There are many normal distributions such as characteristics describing people and in particular their mental characteristics such as achievement motivation, intelligence, reading comprehension, problem-solving ability and verbal aptitude. However, there are differences in these distributions that make it hard to compare data. For instance, their mean and standard deviation greatly varies. Therefore, when comparing data from different distributions, there is need to transform data from these distributions to conform to the standard distribution. The benefit of doing this is that scores from different distributions are able to fit into the same distribution and hence, can be compared directly.
Z-scores play a very important role in this transformation of data from multiple distributions to the standard normal distribution. To begin with, the z-scores represent individual scores in the standard normal distribution. This makes it easier to compare scores under one distribution. In addition, it helps to transform data that can have any mean and standard deviation to a distribution whereby the mean will always be zero and the standard deviation 1.0 (Howel, 2012).
Indeed there is a strong relationship between the z-scores and percentages. To begin with, it would be important to note that a distribution of 1.0 translates to a 100%. Furthermore, because all normal distributions are symmetrical, the percentage of the population between either sides of the mean will have the same absolute value. Therefore, by converting z-scores into percentages, it creates a better mental picture of the nature of the distribution in a particular region under the curve (Howel, 2012).
In my opinion, one does a better job of representing the proportion of the area under the standard curve. This is because; it is easier to work with percentages than z-score. A good example is a situation where a researcher needs to investigate the cholesterol levels in a given population.
Reference
Howel, D. (2012). Statistical Methods for Psychology. Cengage.
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