Let’s look at an example before going into the LOB/FLOB data. The expected frequencies are “the frequencies that we would expect simply by chance (if the independent variable had no relationship to the distribution)” (Hatch and Farhady 1982: 166). Performing the contingency test manually entails six steps: But since working through this test manually enables a better understanding for how the test functions, we are going to do this first. Now, we could just enter our data into R and run a chi-square test on it, and we are going to do so below. HA: there is a difference in the usage of these forms over time. H0: there is no difference in the usage of these forms over time. The hypotheses for the chi-square test function similarly to those for the t-test, which means that we want to phrase a null hypothesis which we can reject in order to continue working with the alternative hypothesis. But is this difference between the ’60s and ’90s statistically significant? Table 6.1: Forms 1 and 2 observedīefore evaluting this, let’s formulate the hypotheses. If we look at the table below, we see a clear difference: in the 1960s form 1 is predominant, while in the 1990s both forms are equally likely. Let’s use the chi-square test to establish whether the usage of prevent NP from doing something (form 1) and prevent NP doing something (form 2) changed in British English between the 1960s and the 1990s. The LOB contains texts from 1961 and the FLOB contains texts from 1991, and both corpora contain 500 texts of about 2,000 words each. Here, we use data from the Lancaster-Oslo-Bergen (LOB) and the Freiburg-LOB (FLOB) corpora. To illustrate what this means, let’s consider the following example which is based on Mukherjee (2009: 86ff). In the next sections, we discuss how the chi-square test is performed in practice.Ī frequently used version of the Chi-square test is the contingency test, in which the expected values are the random distribution of the observed values. Once we have the chi-square value, we can look up the probability of our results and see whether they are significantly different than what would expect if our data were just a bunch of random observations. This is already most of what we need for the chi-square test. We do this because the expected values are often more balanced than the observed values. Since we are not interested in the absolute differences, we normalize the squared differences before summing them, which gives us the following formula for the chi-square value:Īs you can see, we normalize by E. So, we square the difference between each observation and its corresponding expected value. With the standard deviation, we work around this impasse by squaring the differences, and we can use the same approach to calculate the chi-square value. When we discussed the summation of differences in the context of the standard deviation, we saw that if we just sum the differences, positives and negatives cancel each other out. To calculate the chi-square value, expressed by the Greek letter, the differences between observed and expected values are summed up. We discuss how this works in detail below. Frequently, you will calculate the expected values on the basis of the observed values, thereby generating your own model. The expected values either come from a model or from a reference speaker group. In contrast to the t-test, which requires the mean, the standard deviation, the sample size and, of course, normally distributed data, the chi-square test works with the differences between a set of observed values (O) and expected values (E). Perhaps the most versatile of these is the chi-square test. For these cases, we can use different significance tests that don’t assume a normal distribution. Often, however, our data is not normally distributed. In the last chapter, we introduced the t-test and saw that it relies crucially on the assumption that the data in our samples is normally distributed. The affordance of the chi-square test is that it allows us to evaluate data of which we know that it is not normally distributed. In this chapter, we discuss the chi-square test.
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