Introduction to Quantitative Analysis: Confidence Intervals

Age (Q1) Continuous Data 

Taking Random Sample of 100 

In this confidence interval (CI) task, the Age (Q1) variable from the Afrobarometer dataset is used. In calculating the confidence interval, the “One-Samples T-Test” option in SPSS is applied (Wagner, 2020). To randomly select 100 items, the “select cases” function in SPSS was used to choose 100 items from the first 10,000 randomly since the dataset is over 10,000. The tables below show the CIs of the selected 100 data items for the Age variable.

Calculate the 95% confidence interval for the variable 

Based on the output, for the 100 samples, the mean is 35.67 ( M= 35.67 , SD= 13.84), and [we are] 95% confident that for the dataset, its mean lies between 32.92 (lower limit) and 38.42 (upper limit).

Calculate a 90% confidence interval 

Secondly, in this case, for the 100 samples, based on the output, [we are] 90% confident that for the dataset, its mean lies between 33.37 (lower limit) and 37.97 (upper limit).

Taking Another random sample of 400 

In randomly selecting 400 items, the “select cases” function was used on specifying 400 items from the first 10,000. The tables below are outputs for 95% and 90% confidence intervals.

Calculate the 95% confidence interval for the variable 

In the case of 400 randomly selected items from the dataset, the summary table gives useful information ( M= 37.39 , SD= 14.99). Using the output, [we are] 95% confident that for the dataset, its mean lies between 35.92 (lower limit) and 38.86 (upper limit).

Calculate a 90% confidence interval 

In this second case, for the 400 randomly selected items from the dataset, based on the output, [we are] 90% confident that for the dataset, its mean lies between 36.15 (lower limit) and 38.63 (upper limit).

Explaining Confidence intervals are underutilized Statement 

As a statistician or researcher, there is a need to include CI to improve conclusions and raise reliability whenever presenting sample statistics, e.g., reporting means or sometimes individual means differences for groups in studying given population parameters. Secondly, there is a need to provide CIs during undertaking hypothesis testing. The information can help better understand the process and dataset, especially when statistical significance summaries or conclusions. Lastly, it’s essential to include CIs to understand better the practical clinical implications or importance of the reported study findings. Lastly, with differences in sample sizes affecting confidence intervals, it becomes useful to indicate confidence intervals as a researcher. For example, from the dataset, CIs for 100 and 400 samples do vary.

This is also supported in the course text; an inverse relationship exists between/across sample sizes and respective confidence interval width (Frankfort-Nachmias, Leon-Guerrero & Davis, 2020). Hence, in comparing confidence intervals for the two samples, i.e., 100 and 400, it is seen that for the larger sample (400), the width of the confidence interval is less. That is, with sample size increases, there is the respective decreasing of resulting standard error. Hence, with larger sample sizes, confidence interval precision improves, i.e., there is better precision (Frankfort-Nachmias, Leon-Guerrero & Davis, 2020).

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.