PART 2 - Column Percentage: raw numbers divided by the cell column total - Row Percentage: row numbers divided by the cell row total 86. Chi-Square Analysis - Null Hypothesis: No association between the two variables - Difference btw observed frequencies and expected frequencies o Expected cell frequency = (cell column total x cell row total) / grand total o Expected frequencies: numbers if Ho is accepted (if no relationship) - Chi-Square Value = Ɛ(observed - expected) / expected - Critical Chi-Square Value: o Degree of freedom = (r-1) (c-1) D. Correlation Analysis Covariation (co-movement) Null Hypothesis: Ho = there is No Correlation Sign: + or - Coefficient 1 A. Three Assumptions of Pearson Product Moment Correlation - Do not take into account interaction with other variables - No causal relationship - Only linear relationships 87. B. Rank Order Correlation (Ordinal/Ranking Variable) - monotonic relationship - Spearman rank order correlation REGRESSION ANALYSIS 1 Two Ways of Making a Prediction: - Extrapolation: prediction based on the past consistent pattern (times series) - Predictive modelling: prediction based on the relationships with variables 88. The goodness of a prediction: the differences between predicted values and observed values 89. Bivariate Regression Analysis: y = a + bx - The basis of the "least squares criterion" - R square: how well the straight-line model fits the observed points. - Testing the regression model: o Ho of Regression model (F-test): No linear relationship btw DV and IVs
PART 2 o Ho of each IV: No linear relationship btw DV and each IV 90. Multiple Regression Analysis (more than one IV) - R square - Test for the overall regression model (Ho for overall model) - t-test for each coefficient (Ho for each IV) - Multicollinearity: o If VIF (Variance Inflation Factor) >10 or Tolerance is close to zero, multicollinearity is suspected. o How to Fix the Problem? examining the correlation matrix, drop one taking logarithm - Special Uses of Multiple Regression Analysis o Screening device o Standardized betas (used for ranking IVs in terms of their importance) - Stepwise regression: Successive entry of IVs based on p values < .05 - Dummy variable: dichotomous variables (0&1) can also be used for IV
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- Winter '15