Final answer:
A 95% confidence interval including 1.0 in its range suggests that there is a non-zero chance the true likelihood ratio is 1.0, meaning no difference. This interval will contain the true value in 95% of repeated samples, but also implies a 5% probability that the true value lies outside the range.
Step-by-step explanation:
A 95% confidence interval (CI) that includes 1.0 in its range implies that there is a non-zero chance that the 'true value' of the likelihood ratio (LR) could indeed be 1.0, meaning that there is no difference or no effect. However, the CI also suggests that the true LR can be any value within the interval.
In statistical analysis, the construction of a 95% CI means that if we were to take repeated samples and compute a CI from each one, 95% of those intervals would contain the true population parameter we are estimating, such as a mean or proportion. This is because a 95% CI excludes 5% of the probability distribution, which is evenly divided between the lower and upper tails at 2.5% each. Thus, when the interval includes 1, we acknowledge that there is a 95% probability that the interval includes the true effect size, and that effect size could be null (representing no effect or 1 in terms of LR).
Moreover, when considering the confidence i
ntervals, it is important to note that the remaining 5% represents a probability that the true value might fall outside the interval. For example, if we look at CIs for a population mean (µ), and we have a 95% CI of (1.8, 2.2), it both contains the true mean (µ) and allows for a 5% chance that the true mean could lie outside this interval. This is based on the concept that these intervals are derived from sample statistics and are used to infer about the true population parameter.