Estimation and Decision Theory

Abstract

This chapter covers the basic concepts of inferential statistics and hypothesis testing. The section commences with an explanation of the confidence intervals for the population mean and population standard deviation. Also discussed are the concepts of cut-off, Type I and Type II errors, false positives, and false negatives. We investigate performance metrics including sensitivity, specificity, true positive rate, and true negative rate. In addition, receiver operating characteristic (ROC) curves are introduced and their usefulness in assessing test performance is emphasized. In addition, binomial and normal distribution tests are discussed. This chapter provides a solid foundation for comprehending the principles and practical applications of inferential statistics in decision-making and the interpretation of scientific results.

Keywords: Confidence interval for a population mean, confidence interval for a population standard deviation, cut-off, false negatives, false positives, sensitivity, specificity, statistical hypothesis and significance, receiver operating characteristic curve, ROC curve, tests involving binomial distributions, tests involving normal distributions, true negatives, true negative rate, true positives, true positive rate, type I error, type II error.