RAJIV KUMAR SINGH
ROLL-2013031
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.
Most statistical tests begin by identifying a null hypothesis. The null hypothesis for pattern analysis tools essentially states that there is no pattern; the expected pattern is one of hypothetical random chance. The Z Score is a test of statistical significance that helps you decide whether or not to reject the null hypothesis.
Z scores are measures of standard deviation. For example, if a tool returns a Z score of +2.5 it is interpreted as "+2.5 standard deviations away from the mean". Z score values are associated with a standard normal distribution. This distribution relates standard deviations with probabilities and allows significance and confidence to be attached to Z scores.
Very high or a very low Z scores are found in the tails of the normal distribution. From the graph above, it is evident that the probabilities in the tails of the distribution are very low. When you perform a feature pattern analysis and it yields either a very high or a very low Z Score, this indicates it is very UNLIKELY that the observed pattern is some version of the theoretical spatial pattern represented by your null hypothesis.
In order to reject or accept the null hypothesis, you must make a subjective judgment regarding the degree of risk you are willing to accept for being wrong. This degree of risk is often given in terms of critical values and/or confidence level.
To give an example: the critical Z score values when using a 95% confidence level are -1.96 and +1.96 standard deviations. If your Z score is between -1.96 and +1.96 you cannot reject your null hypothsis; the pattern exhibited is a pattern that could very likely be one version of a random pattern. If the Z score falls outside that range(for example -2.5 or +5.4), the pattern exhibited is probably too unusual to be just another version of random chance. If this is the case, it is possible to reject the null hypothesis and proceed with figuring out what might be causing either the statistically significant clustered or statistically significant dispersed pattern.
