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Basic guidelines regarding statistical tests (Chi-Square)

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  1. Basic guidelines regarding statistical tests (Chi-Square) • If you want to know if there’s a relationship between two categorical variables (with two of more levels each) the appropriate test is a chi-square. • Examples: • Is there a relationship between gender and hair color? • Is there a relationship between state of residence and whether or not one is married or unmarried? • Is there a relationship between make of car one drives and ethnicity? • Ho is that there is no relationship between the two variables while Ha is that there is a relationship. • Interpretation: • If the calculated chi-square exceeds the critical value of the chi-square or if the associated p value is less than alpha (in our class we’re using .05 for alpha), you would conclude that Ha is supported and that there is a significant relationship. • Other: Sample proportion vs. population proportion

  2. Basic guidelines regarding statistical tests (Ttest) • If you want to know if there’s a difference between two groups (a categorical variable with exactly two levels) on a continuous variable the appropriate test is a ttest. • Examples: • Is there a difference between men and women in terms of how many hours per week they devote to housework? • Is there a difference between whether one is in management or not and how satisfied one is with the job (measured continuously)? • Do individuals who have at least one month of vacation per year have lower blood pressure than those who have less than one month of vacation per year? • Ho is that there is no difference on the continuous variable between the two groups while Ha is that there is a difference (two-tailed test) or that one group is greater than the other (one-tailed test). • Interpretation: • Initially test for whether the variances are equal. If the p < .1 use the ttest for unequal variances else use the ttest for equal variances. • If the absolute value of the calculated t statistic exceeds the critical value of the t statistic or if the associated p value is less than alpha (in our class we’re using .05 for alpha), you would conclude that Ha is supported and that there is a significant difference. • Other: Ttest for dependent means; Z test for difference between two proportions

  3. Basic guidelines regarding statistical tests (one-way or single-factor ANOVA) • If you want to know if there’s a difference between groups (a categorical variable with more than two levels) on a continuous variable the appropriate test is a one-way ANOVA. • Examples: • Is there a difference between people in managerial, professional, and blue collar occupations in terms of how many hours per week they devote to housework? • Is there a difference between individuals less than 30 years old, individuals between 30 and 50, and individuals over 50 in job satisfaction (measured continuously)? • Do average household income levels vary depending on state of residency? • Ho is that there is no difference on the continuous variable between the groups while Ha is that there is a difference. • Interpretation: • If the p value associated with the one-way ANOVA is less than alpha (in our class we’re using .05 for alpha), you would conclude that Ha is supported and that there is a significant difference.

  4. Basic guidelines regarding statistical tests (correlation) • If you want to know if there’s a relationship between two continuous variables the appropriate test is a correlation. • Examples: • Is there a relationship between age and income? • Is there a relationship between number of years of education and cholesterol level? • Is there a relationship between number of close friends an individual reports having and number of days work is missed per year? • Ho is that there is no relationship between the two continuous variables while Ha is that there is a relationship (either positive or negative). • Interpretation: • If the p value associated with the correlation coefficient is less than alpha (in our class we’re using .05 for alpha), you would conclude that Ha is supported and that there is a significant relationship. NOTE: To get the p value in Excel, you must use the regression test; the correlation test does not return the associated p value. • Other: Covariance

  5. Basic guidelines regarding statistical tests (simple linear regression) • If you have two continuous variables and 1) one of the variables can be considered the dependent variable and the other can be considered the independent variable, and 2) you are interested in prediction, the appropriate analysis is simple linear regression. • Examples: • Is income predicted by the number of years of education one has? • Is the demand for new dishwashers in a year predicted by the average age of installed dishwashers? • Is the price of a stock predicted by the general move of the stock market as measured by the Russell 5000? • Ho is that the model (the independent variable is predictive of the dependent variable) is not significant while Ha is that the model is significant. • Interpretation: • If the p value associated with the model is less than alpha (in our class we’re using .05 for alpha), you would conclude that Ha is supported and that the model is significant. • You would also want to look at the values for r square that expresses the percentage of variation in the dependent variable that is accounted for by the independent variable. And if the model is statistically significant, you’d normally be interested in developing the prediction equation in the form Y = a + bX.

  6. Basic guidelines regarding statistical tests (multiple regression) • If you have more than two continuous variables and 1) one of the variables can be considered the dependent variable and the others can be considered as independent variables, and 2) you are interested in prediction, the appropriate analysis is multiple regression. • Examples: • Is income predicted by the number of years of education one has and age? • Is the demand for new dishwashers in a year predicted by the average age of installed dishwashers, the number of new housing starts, and the unemployment rate? • Is the price of a stock predicted by the general move of the stock market as measure by the Russell 5000, the stock’s price/earnings ratio, and earnings per share? • Ho is that the model (the independent variables are predictive of the dependent variable) is not significant while Ha is that the model is significant. • Interpretation: • If the p value associated with the model is less than alpha (in our class we’re using .05 for alpha), you would conclude that Ha is supported and that the model is significant. • You would also want to look at the value for r square that expresses the percentage of variation in the dependent variable that is accounted for by the independent variables. And if the model is statistically significant, you’d normally be interested in developing the prediction equation in the form (for two independent variables) Y = a + bX1 +bX2. Finally, and only if the model is significant, you’d interpret the significance level of each of the independent variables.

  7. Basic guidelines regarding statistical tests (other tests) • If you have a categorical dependent variable with two levels and one or more continuous independent variables you’d use logistic regression or probit or some similar technique. • If you have a continuous dependent variable and a combination of continuous and categorical independent variables one technique that would be appropriate would be dummy variable regression. • If you have a continuous dependent variable and more than one categorical independent variable you’d use analysis of variance (ANOVA) or dummy variable regression.