Review Question - QID 103893

In order to determine a confidence interval of a sample mean at a given alpha value, the mean, standard deviation, and sample size are necessary.

Confidence intervals (CI) are a commonly reported summary statistics as they succinctly convey more information than effect sizes and p values alone. In the literature, means are frequently reported as the summary statistic. The CI about that mean gives the reader a sense of where the true value of what they are measuring lies. Four factors determine the confidence interval. The mean determines the center of the CI. The standard deviation, sample, size and alpha value all determine how wide the CI will be. Increasing sample sizes and alpha values decrease the width, while increasing standard deviations widen the width of the CI.

Rosner formally defines a 95% confidence interval: Given an infinite number of 95% CIs that can be constructed around the mean of random samples of size n, 95% will contain the true mean of the population. The sample mean is the investigators' best estimate of the true value that they are trying to determine: the population mean. As collecting data on the entire population is frequently impossible, investigators settle for measuring the mean of a sample from that population. The downside of this is that the sample mean is only an estimate of the population mean. They construct 95% CIs around the sample mean to give a sense of the range over which the true population mean lies. The width of this confidence interval is affected by all the aforementioned factors. Furthermore, by definition given infinite iterations of 95% CIs, not only will many of the sample means differ from the true mean but 5% of the CIs won't contain the true population mean at all.

Guyatt et al. describe some of the differences between CIs about means (continuous variables) and CIs in studies in which the outcome is dichotomous. The sample size is a direct determinant of the width of the CI in continuous variables. For dichotomous outcomes (e.g. death or survive, or disease or healthy) it is not the sample size which determines the width of the CI but the absolute number of events. For example, if Study A includes 1000 patients with 10 deaths, and Study B includes only a 100 patients but with 50 deaths, Study B will have the narrower (i.e. more precise) CI.

Incorrect Answers:
Answers 1,2,3, and 5: Power is not a necessary value when determining a confidence interval about a mean. Power is generally set at 80% and defines the level of Type II errors that the investigators were willing to tolerate when designing the study.