Application of Standardized Scores to Reflect on their Benefits

Application of Standardized Scores to Reflect on their Benefits

Application of Standardized Scores to Reflect on their Benefits

Benefits of Transforming Data from Multiple Distributions to Conform to a Standard Distribution

For the purpose of data comparison from different distributions, it is beneficial to transform data from multiple distributions to conform to a standard distribution since it makes comparison easier between different distributions (Tanner, 2016). For instance, when comparing two test scores with a scale of 0-100 and 0-500, respectively, converting the distributions to a standard distribution (common metric) makes comparison easier, such as by looking at the probability values.

The Role of Z Scores in Standard Normal Distribution

When transforming data from multiple distributions to the normal standard distribution, the different scores are converted to z-scores, which makes it possible to apply the z-transformation formula (Tanner, 2016). The z-scores act as the metrics for comparing to other scores in a normal distribution.

The Relationship between Z Scores and Percentages

The relationship between the two measures can be discussed under two dimensions. Firstly, z-scores use the standard deviation of a population to tell how individual data compares to the population mean, while percentages represent a population sample (Beyer, 2021). Secondly, the relationship between z-scores and percentages is that both use two closely related measures of central tendency as their average. Particularly, z-scores use the mean as the average (z-score of 0), while percentiles use the median as the average (50^th percentile).

An Example and Application in a Real-Life Situation

An example of a normally distributed variable whose z-scores would be useful in a real-life situation is the number of adults between 18-25 years who have attained an undergraduate degree in a population or country. The distribution of the adults would be a normal distribution. The z-scores can be used to calculate the probability that an adult between 18 and 25 years old has attained an undergraduate degree.

References

Beyer, A. (2021). Introduction to Statistics for Psychology. Creative Commons.

Tanner, D. (2016). Statistics For the Behavioral & Social Sciences (2nd Ed.). Bridgepoint Education, Inc.

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For this discussion, identify the appropriate application of standardized scores to reflect on their benefits and interpret how test scores and measures are commonly presented.

Application of Standardized Scores to Reflect on their Benefits

Prior to beginning work on this discussion, read the Instructor Guidance for Week 3 and Chapter 3 of your course text, which introduces probability and the standard normal distribution. Also review the required videos for this week: The Shape of Data: Distributions: Crash Course Statistics #7Links to an external site., Z-Scores and percentiles: Crash Course Statistics #18Links to an external site., and The Normal Distribution: Crash Course Statistics #19Links to an external site.. It will also be helpful to review Section 2.3 in the textbook about normal distribution. Examine the assumptions and limitations presented in these topics and then consider and discuss the following questions:

When comparing data from different distributions, what is the benefit of transforming data from these distributions to conform to the standard distribution?
What role do z scores play in transforming data from multiple distributions to the standard normal distribution?
What is the relationship between z scores and percentages?
Give an example of a variable likely to be normally distributed in the population and explain how z scores pertaining to that variable would be useful in a real-life situation.