Tillitsintervaller

Tillitsintervaller, or confidence intervals in English, are a fundamental concept in statistical inference. They provide a range of plausible values for an unknown population parameter, such as the population mean or proportion, based on sample data. Instead of reporting a single point estimate, which is unlikely to be exactly correct, a confidence interval acknowledges the uncertainty inherent in using a sample to represent a whole population.

A confidence interval is calculated from sample statistics and includes a confidence level. The confidence level, typically expressed as a percentage like 95%, indicates the long-run proportion of such intervals that would contain the true population parameter if the sampling process were repeated many times. For example, a 95% confidence interval means that if we were to take numerous samples and construct a confidence interval from each, about 95% of those intervals would capture the true population parameter.

The width of a confidence interval is influenced by two main factors: the variability in the data and the desired confidence level. Higher variability in the sample data leads to a wider interval, reflecting greater uncertainty. A higher confidence level also results in a wider interval, as we need a broader range to be more certain of capturing the true parameter. Conversely, a lower confidence level or less variable data will produce a narrower interval. Confidence intervals are crucial for making informed decisions and drawing conclusions when dealing with uncertainty in data.