# Confidence Intervals

## Confidence Intervals

Confidence Intervals 150 150 Peter

Confidence Intervals

In everyday terms, a confidence interval is the range of values around a sample statistic (such as mean or proportion) within which clinicians can expect to get the same results if they repeat the study protocol or intervention, including measuring the same outcomes the same ways. As you ask yourself, &quot;Will I get the same results if I use this research?&quot;, you must address the precision of study findings, which is determined by the Confidence Interval. If the CI around the sample statistic is narrow, you can be confident you will get close to the same results if you implement the same research in your practice.

Consider the following example. Suppose that you did a systematic review of studies on the effect of tai chi exercise on sleep quality, and you found that tai chi affected sleep quality in older people. If, according to your study, you found the lower boundary of the CI to be .49, the study statistic to be 0.87, and the upper boundary to be 1.25, this would mean that each end limit is 0.38 from the sample statistic, which is a relatively narrow CI.

(UB + LB)/2 = Statistic [(1.25 + .49)/2 = .87]

Keep in mind that a mean difference of 0 indicates there is no difference; this CI does not contain 0. Therefore, the sample statistic is statistically significant and unlikely to occur by chance.

Because this was a systematic review, and tai chi exercise has been established from the studies you assessed as helping people sleep, based on the sample statistics and the CI, clinicians could now use your study and confidently include tai chi exercises among possible recommendations for patients who have difficulty sleeping.

Now you can apply your knowledge of CIs to create your own studies and make wise decisions about whether to base your patient care on a particular research finding.

Initial Post Instructions

Thinking of the many variables tracked by hospitals and doctors’ offices, confidence intervals could be created for population parameters (such as means or proportions) that were calculated from many of them. Choose a topic of study that is tracked (or that you would like to see tracked) from your place of work. Discuss the variable and parameter (mean or proportion) you chose, and explain why you would use these to create an interval that captures the true value of the parameter of patients with 95% confidence.

Consider the following:

How would changing the confidence interval to 90% or 99% affect the study? Which of these values (90%, 95%, or 99%) would best suit the confidence level according to the type of study chosen? How might the study findings be presented to those in charge in an attempt to affect change at the workplace?

### Sample Paper

Confidence Intervals

Low-density lipoprotein (LDL) cholesterol is one of the essential variables that healthcare facilities track. Past scientific evidence has shown a correlation between high LDL levels and heart disease and stroke risk. Hence, care providers measure it among patients whose age or weight imposes a greater concern for developing either condition.

Clinicians consider levels below 100mg/dL to be optimal and those above 190mg/dL extremely high (Fletcher, 2021). However, the LDL values are more meaningful to clinicians when the patient is inherently at risk of heart disease and stroke. Thus, they mainly track LDL levels for people who are overweight or above 65 years. Suppose seventy-five patients falling in this clinical group visit the clinic in a month, and their mean LDL level is 135 mg/dL (standard deviation = 28 mg/dL). Then, one can create an interval to capture LDL’s true value with 95% confidence.

First, one computes alpha, α: = 1-confidence level = 0.05

p* = 1 – α /2 = 0.975

The degrees of freedom = n-1 = 75-1 = 74.

The critical value (from the t-distribution calculator) = 1.993

Next, the standard error of the mean would be: 28/ (√75) = 3.233

Therefore, the margin of error will be 1.993 * 3.233 = 6.44

Thus, the interval that reflects a 95% confidence level will be 135 ± 6.44 mg/dL

Changing the confidence level to 99% would reduce the margin or error, resulting in a smaller confidence interval, while a 90% confidence level expands the interval (Holmes et al., 2017). Thus, the 95% confidence level is ideal for this measurement since it provides a reasonable range for LDL cholesterol levels for most older adults without immediate health concerns. The intervals at the other confidence levels would be too narrow or too broad to have any significant clinical meaning. Finally, one could use tables to display these findings to the facility leaders. They would, in turn, use the data to create an intervention, empowering patients to reduce their cholesterol levels, thus lowering the risk of heart disease and stroke.

References

Fletcher, J. (2021, Dec. 22). What should my cholesterol level be at my age? https://www.medicalnewstoday.com/articles/315900

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