Jluterminology 101 Confidence Intervals Part 2 Maher M El Ma ✓ Solved

Jluterminology 101confidence Intervals Part 2maher M El Masri

This article explains how to compare the CIs of two mean scores to draw a conclusion about whether or not they are statistically different. Two mean scores are said to be statistically different if their respective CIs do not overlap. Overlap of the CIs suggests that the scores may represent the same "true" population value; in other words, the true difference in the mean scores may be equivalent. Some researchers choose to provide the CI for the difference of two mean scores instead of providing a separate CI for each of the mean scores. In that case, the difference in the mean scores is said to be statistically significant if its CI does not include zero (e.g., if the lower limit is 10 and the upper limit is 30). If the CI includes zero (e.g., if the lower limit is -10 and the upper limit is 30), we conclude that the observed difference is not statistically significant.

To illustrate this point, let's say that we want to compare the mean blood pressure (BP) of exercising and sedentary patients. The mean BP is 120 mmHg (95% CI mmHg) for the exercising group and 140 mmHg (95% CI mmHg) for the non-exercising group. We notice that the mean BP values of the two groups differ by 20 mmHg, and we want to determine whether this difference is statistically significant. Notice that the range of values between 120 and 130 mmHg falls within the CIs for both groups (i.e., the CIs overlap). Thus, we conclude that the 20 mmHg difference between the mean BP values is not statistically significant. Now, say that the mean BP is 120 mmHg (95% CI mmHg) for the exercising group and 140 mmHg (95% CI mmHg) for the sedentary group. In this case, the two CIs do not overlap: none of the values within the first CI fall within the range of values of the second CI. Thus, we conclude that the mean BP difference of 20 mmHg is statistically significant.

Remember, we can use either the CIs of two mean scores or the CI of their difference to draw conclusions about whether or not the observed difference between the scores is statistically significant.

Paper For Above Instructions

Confidence intervals (CIs) are a vital component of statistical analysis, particularly in the field of health sciences. Their significance lies in providing a range within which the true population mean or parameter is expected to lie, with a specified level of confidence, typically 95%. Understanding how to compare CIs for two sample means is crucial for drawing conclusions about the data at hand. In this context, the overlapping of CIs indicates that the two groups may not exhibit a statistically significant difference, whereas non-overlapping CIs suggest a significant difference between the groups.

To illustrate the concept further, let us consider a practical example: analyzing the mean blood pressure of two groups of patients—those who exercise and those who do not. Suppose we find that the mean blood pressure for the exercising group is 120 mmHg, and for the sedentary group, it is 140 mmHg. The respective 95% confidence intervals for both groups play a critical role in determining whether or not the observed difference in mean blood pressure is statistically significant.

If the confidence interval for the exercising group ranges from 115 to 125 mmHg and that for the sedentary group spans from 135 to 145 mmHg, we observe that these two intervals do not overlap. This indicates that the difference in blood pressure readings between the two groups is statistically significant, as the mean values fall outside each other's range. Conversely, if the confidence interval for the exercising group is 118 to 128 mmHg, and that for the sedentary group is 136 to 144 mmHg—and importantly, the intervals overlap—this indicates that we cannot conclude that the mean blood pressure differs significantly between the two groups.

Additionally, researchers may choose to compute the confidence interval for the difference in means rather than for each mean individually. If we calculate a confidence interval for the difference in mean blood pressures and find it ranges from -5 to 15 mmHg, given that this interval includes zero, we conclude that the observed mean difference is not statistically significant. In this case, we would infer that exercise does not lead to a significant difference in blood pressure compared to a sedentary lifestyle.

Moreover, the width of the confidence interval provides insight into the reliability of our sample estimate. A narrower interval indicates a more accurate estimate of the population parameter, while a broader interval suggests more variability within the sample and less certainty surrounding the estimated mean. For instance, if we had a mean blood pressure of 120 mmHg with a 95% CI of 110 to 130 mmHg, we can infer that our estimate is relatively precise. However, if the CI were 80 to 160 mmHg, this wide range signals a potential lack of reliable data, warranting further investigation.

The empirical rule is also valuable in determining the boundaries within which a certain percentage of observations lie. For instance, in a normally distributed dataset, approximately 68% of the values will fall within one standard deviation of the mean, 95% will fall within two standard deviations, and 99.7% will fall within three standard deviations. Applying this rule in the context of health assessments, one can create a clearer picture of the distribution of health measurements, such as height or blood pressure, among a population.

For the case presented earlier with a sample comprised of students, the mean height of 70.85 inches could be interpreted using the empirical rule. Knowing the confidence intervals for height can help determine how typical or atypical a certain individual's height is among the sample population. For example, if we calculate that 95% of the student heights fall between 59.75 inches and 81.94 inches, we can affirm that an individual height that falls within these bounds is considered statistically normal within this group.

In conclusion, understanding confidence intervals and their implications in statistical analysis is essential for comprehensive and reliable research outcomes. When attempting to establish whether differences between groups are statistically significant, researchers must consider the overlap of confidence intervals or confidence intervals for their differences. This statistical approach allows them to better assess whether interventions or differences in behavior, such as exercise or dietary changes, have significant health impacts.

References

• Lang, T.A., & Secic, M. (2006). How to Report Statistics in Medicine (2nd ed.). Philadelphia: American College of Physicians.
• Hildebrandt, M., Vervà¶lgyi, E., & Bender, R. (2009). Calculation of NNTs in RCTs with time-to-event outcomes: A literature review. BMC Medical Research Methodology, 9, 21.
• Hildebrandt, M., Bender, R., Gehrmann, U., & Blettner, M. (2006). Calculating confidence intervals for impact numbers. BMC Medical Research Methodology, 6, 32.
• Altman, D. G. (1998). Confidence intervals for the number needed to treat. BMJ (Clinical Research Ed.).
• Campbell, M. J., Machin, D., & Walters, S. J. (2010). Medical statistics: A textbook for the health sciences (4th ed).
• Mateo, M. A., & Kirchhoff, K. T. (Eds.). (2009). Research for advanced practice nurses: From evidence to practice.
• Webb, C., & Roe, B. (Eds.). (2007). Reviewing research evidence for nursing practice: Systematic reviews.
• Jaggia, S., & Kelly, A. (2019). Business Statistics: Communicating with Numbers, 3e.
• Vernon, W. (2018). Introduction to Statistics in Healthcare. New York: Routledge.
• Dawson, B., & Trapp, R. G. (2004). Basic & Clinical Biostatistics (4th ed.). New York: Lange Medical Books.