8210 wk 4 dis

Assignment Task 2

Respond to one of your colleague’s posts in 125 words response and explain how you might see the implications differently.

Colleague Response

Romel Jimera 

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For this week's discussion on the relationship between data variability, sample size, and confidence level, I chose the "Size of the Place in 1000s" as my quantifiable variable, utilizing the General Social Survey dataset. The mean Age from that dataset is 49.01. To better appreciate the tradeoff between lowering the risk of our confidence in estimations and increasing precision, I entered a random sample size of 100 and 400 with 90 and 95 percent confidence levels, using IBM SPSS Statistics software.

Table 1

In Table 1, the left table shows a random sample of 100, a mean of 324.90, and a standard error of 121.911. Using a 95% confidence interval (CI), the estimation was only 5% off (Frankfort-Nachmias et al., 2021). Meaning we are 95% confident that the actual average size of the place in 1000s is not less than 83 and not more than 566.8. However, with a 90% confidence level in the right table, all the values remain the same except for the CI (122.48, 527.32). Although the CI width is shorter than the previous one, there is more precision, but the chance of error has increased to 10%. Can we lower the error probability by expanding the sample size to 400?

Table 2

In Table 2, the left table displays a random sample of 400, which has a lower standard error of 48.931 than a smaller sample of 100. In a 95% CI, the width has become narrower, and the values of the lower and upper bounds (187.58, 379.96) are more proximate to the mean (283.77). By increasing the sample size, researchers can enhance the precision of their estimates by decreasing the CI width (Frankfort-Nachmias et al., 2021). Consequently, the sample size and the confidence interval width are inversely related. On the other hand, the right table shows the same outcome as the left table, but with a lower bound of 203.10 and an upper bound of 364.44, based on a 90% CI. Hence, the CI becomes more precise when decreasing the confidence level from 95% to 90%.

Confidence intervals are underutilized because they can lead to unjustified or arbitrary inferences (Morey et al., 2016), resulting in conclusions without sufficient evidence then requiring a larger sample size. However, they can be an efficient approach for statistical inference (Sim & Reid, 1999). For instance, on November 18, 2020, Pfizer summarized its Phase 3 study of the COVID-19 vaccine, resulting in a 95% probability of the vaccine efficacy rate between 90.3% and 97.6% (Wang, 2021). After the vaccine was made accessible to the public, the pooled efficacy of the vaccination in preventing mortality from COVID-19 was 96.1% (95% CI: 91.5–98.2%) (CDC, 2021). These studies provide a grounded illustration of the critical nature of CI.

While increasing the confidence level to minimize the error probability, the estimate becomes less exact. Increasing the precision of an estimate demands a larger sample size, which might be challenging. It is crucial to recognize the tradeoff relationships when deciding whether we want more accuracy, a lower error probability, or a higher confidence level. Unfortunately, we cannot have them all, and this is the caveat.

References

CDC. (2021). Grading of recommendations, assessment, development, and evaluation (GRADE): Pfizer-BioNTech COVID-19 vaccine.  https://www.cdc.gov/vaccines/acip/recs/grade/covid-19-pfizer-biontech

Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2021). Social statistics for a diverse society (9th ed.). Sage.

Morey, R. D., Hoekstra, R., Rouder, J. N., Lee, M. D., & Wagenmakers, E. J. (2016). The fallacy of placing confidence in confidence intervals. Psychonomic bulletin & review, 23(1), 103-123.  https://doi.org/10.3758/s13423-015-0947-8

Sim, J., & Reid, N. (1999). Statistical inference by confidence intervals: Issues of interpretation and utilization. Physical Therapy, 79(2). 186-195.  https://doi.org/10.1093/ptj/79.2.186

Wang, F. (2021). Confidence intervals of COVID-19 vaccine efficacy rates. Numeracy: Advancing Education in Quantitative Literacy, 14(2), 1-19.  https://doi.org/10.5038/1936-4660.14.2.1390

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