The analysis of frequencies
Lorena Madrigal · Cambridge University Press eBooks · 2012
This chapter presents a departure from the statistical tests covered so far: we do not deal with quantitative variables such as fertility, prestige ranks, height, weight, etc., within a sample or among several samples. Instead we deal with frequencies of occurrences or events. We work with variables which have a few possible outcomes, and we are concerned with the number of individuals who have each of the outcomes (where a is the number of outcomes). Often-used anthropological frequency data are gene frequencies, the frequencies of males and females, the frequencies of different ethnic groups, the frequencies of different pottery styles in archaeological sites, etc. The X 2 test for goodness-of-fit In this section we discuss the well-known and widely used chi-square test (X 2 ), applied as a goodness-of-fit test and as a test for independence of two variables. Not only is the X 2 test widely used in anthropology, but unfortunately it has also been widely misused. The most common error about the X 2 test is its own name: it is frequently referred to as χ 2 , which is the parametric notation for a theoretical frequency distribution against which the statistic computed from the sample (X 2 ) should be compared. Therefore, the test statistic is X 2 , while the theoretical distribution is χ 2 . In addition, a correction which must be applied to small data sets is also discussed.