Essay Example on 95% CI of R's Socioeconomic Index (2010)

The quantitative variable that was chosen for this assignment is sei10, also known as R's socioeconomic index (2010).

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Effect of Different Levels of Confidence and Sample Size on the Width of The Confidence Interval

At the same level of confidence, an increase in the sample size leads to decreased width of confidence intervals, because it reduces the standard error (DeFusco et al., 2015). For example, when the sample size is 100, the width is between 45.329 and 55.048. However, increasing the sample size to 400 decreases the width to between 44.459 (lower limit) and 49.012 (upper limit).

The width of the confidence interval is increased as the confidence level increase (Ayyub & McCuen, 2016). For example, at 90% confidence level of confidence, the width of confidence interval ranges from 44.826 (lower limit) to 48.644 (upper limit). However, increasing the confidence interval to 95%, increases the width to between 44.459 (lower limit) and 49.012 (upper limit).

Implications of underutilization of Confidence Interval

Past empirical studies have reported that confidence intervals are underutilized (Sim & Reid, 1999). There are various implications associated with the use of confidence intervals. First, the width of confidence interval its use allows a researcher to have an achieve precision of the point estimate. Second, confidence intervals help researchers to reject or retain the null hypothesis (Akobeng, 2008). On the other hand, by failing to use confidence intervals, the researcher cannot fully explore the clinical importance of research findings (Akobeng, 2008). Additionally, when confidence intervals are not used, it is impossible to understand a range of possible values for a population parameter and the precision of the measured treatment effect (Akobeng, 2008).

References

Akobeng, A. K. (2008). Confidence intervals and p-values in clinical decision making. Acta Paediatrica, 97(8), 1004–1007. https://doi.org/10.1111/j.1651-2227.2008.00836.x

Ayyub, B. M., & McCuen, R. H. (2016). Probability, statistics, and reliability for engineers and scientists. CRC Press.

DeFusco, R. A., McLeavey, D. W., Pinto, J. E., Runkle, D. E., & Anson, M. J. P. (2015). Quantitative investment analysis. John Wiley & Sons.

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