MATH 225 Week 6 Discussion: Confidence Intervals

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Chamberlain University

MATH-225 Statistical Reasoning for the Health Sciences

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Date

Confidence Intervals

In simple terms, a confidence interval (CI) represents a range of values surrounding a sample statistic, such as a mean or proportion. This interval indicates where clinicians can expect to find similar results if they replicate the study’s protocol or intervention, including the same outcome measurements. When considering whether research findings can be applied to practice, it is crucial to evaluate their precision, which is reflected in the confidence interval. A narrow CI around a sample statistic suggests a high degree of reliability, meaning the results can be expected to remain consistent across different implementations of the research.

For instance, consider a systematic review that examines the impact of tai chi on sleep quality in older adults. If the analysis yields a lower boundary CI of 0.49, a study statistic of 0.87, and an upper boundary of 1.25, this indicates that each limit is 0.38 units away from the sample statistic, reflecting a relatively narrow CI. The calculation (UB + LB)/2 = Statistic results in (1.25 + 0.49)/2 = 0.87. It’s important to note that a mean difference of 0 signifies no difference, and since this CI does not encompass 0, the sample statistic is statistically significant and unlikely to arise by chance. Given that the systematic review supports tai chi as beneficial for sleep, clinicians can confidently recommend tai chi exercises to patients experiencing sleep difficulties based on these findings.

Initial Post Instructions

Reflecting on the various variables tracked by healthcare facilities, confidence intervals can be generated for population parameters such as means or proportions derived from these variables. Select a topic of study relevant to your workplace, describe the chosen variable and parameter (mean or proportion), and explain your rationale for creating an interval that captures the true parameter value with 95% confidence. Consider how adjusting the confidence interval to 90% or 99% might influence the study outcomes and which level (90%, 95%, or 99%) is most appropriate based on the selected study type. Additionally, contemplate how the study results could be presented to management in a bid to drive change within the organization.

Concept	Explanation
Definition of Confidence Intervals	Confidence intervals are estimated ranges derived from sample data that likely include the true population mean. They provide upper and lower limits around the sample mean, instilling confidence in capturing the population mean.
Common Confidence Levels	Confidence intervals are often set at 95% or 99%. The 95% CI is commonly used because higher confidence levels increase the margin of error, potentially leading to an impractically wide interval that may diminish the data’s usefulness.
Application in Healthcare	In healthcare, blood glucose control is frequently monitored, particularly in critically ill patients. Utilizing confidence intervals can help determine the best glucose control algorithm for similar patient groups. For example, in a sample of 30 patients with a mean glucose level of 111, the 95% confidence interval might range from 102 to 120, suggesting that 95% of patients using this algorithm can expect their blood glucose levels to fall within that range.

Concept

Explanation

Definition of Confidence Intervals

Confidence intervals are estimated ranges derived from sample data that likely include the true population mean. They provide upper and lower limits around the sample mean, instilling confidence in capturing the population mean.

Common Confidence Levels

Confidence intervals are often set at 95% or 99%. The 95% CI is commonly used because higher confidence levels increase the margin of error, potentially leading to an impractically wide interval that may diminish the data’s usefulness.

Application in Healthcare

In healthcare, blood glucose control is frequently monitored, particularly in critically ill patients. Utilizing confidence intervals can help determine the best glucose control algorithm for similar patient groups. For example, in a sample of 30 patients with a mean glucose level of 111, the 95% confidence interval might range from 102 to 120, suggesting that 95% of patients using this algorithm can expect their blood glucose levels to fall within that range.

References

Holmes, A., Illowsky, B., & Dean, S. (2017). Introductory to Business Statistics. OpenStax. Retrieved from https://openstax.org/details/books/introductory-business-statistics

MATH 225 Week 6 Discussion: Confidence Intervals