Confidence Intervals
Confidence intervals are a statistical concept used to estimate the range within which a population parameter is likely to fall, based on sample data. They provide a way to quantify the uncertainty in an estimate, giving a lower and upper bound around a central value like a mean or proportion. For example, a 95% confidence interval means there is a 95% probability that the true parameter lies within the specified range, assuming the sampling process is repeated under identical conditions. Confidence intervals are widely used in fields such as public health and economics to make informed decisions based on limited data.
https://en.wikipedia.org/wiki/Confidence_interval
The width of a confidence interval depends on factors such as the variability of the data, the sample size, and the chosen confidence level. A larger sample size reduces variability and narrows the interval, while a higher confidence level (e.g., 99%) increases the width of the interval to account for greater certainty. In machine learning and predictive modeling, confidence intervals are often used to assess the reliability of model predictions, helping researchers evaluate how well a model might generalize to unseen data.
https://en.wikipedia.org/wiki/Sampling_distribution
Confidence intervals are essential in hypothesis testing, where they provide an alternative to p-values for assessing the significance of results. By examining whether a confidence interval includes a null hypothesis value, such as zero in regression analysis, researchers can determine the statistical significance of their findings. Tools like Python’s SciPy library (introduced in 2001) and R (introduced in 1995) include functions for calculating confidence intervals, making them accessible for a wide range of applications.
https://en.wikipedia.org/wiki/Statistical_hypothesis_testing