We consider how well we predict using a naive model (assuming no relationship) and compare it to how much better we predict when we use our independent variable to make that prediction. For that type of case, we may use a reduction in error or a proportional reduction in error (PRE) model. Women might be more concerned about climate change than are men, for example. Still, we might see a recognizable pattern of change in one variable as the other variable varies. If one or both of our variables is nominal, we cannot specify directional change. Co-variation models are directional models and require ordinal or interval level measures otherwise, the variables have no direction. One type of measure of association relies on a co-variation model as elaborated upon in Sections 6.2 and 6.3. Measures of association are used to determine the strength of a relationship. Having rejected the null hypothesis, we believe there is a relationship between the two variables, but we still want to know how strong that relationship is. 005 level of significance and, almost but not quite, at the. In fact, if we follow the row for one degree of freedom across, we see we can reject our null hypothesis even at the. 05 probability that we could have found the results in our sample if there is no relationship in the population. Since our chi-square is larger than that we can reject our null hypothesis - there is less than a. The critical value for one degree of freedom with a. Table 6.9 (at the end of this chapter) is a chi-square table that shows the critical values for various levels of significance and degrees of freedom.
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