GEOG 4/517:  Geographic Data Analysis
Statistical Inference

The general idea that underlies statistical inference is the comparison of particular statistics from on observational data set (i.e. the mean, the standard deviation, the differences among the means of subsets of the data), with an appropriate reference distribution in order to judge the significance of those statistics.  When various assumptions are met, and specific hypotheses about the values of those statistics that should arise in practice have been specified, then statistical inference can be a powerful approach for drawing scientific conclusions that efficiently uses existing data or those collected for the specific purpose of testing those hypotheses.  Even in a context when a formal experimental design is not possible, or when the objective is to explore the data, significance evaluation can be useful.

As a consequence of the central limit theorem, we know that the mean is normally distributed, and so we can use the normal distribution to describe the uncertainty of a sample mean.

• characterization of samples (mean, s.e. mean, and confidence intervals for the mean)

Hypotheses are an explicit feature of formal significance testing, but also underlie the general interpretation of data.

• hypothesis tests

The t-test provide a mechanism for the simple task of testing whether there is a significant difference between two groups of observations, as reflected by differences in the means of the two groups.

• a simple hypothesis test for the equality of two mean values

Readings: 

Owen (The R Guide):  section 7.1; Rogerson (Statistical Methods):  Ch. 3 and 4.