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.
Prior to beginning work on this discussion, read 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 #7 (Links to an external site.), Z-Scores and percentiles: Crash Course Statistics #18 (Links to an external site.), and The Normal Distribution: Crash Course Statistics #19 (Links 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.
Discusiion 1
Hello all,
When comparing data from different distributions, it is beneficial to transform data from these distributions to conform to the standard distribution because there would be an interpretation issue. “One way to resolve this interpretation problem is to convert the scores from different distributions into a common metric, or measurement system (Tanner, 2016).”
Z scores represent individual scores in the standard distribution. It makes it comprehensible and easier to compare scores under one distribution. “It shows how many standard deviations a particular value is away from the mean (Study.com).”
The relationship between z scores and percentages is that once z scores are converted, then they are able to be converted into percentages. The percentages can be converted into a percentile and then used to determine where a score ranks in comparison to another score (Tanner, 2016).
One real-life variable that is likely to be normally distributed in population is SAT scores. Z scores would be used to bring identity to the parameter of the scores being that they could vary a lot. Bringing them into a view of where the scores are above or below the mean.
References:
Tanner, D. (2016). Statistics for the behavioral & social sciences (2nd ed.). Bridgepoint Education.
Discussion 2
*When comparing data from different distributions, what is the benefit of transforming data from these distributions to conform to the standard distribution?
There are varied normal distributions making it challenging to compare an individual’s performance over several normally distributed measures (Hill, 2018). On the other hand, both the mean and standard deviation have set values. Therefore, transforming data from varied distributions to go with the standard deviation makes it easier to collect data. We can gather more information from data with normal distribution.
*What role do z scores play in transforming data multiple distributions to the standard normal distribution?
Z-scores also referred to as standard scores are normal random individual scores of a standard normal distribution (Hill, 2018). Notably, an individual may be provided with scores from varied distributions. Therefore, he/she should change the provided scores with the help z-transformation equation. Once the scores are in the form of z-scores, one can compare them to other scores in the normal standard distribution more precisely.
*What is the relationship between z scores and percentage?
While Z-scores utilize mean as average, percentiles utilize median as average. The above relationship provides significant information and allows z-scores to be changed into percentages. Besides, Z-scores turn raw scores into standard deviations through the transformation formula (Hill, 2018).
*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.
Height is one of the few variables that are normally distributed in the population. Z-scores would be used to show the relationship between one variable and other variables. For instance, in a research on malnutrition among children in a certain country, z-scores can be used to determine the spread of children’s weight over different heights.
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