VCU STAT 210 - Lecture17 (54 pages)

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Lecture17



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Lecture17

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Pages:
54
School:
Virginia Commonwealth University
Course:
Stat 210 - Basic Practice of Statistics
Basic Practice of Statistics Documents

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STAT 210 Lecture 17 Describing Relationships For Categorical Variables October 4 2017 Test 3 Friday October 6 Covers chapter 5 pages 99 138 Combination of multiple choice questions and short answer questions and problems Formulas provided please bring calculator and writing instrument Practice Problems Pages 130 through 137 Relevant problems V 12 through V 16 Recommended problems V 12 V 15 and V 16 Additional Reading and Examples Read pages 127 through 129 Top Hat 2 Motivating Example Over the years much debate has occurred on whether such demographics as race sex religious preference sexual preference etc should impact decisions on whether a student is admitted to a college or university In cases where discrimination is charged statistics can be used to analyze whether discrimination has occurred and if so the extent of the discrimination Quantitative Variables Everything to this point has assumed two quantitative variables an independent or explanatory variable X and a dependent or response variable Y We have talked about how to describe the relationship between the two variables direction form and strength and how the scatterplot correlation coefficient and regression line can be used to help do this E Categorical Data Now suppose we have two qualitative or categorical variables the variables vary in name but not in magnitude implying that they cannot be ranked All we can do is name the categories and count the number of observations falling in each category The question remains is there a relationship between the two variables Categorical Data With two variables we can count the number of observations that fall in each pair of categories The counts are displayed in a two way table Categorical Data Freshman Sophomore Warning 48 Probation 29 Good standing 71 36 42 Junior Senior 15 12 37 23 14 18 62 Marginal Distribution There exists a marginal distribution for each variable A marginal distribution lists the categories of the variable together with the frequency count or relative frequency percentage of observations in each category Categorical Data Freshman Sophomore Junior Senior Warning 48 36 15 23 122 Probation 29 42 12 14 97 Good standing 71 37 18 62 188 148 115 45 99 407 Example 31 Variable 1 Smoking Status Smoker Nonsmoker Variable 2 Cough Status Cougher Noncougher Example 31 Two Way Table Cough Smoker Nonsmoker No Cough Example 31 Two Way Table Cough Smoker 43 Nonsmoker No Cough Example 31 Two Way Table Cough Smoker 43 Nonsmoker No Cough 43 Example 31 Two Way Table Cough Smoker 43 Nonsmoker No Cough 43 19 Example 31 Two Way Table Cough Smoker 43 Nonsmoker No Cough 43 19 95 Example 31 Two Way Table Cough Smoker 43 Nonsmoker No Cough 43 19 86 95 114 Example 31 Marginal Distribution for Smoking Status Frequency Smoker 86 Nonsmoker Relative Frequency 86 200 43 114 114 200 57 Example 31 Two Way Table Cough Smoker 43 Nonsmoker No Cough 43 19 62 95 138 Example 31 Marginal Distribution for Coughing Status Frequency Cough 62 No Cough 138



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