Introduction to Quantitative Analysis: Confidence Intervals

In this exercise, the Age (Q1) dataset is used in calculating the confidence interval, with consideration of the 95%, which forms the default case (Wagner, 2020). In the Age dataset, the sample has various items ( N= 10250). Hence, by following the steps of Wagner's (2020), the following tables show the confidence interval summaries.

Tables from IBM-SPSS Showing the Summaries 

Reporting the Mean and Analysis Of the Results 

The summary shows the one-sample t-test results, which helps depict the confidence intervals (CI), which in this case, the chosen one is 95%. Of the total items in the dataset ( N= 10250), the mean (M) is 37.01, and the standard deviation is 14.536.

In interpreting the CI, ideas from Frankfort-Nachmias, Leon-Guerrero, and Davis (2020) textbook become useful in this case. From the table, with a test value of 0, the illustrated CI above is 36.73 as the lower value, and 37.29 as the upper value. Hence, in this case, with the 95% CI utilization, based on these results, I am 95% confident that its mean, i.e., the population´s mean, lies between 36.73 (lower limit) and 37.29 (upper limit).

In simplified terms, the confidence is 95%, that Age´s real is not below 36.73 years, and it is not over 37.29 years. In collecting a larger sample in this study from its population (N = 10250), out of 100 cases, 95 of the cases or time, the subject´s true population mean lies between 36.73-37.29 years. This means that there is a risk of 5% for a researcher that making this decision or conclusion is wrong (Frankfort-Nachmias, Leon-Guerrero & Davis, 2020). In five (5%) cases, when choosing from 100 cases, the mean for the examined population will lie outside the interval of 36.73 years to 37.29 years. This interval is very slim (smaller width), something associated with its sample size, i.e., with increasing sample sizes, there is the resulting attainment of smaller confidence intervals, as these two have an inverse relationship (Frankfort-Nachmias, Leon-Guerrero & Davis, 2020). In this case, the sample is large ( N= 10250), resulting in the study's small CI width. This is advantageous, as it gives better and precise effects estimations for the chosen dataset, better than utilizing a smaller sample.

Explanation of Likely Implications for Social Change 

Confidence interval has many social change implications, and as a researcher, understanding and utilizing the concept is essential, especially in making the right conclusions. The Confidence interval concepts are paramount for decision-makers and other stakeholders, e.g., policy-makers, social and economic planners, among other stakeholders relying on understanding the community´s or population´s Age.

There is risk in life or social settings, and with confidence intervals, this forms one of the significant risks one makes. First, since during studies, sometimes, with the resources being limited and the constraints on time, utilizing samples becomes possible. Hence, with a desire to make population-based conclusions, relying on confidence interval becomes very pivotal from a distinctively chosen small sample. From a selected sample, one researcher can effectively decipher any likely variation within a specific population and give the researcher the range estimate for the population (Frankfort-Nachmias, Leon-Guerrero & Davis, 2020; Wagner, 2020). Through this process, confidence intervals are essential in helping social scientists or other researchers in gauging ranges that a specific parameter or answer lies.

As seen in this exercise of the Afrobarometer dataset, with a focus on Age (Q1), since the interest is on Age, one can successfully gauge the range that the real population lies, and in this case, this is 36.73 years to 37.29 years. As a decision-maker or the different policymakers, they can create proper measures and policies to meet community needs. with this information

As a researcher, either when planning for social improvement practices or other policies needed in helping communities, using CI is useful. Apart from providing a specific range, CI's values are essential in informing the interested stakeholders and the respective stability in the estimation (i.e., 36.73-37.29 years). Thus, if there is obtaining a stable estimate, for example, between 36.73 years to 37.29 years, there is a better chance that when there is repeating this survey with the collection of information on Age, getting the same results will be simplified or possible.

In researching, like in this case with the Age (Q1) dataset, there is calculating its mean, which is only one parameter or metric that is fully estimated. Hence, in applying confidence intervals, there is offering more information or better data. In this case, there is showing as a researcher some of the potential values making up the population´s real mean (M). Hence, when planning, especially by interested stakeholders, e.g., government agencies, health planners or economic decision-makers and other policy-makers, using confidence interval offers some critical aspects about the data, better than only relying on the mean (M).

References

Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society (9th ed.). Thousand Oaks, CA: Sage Publications.

Wagner, III, W. E. (2020). Using IBM® SPSS® statistics for research methods and social science statistics (7th ed.). Thousand Oaks, CA: Sage Publications.