Question

What is trade off for using a wide range of confidence versus a more narrow range of confidence to report performance on tests? Think about the ranges from the perspective of a client who needs resources or services and a person who manages scarce social services or resources.

Answer 1

A confidence interval, in statistics, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times. Confidence intervals measure the degree of uncertainty or certainty in a sampling method. They can take any number of probability limits, with the most common being a 95% or 99% confidence level.

There are many situations where it is of interest to compare two groups with respect to their mean scores on a continuous outcome. For example, we might be interested in comparing mean systolic blood pressure in men and women, or perhaps compare body mass index (BMI) in smokers and non-smokers. Both of these situations involve comparisons between two independent groups, meaning that there are different people in the groups being compared.

We could begin by computing the sample sizes (n1 and n2), means ( and ), and standard deviations (s1 and s2) in each sample.

In the two independent samples application with a continuous outcome, the parameter of interest is the difference in population means, μ1 - μ2. The point estimate for the difference in population means is the difference in sample means: