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sLecture8dPBS

# sLecture8dPBS - Lecture#8 Learning Objectives 1 Know how to...

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Lecture #8 Learning Objectives 1. Know how to identify the row variable and the column variable in a two- way table. 2. Know how to create a two-way cross-classification table for nominal data. a. Using counts b. Using percents (or probabilities) 3. Be able to identify the relevant null and alternative hypotheses. 4. Know how to determine the expected cell counts. 5. Learn how to calculate the chi-square test statistic. 6. Learn about the chi-square probability distribution. 7. Know how to use the chi-square test statistic and the chi-square probability distribution to draw a conclusion about the association between the row and column variables. 8. Know the definition of the following terms: Row variable Column variable Two-way table Joint probability Marginal probability Conditional probability Chi-square random variable Contingency table Two-way cross-classification table

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BM330 – Lecture 8 Two-Way Tables To analyze categorical (nominal, ordinal) data, we use counts or percents of the items or individuals that fall into various categories. One way to organize these counts or percents is to create a cross-classification (contingency) table. If we have only two categorical variables , the cross-classification table is called a two-way table . The rows of the table are created by the categories of one of the variables, and the columns are created by the categories of the other variable. In deciding whether a variable should be a row variable or a column variable, it is customary to follow the protocol used when creating scatter plots – the response variable (y) is placed on the vertical axis and the explanatory variable (x) is placed on the horizontal axis. Note that not all problems will have a “response” variable and an “explanatory” variable. The number of rows in the table is identified as r . The number of columns in the table is identified as c . The size of the table is then identified as r x c . That is, if the row variable has 4 categories and the column variable has 3 categories, we have a 4 x 3 two-way table. If the categories of a variable have a natural order, small, medium and large for example, they will generally be listed in the table to reflect that order. 1
BM330 – Lecture 8 Example : At a retail shop four employees are responsible for handling the cash register. One item that needs to be recorded for each sale is the type of payment: cash, check, or credit card. For a number of transactions this information is missing, though. Are certain employees responsible, or is everyone equally guilty in forgetting this information? The table below summarizes the last 3501 transactions. y Employee Info. Status 1 2 3 4 Total Recorded 897 679 1169 497 3242 Not Recorded 68 62 90 39 259 Total 965 741 1259 536 3501 x This is a 2 x 4 table with Employee as the explanatory variable and Availability of the Transaction Information as the response variable.

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sLecture8dPBS - Lecture#8 Learning Objectives 1 Know how to...

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