Class Notes 9 - Lambda measures the strength of association between two nominal variables, by PDF

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Lambda measures the strength of association between two nominal variables, by assessing the proportional reduction of error (PRE) by considering the independent variable. ...

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Lambda measures the strength of association between two nominal variables, by assessing the proportional reduction of error (PRE) by considering the independent variable, when compared to ignoring the independent variable in the prediction of the dependent variable. 95−35 =0.6135→ which is the For example: Error 1 = 95 and Error 2 = 35, so 95 quantitative measure of the reduction in the error (how closely the 2 variables are associated is 63.2%). THUS, 63.2% is the percent reduction in error. Error 1: Look at the dependent results (right) and find the higher value, and your error 1 becomes the other one you did not choose. Error 2: find the higher value from each column, but choose the smaller values as the errors, and + add them. BASICALLY, the error is how much you would get wrong if you only chose the more common answer (higher value). If Error 1 = 95 and Error 2 = 0, the PRE = 1 which is a perfect association because if you know the independent variable, you can predict the dependent variable without error. Lambda Associations = Low Below 15%  Moderate 15% - 35%  Strong Above 35% You cannot calculate lambda if the modal values are on the same row (modal values are the bigger of the two in each column).

1. Control variable (in bivariate relationship) - The control variable is kept constant throughout the experiment. If the control value does not intervene between the other two variables, or the original bivariate relationship, it is called an explanation of the relationship. In a survey asking whether we should invade Venezuela, we ask men and women if they think Yes or No, but the third control variable we introduce is whether the individual cases identify as Hispanic or Non-Hispanic (Stata calls this creating a super column). If you see the same relationship in these partials, it is called a replication of the first relationship, and thus it can be sustained. A suppressor is when the initial relationship does not look strong, but adding a third control variable makes it look like a strong correlation (making original disappear). An initial relationship can be spurious when there falsely appears to be a correlation between the two variables, but the presence of a third variable involved shows there is no logical connection between the initial variables. 2. Tests of statistical significance – tells us how likely it is that the result or statistic we get by looking at the true random sample, is not in the population. It tells us when we can reject the claim that there is no relationship between the variables in the population and tells us how likely it is to get a sample with this result when it does not exist in the population. The test of statistical significance never deals with correlation, that is lambda. 3. Using a table to determine to accept/ reject the null hypothesis - Before interpreting statistical tests, researchers set an alpha level ( p critical), which is the probability of rejecting the null hypothesis when it is true, or a Type 1 Error (typically set at 0.05). The larger the alpha level, the more likely you are to find statistically significant results. If the p-value ≤ alpha level, we reject the null hypothesis. If p-value ¿ alpha level, then we do NOT reject the null hypothesis. (Ex: our results are p- value = 0.16 and alpha level = 0.05, so we do not reject the null hypothesis. THUS there is not enough evidence to conclude that students who took the courses earned a significantly higher/lower score than the student population at high school X).

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