Solutions - Question 1 Explain the difference between the...

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Question 1: Explain the difference between the information given by the tests of statistical significance t and Chi Square , and measures of association Cramer’s V, Gamma and Pearson’s correlation coefficient, r . Can a test of significance show a statistically significant relationship while a measure of association shows a weak relationship between the variables? If yes, present an example illustrating how such a situation might occur. Solution: Tests of Statistical Significance (t and Chi Square) : The information provided by the test of statistical significance is basically used to check the estimation of population mean or proportion based on sample mean and proportion. It checks the significance of sample mean and proportion based on a particular significance level. The test of statistical significance is also used to check whether the mean or proportion of two different population is equal or not. Measures of Association (Cramer’s V, Gamma and Pearson’s correlation coefficient, r) : The information provided by the measure of association, like Cramer’s V (Gamma) and Pearson’s correlation coefficient (r), helps determine whether two or more variables have a significant linear correlation or not. It also helps in determine the direction and the magnitude of correlation between two or more variables. A case where a test of significance show a statistically significant relationship while a measure of association shows a weak relationship between the variables is possible. For example, while looking at a relationship between the Self-Control score and the number of adult arrests per person, a Chi square test could show that there is a statistically significant relationship between the variables. However, a weak correlation could be noticed while analyzing the case through measure of association.
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Question 2: You hypothesize that there is a relationship between an individual’s level of Self Control as measured by the Grasmick Self Control Scale (Self_Con) and his or her Number of Adult Arrests (ARR). Theory postulates that low self control is associated with higher number of arrests. Use the definitions of the variables contained in the Week One Dataset, reprinted below. State your null and research hypotheses.
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