Confidence Interval

Constructing Confidence Intervals

One of the fundamental tenets of the sciences—both social and physical—is the reliance on samples to estimate phenomena happening in much larger populations. This simple statistic—the point estimate—is that which researchers use to estimate the value of a said variable in the population at large. For the most part, the sciences rely upon sample means—the average mean of a particular measure—in the population as an estimate of that measure across the entire population. The central limit theorem tells researchers that across a large enough sample, the distribution of this score should be approximately normal, and the calculation of standard deviations associated with these group means can give researchers an idea of their approximate dispersion.

Given these known factors, the confidence interval can be calculated as an estimate of the range in which the mean score is likely to fall within the population in question. Calculating the confidence interval is fairly simple. One must first calculate the standard error of the estimate, which can be computed by dividing the standard deviation by the square root of n.

[Page 226]Once the standard error is obtained, researchers can then consider the confidence level at which they want to construct the confidence interval. Given that most research in the social sciences aspires for 95% or 99% degrees of confidence, a reconsideration of the normal distribution takes us to the next step.

Because it is known that 95% of the scores in a normal distribution fall within 1.96 standard deviations of a mean score, and that 99% of all scores in a said population fall within 2.58 standard deviations, this information can be combined with the standard error of the estimate to produce the confidence interval. For a 95% confidence interval, where the mean is represented by Y, we can then calculate the confidence interval as: Y ± (1.96)(SE). Likewise, to produce a 99% confidence interval, we would use the formula Y ± (2.58)(SE). This will produce two scores between which we can estimate the true score in the population will fall.

...