Читать книгу Applied Regression Modeling - Iain Pardoe - Страница 27

We spent some time in this chapter coming to grips with summarizing data (graphically and numerically) and understanding sampling distributions, but the four major concepts that will carry us through the rest of the book are as follows:

1 Statistical thinking is the process of analyzing quantitative information about a random sample of observations and drawing conclusions (statistical inferences) about the population from which the sample was drawn. An example is using a univariate sample mean, , as an estimate of the corresponding population mean and calculating the sample standard deviation, , to evaluate the precision of this estimate.

2 Confidence intervals are one method for calculating the sample estimate of a parameter (such as the population mean) and its associated uncertainty. An example is the confidence interval for a univariate population mean, which takes the form

3 Hypothesis testing provides another means of making decisions about the likely values of a population parameter. An example is hypothesis testing for a univariate population mean, whereby the magnitude of a calculated sample test statistic,indicates which of two hypotheses (about likely values for the population mean) we should favor.

4 Prediction intervals, while similar in spirit to confidence intervals, tackle the different problem of predicting the value of an individual observation picked at random from the population. An example is the prediction interval for an individual univariate ‐value, which takes the form