## Average Income Discussion Responses

Average Income Discussion Responses

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Discussion 1: Meredith

Using only a selected population for estimating an average is not a good approach. In this case, using just the income of business school students is not an accurate portrayal of the entire GCU population and can mislead inferences. A better approach would be to use random sampling. According to Piegorsch (2015), the “fundamental requirement of any random sample is that it be representative of the population under study”. Everyone within the GCU student population needs to have an equal chance of being chosen for the study (Shin, 2020).

The selection for the study needs to remain unbiased. Shin (2020) discusses four methods for collecting a random sample of data. Average Income Discussion Responses

1. Simple – creating a list

2. Stratified – gathering from predetermined segments of the population

3. Cluster – gathering from groups that represent the entire population

4. Systematic – selecting every k’th member

In our example of income of GCU students, the easiest way to ensure a random population would be to use the first method – Simple Random Sampling. We could request a list of all students from the registrars office, then use a random number generator to determine which students would be surveyed. This would keep the selection random and unbiased.

Piegorsch, W. W. (2015). *Statistical data analytics: Foundations for data mining, informatics, and knowledge discovery (Ch. 3). *West Sussex, UK: Wiley. ISBN-13: 9781118619650

Shin, T. (October 25, 2020). *Four types of random sampling techniques explained with visuals: the secret to minimizing biased data!* Towards Data Science. Retrieved on December 2, 2021 from https://towardsdatascience.com/four-types-of-random-sampling-techniques-explained-with-visuals-d8c7bcba072a

Discussion 2: Royce

When it comes to the process described, it would not be a beneficial way for anyone to say the average income of all GCU students. First off using just the business school students is creating a severe bias in our population and does not reflect all other majors that are included in GCU. For a real average we would need random sampling from the whole school. According to Piegorsch “Left unrecognized, distorted or haphazard sampling can introduce severe biases into the data, restricting the scope of the corresponding statistical inferences” meaning that whatever analysis we produce from that information is useless. It just comes down to random sampling throughout all students and then average the incomes would give us a better tall tell sign. The only saving grace of doing just the business school would be that the salaries can be a wide range that it would not be the absolute worst case. But then if you ignore something like a medical field where the salary ranges are typically way higher compared to something like teaching where salaries are not the best (that’s what my high school teachers told me in Nevada) then we would need to get a better random sampling. Again, if we just wanted to change the question of ALL income to just the students in business we wouldn’t have a problem, its when we have a biased sample of business students trying to be the sample for all that we get the bias and can see issues coming about for our analysis.

Reference:

Piegorsch, W. (2015). *Statistical data analytics foundations for data mining, informatics, and knowledge discovery. *Retrieved from our topic resources

Discussion 3: Arcelia

The process described above deviates from best practices when creating a sample group that is representative of the whole. As noted by Young (2021), the sample must accurately represent and reflect the larger population for it to be meaningful. Intuitively, there is no basis for assuming that the average income of a small subset of GCU business majors is representative of the broader GCU student body. A more formal sampling strategy would reduce distortion and provide more meaningful insights.

A major issue with the sampling method used in the example is that the method by which the sample was collected does not utilize any formal sampling strategies. The use of these strategies reduces distortion, bias, and allows for meaningful insights to be obtained.

As noted by Piegorsch (2015), Simple Random Sample (SRS) is a basic sampling strategy that samples a larger population randomly. This method reduces bias by creating a sample where each data point has no influence on any other. For example, if we wanted to use random sampling in the scenario discussed above, we would increase our sample size to include students outside of the College of Business and our social circle. Then we would, at random, create a sample from the greater population to conduct our study on where the criterion would be students who attend Grand Canyon University.

Young (2021) discusses Stratified Random Sampling, another sampling method that can be utilized to create a representative sample. While more time-consuming and difficult to implement, this method allows an analyst to examine the population characteristics and use these to divide the population into strata. With this information handy, the analyst can create a more representative sample by utilizing the information gleaned from the classifications of the population.

References

Piegorsch, W. W. (2015). *Statistical data analytics: Foundations for data mining, informatics, and knowledge discovery* (1st ed.). Wiley.

Young, J. (2021, October 29). *Representative Sample is often used to extrapolate broader sentiment*. Investopedia. Retrieved November 30, 2021, from https://www.investopedia.com/terms/r/representative-sample.asp

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