Please solve Part 1. PAF 301 Applied Statistics-Spring 2018 Assignment #5 (10 po
ID: 3042515 • Letter: P
Question
Please solve Part 1.
PAF 301 Applied Statistics-Spring 2018 Assignment #5 (10 points) Due: February 13, 2018 Name: PART Answer the following question (1 point). What is the difference between Yule's Q, Gamma, and Lambda? Provide examples of a situation in which you would use each to measure association between two variables in a cross-tab. 1. PARTI The city manager of Scottsdale feels that city employees who access Facebook at work receive worse annual performance evaluations than employees who do not access Facebook. The city manager has asked you to survey city employees and collect the data in a cross-tab. In a paragraph, analyze the cross-tab below in terms of its percent distribution and the measure of association. Make certain to answer each of the following: Facebook use at work Annual Performance Evaluations Good evoluation Bod evaluotion TOTAL Yes 225 TOTAL 290 65 185 305 2. Calculate Yule's Q for the cross-tab above. 3. Change the frequencies in the cross-tab to percentages [S points 4. In a paragraph (at least 4-5 sentences), discuss the results above. Show all your wark (-5 points) What does Yule's Q and the percent distributian in the cross-tab tell you about the rels IV and the DV? Do they support your hypothesis? why or why not? What do you te the city manager? Be specific in your answer, and make certain to reference the statistics calculated in questions 3 above (1 point) PART in a recent survey, a random sample of working aduits throughout the US was how happy they asked to indicate were with their situation in life. Researchers believe that the level of happiness income such that those who have a higher income are more likely to be happier The results are shown in the cross tab belowExplanation / Answer
The Yule’s Q is a nominal level measure of association that could be used to determine the association or relationship between variables . Yule originated this measure of association for variables which have two and only two values. It is used with 2 x 2 tables, each variable being expressed as a dichotomy. These dichotomies may be male-female, yes-no, true-false, for-against, agreedisagree, graduate-non-graduate, tall-short, high-low and so on . The Yule‘s Q coefficient is a distribution-free statistic. For variables having infinite values, the researcher may want to put these variables into dichotomies. The process involves the construction of dichotomies that would affect the value of the Yule depending on how the original categories were collapsed. Yule’ Q is, therefore, the ratio of the differences between the products of the diagonal cell frequencies and the sum of the products of the diagonal cell frequencies . This could be done by using the following formula. Q = (ad – bc) / (ad + bc)
Suppose a researcher intends to determine whether or not attending films on campus would affect students’ grade-point averages and involved 200 students in the study. Thirty (30) of the students who had high grade-point average said yes to attending films on campus while the remaining 70 said no. On the other hand, 70 of the students who had low grade-point average said yes to attending films on campus while the remaining 30 said no. Is there is any association between the number of responses given on the grade-point average of students and attending films on campus.
Q = (ad – bc) / (ad + bc)=[(30)(30) – (70)(70)]/[(30)(30) + (70)(70)]=-0.68
The gamma coefficient (also called the gamma statistic, or Goodman and Kruskal’s gamma) tells us how closely two pairs of data points “match”. Gamma test for an association between points and also tells us the strength of association. The goal of the test is to be able to predict where new values will rank. For example, if score A scores “LOW” for question 1 and “HiGH” for question 2, will score B also result in a LOW/High response?
The gamma coefficient ranges between -1 and 1.
Lambda is defined as an asymmetrical measure of association that is suitable for use with nominal variables. It may range from 0.0 to 1.0. Lambda provides us with an indication of the strength of the relationship between independent and dependent variables.
As an asymmetrical measure of association, lambda’s value may vary depending on which variable is considered the dependent variable and which variables is considered the independent variable.
To calculate lambda, you need two numbers: E1 and E2. E1 is the error of prediction made when the independent variable is ignored. To find E1, you first need to find the mode of the dependent variable and subtract its frequency from N. E1 = N – Modal frequency.
E2 is the errors made when the prediction is based on the independent variable. To find E2, you first need to find the modal frequency for each category of the independent variables, subtract it from the category total to find the number of errors, then add up all the errors.
The formula for calculating lambda is: Lambda = (E1 – E2) / E1.
Lambda may range in value from 0.0 to 1.0. Zero indicates that there is nothing to be gained by using the independent variable to predict the dependent variable.
In other words, the independent variable does not, in any way, predict the dependent variable. A lambda of 1.0 indicates that the independent variable is a perfect predictor of the dependent variable. That is, by using the independent variable as a predictor, we can predict the dependent variable without any error.