 Standard Deviations below the mean.

Properties of Z-score:

1. Mean of Z-score is o and Standard deviation of Z-score is 1.

2. Z-score distribution for normal distribution is the same as the data distribution.

Practical applications of Z-score:

Z-scores enable us to compare scores on different kinds of measures of the same variable.

For example: Measurement of child nutrition

Nutritional deterioration and improvement of individuals can be monitored using Z-scores as long as the mean and standard deviation for a given height are known.

Sources:

http://fex.ennonline.net/1/practical

http://www.coedu.usf.edu/ychen/EDF6432/pdf/module11.pdf.

http://en.wikipedia.org/wiki/Standard_score.

http://statistics-help-for-students.com/What_are_Z_scores.htm#.UlI8GNJHKSo.