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RES/342 RES/342 Business Business Research and Research and Evaluation II Evaluation II Week 4 Week 4

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Today’s Agenda Correlation and Regression Analysis Theory of Regression Regression Terms and Symbols Practical Examples of Regression Analysis Interpretation of Regression Outputs Preview of Week 5
Parametric vs. Nonparametric Determined by shape of distribution and data level of dependent variable Ratio & interval data are tested PARAMETRICALLY Generally follow a “bell-shaped” curve Emphasis is on center and width of curve Nominal & ordinal data are tested NON- PARAMETRICALLY Essentially have only counts in categories Center and width make little sense Not normally distributed Distinctions Combination of levels of independent and dependent variables require different types of tests

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Chi-Square Goodness of Fit Test Checks to see how well a set of data fit the model for a particular “expected” probability distribution Compares the observed frequency distribution to what would be expected if the H0 were true. F0 = observed frequencies Fe = expected frequency H0: fo = fe (the data comes from a population with a specific distribution) H1: fo fe (not H0) The test statistic is: The critical value is a chi-square value with ( c – 1) degrees of freedom , where c is the number of categories. ( 29 - = e e o f f f Σ Χ 2 2 ( 29 - = E E O Σ Χ 2 2
Chi-Square Chi-Square Goodness of Fit Test The observed frequencies ( fo ) (or simply “O”) are the actual number of observations that fall into each class in a frequency distribution or histogram. The expected frequencies ( fe ) (or simply “E”) are the number of observations that are expected in each category….the expected distribution is also known for as the “hypothesized probability distribution”

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Chi-Square Distribution Used in a frequency distribution to determine if the observed frequency differ significantly from expected frequency The major characteristics of the chi-square distribution are: It is positively skewed It is non-negative It is based on degrees of freedom When the degrees of freedom, change a new distribution is created Text, Appendix Table
Critical Values of Chi-Square

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Goodness of Fit Test Used to determine whether a frequency distribution fits a specific pattern Example; Manufacturer of running shoes wants to find out if customers have preference among styles. Example; Test whether there is a difference between four competing cold prevention medicines. Hypothesis testing procedure: Step 1: State the hypothesis Step 2: Select test statistic (Use Chi-Square for frequency distribution) Step 3: Find the critical value of Chi-Square Step 4: Compute the chi-Square test value Step 5: Make the decision

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Goodness of Fit Test Test Statistic for a Goodness of Fit Test: O and E are the observed and expected frequencies respectively.
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