Midzuno the Whiz -As previously discussed

Examination of all elements within a population presents insurmountable challenges; therefore researchers observe samples, smaller representative subsets extracted from a larger population and draw inferences from those samples. Statistical inference processes, researchers, and statisticians employ confidence intervals to ascertain estimates of unknowns with a population parameter (Chernick, 2008).

Determining intervals within which one expects the parameter may fall with a certain degree of confidence holds significance.  Confidence intervals inform levels of certainty for estimates.  Formulaically CI presents as Confidence Interval = Estimate ± Margin of error.

The designation of 95% shows the probability associated with the process that generated the interval and one must not misinterpret this as the interval having a probability of 0.95 that the true value of the parameter falls inside of the interval (Lawless, 2005).

Table1.0 One-Sample T-Test Age Variable

Sample Size	Mean	95% CI	90%CI
[N=100]	46.66	[43.21, 50.11]	[43.78, 49.54]
[N=400]	49.51	[47.79, 51.23]	[48.07, 50.95]

 

Table 1.0 presents the results of a One-Sample T-Test analysis of the age variable extrapolated from the General Social Survey dataset.  This activity aims to determine the age of most responding participants within the parameter.  

Larger samples result in smaller margins of error, thus resulting in distributions presenting as more clustered around the population parameter. A tightly clustered distribution implies more narrow confidence intervals and therefore more precision. As the sample size increased from n=100 to n=400, the Confidence Interval remained constant for the first case 90% and the interval width decreased, [43.78, 49.54] to [48.07, 50.95] and 5.76 to 2.88 respectively.

If confidence levels increase from 95% to 99% in both sample sizes, N=100 and N=400, the confidence interval also increased. For the sample of N=100, as the confidence level increased from 90% to 95% the confidence interval increased from [43.78, 49.54] to [43.21, 50.11] respectively. Likewise, for the sample of N=400 as the confidence level increased from 90% to 95% the confidence interval increased from [48.07, 50.95] to [47.79, 51.23] respectively.

This suggests that for one to achieve a greater level of confidence that the interval contains the population parameter, one must increase the size of the interval. To ameliorate any compromise between the level of confidence and the precision of the range, one must increase the sample size.

While confidence intervals offer a more accurate degree of certainty, this approach is underutilized perhaps because of the complexity, the perspective of the researcher setting the confidence level, and the fact that application of confidence intervals may vary across different types of research complicating interpretation.

Work by Durkin et al. demonstrates both the complexities and usefulness of confidence intervals.  These researchers study the effects of parental age on the probability of occurrences of child autism spectrum disorder.  The authors present a quantitative analysis using data from 10 study sites within the Unites States participating in the Centers for Disease Control’s Developmental Disabilities Monitoring Network (ADDM).  This study identified increased risk for autism in for children with older parents.  The authors use confidence intervals to evaluate the magnitude of associations between each potential confounding factor (e.g. birth order, gender), the independent variables of maternal and paternal age in addition to the dependent variable Autism Spectrum Disorder (ASD) case status (Durkin, 2008).    Risk reduction correlates with increased confidence level resulting in a wider confidence interval.  This study seeks to provide information that may reduce the risk of ASD occurrences.  Furthermore, this example confirms the effectiveness of confidence intervals as a reporting tool and statistics presented in this study using confidence intervals hold implications for public health, forecasting, and autism etiology research (Durkin, 2008). 

 

References

Chernick, M. R. (2008). Bootstrap Methods: A Guide for Practitioners and Researchers by CHERNICK, M. R. Biometrics, 64(3), 998-999. doi:10.1111/j.1541-0420.2008.01082_17.x

Durkin, M. S., Maenner, M. J., Newschaffer, C. J., Lee, L., Cunniff, C. M., Daniels, J. L., Schieve, L. A. (2008). Advanced Parental Age and the Risk of Autism Spectrum Disorder. American Journal of Epidemiology, 168(11), 1268-1276. doi:10.1093/aje/kwn250

Frankfort-Nachmias, C., & Leon-Guerrero, A. (2017). Social statistics for a diverse society. Thousand Oaks, CA: Sage Publications.

Lawless, J. F. (2005). Frequentist prediction intervals and predictive distributions. Biometrika, 92(3), 529-542. doi:10.1093/biomet/92.3.529