11 Chapter 12 Quantitative Data Analysis: Hypothesis Testing © 2009 John Wiley & Sons Ltd.
Type I Errors, Type II Errors and Statistical Power Type I error ( ): the probability of rejecting the null hypothesis when it is actually true. Type II error ( ): the probability of failing to reject the null hypothesis given that the alternative hypothesis is actually true. Statistical power (1 - ): the probability of correctly rejecting the null hypothesis. 2 © 2009 John Wiley & Sons Ltd.
Choosing the Appropriate Statistical Technique 3 © 2009 John Wiley & Sons Ltd.
Testing Hypotheses on a Single Mean One sample t -test: statistical technique that is used to test the hypothesis that the mean of the population from which a sample is drawn is equal to a comparison standard. 4 © 2009 John Wiley & Sons Ltd.
Testing Hypotheses about Two Related Means Paired samples t -test: examines differences in same group before and after a treatment. The Wilcoxon signed-rank test: a non-parametric test for examining significant differences between two related samples or repeated measurements on a single sample. Used as an alternative for a paired samples t- test when the population cannot be assumed to be normally distributed. 5 © 2009 John Wiley & Sons Ltd.
Testing Hypotheses about Two Related Means - 2 McNemar's test: non-parametric method used on nominal data. It assesses the significance of the difference between two dependent samples when the variable of interest is dichotomous. It is used primarily in before-after studies to test for an experimental effect. 6 © 2009 John Wiley & Sons Ltd.
Testing Hypotheses about Two Unrelated Means Independent samples t -test: is done to see if there are any significant differences in the means for two groups in the variable of interest. 7 © 2009 John Wiley & Sons Ltd.
Testing Hypotheses about Several Means ANalysis Of VAriance (ANOVA) helps to examine the significant mean differences among more than two groups on an interval or ratio-scaled dependent variable. 8 © 2009 John Wiley & Sons Ltd.
Regression Analysis Simple regression analysis is used in a situation where one metric independent variable is hypothesized to affect one metric dependent variable. 9 © 2009 John Wiley & Sons Ltd.
Scatter plot 10 © 2009 John Wiley & Sons Ltd.
Simple Linear Regression 11 Y X `0 1 © 2009 John Wiley & Sons Ltd.
Ordinary Least Squares Estimation 12 YiYi XiXi YiYi eiei ˆ © 2009 John Wiley & Sons Ltd.
SPSS Analyze Regression Linear 13 © 2009 John Wiley & Sons Ltd.
SPSS cont’d 14 © 2009 John Wiley & Sons Ltd.
Model validation 1.Face validity: signs and magnitudes make sense 2.Statistical validity: –Model fit: R 2 –Model significance: F-test –Parameter significance: t-test –Strength of effects: beta-coefficients –Discussion of multicollinearity: correlation matrix 3.Predictive validity: how well the model predicts –Out-of-sample forecast errors 15 © 2009 John Wiley & Sons Ltd.
SPSS 16 © 2009 John Wiley & Sons Ltd.
Measure of Overall Fit: R 2 R 2 measures the proportion of the variation in y that is explained by the variation in x. R 2 = total variation – unexplained variation total variation R 2 takes on any value between zero and one: –R 2 = 1: Perfect match between the line and the data points. –R 2 = 0: There is no linear relationship between x and y. 17 © 2009 John Wiley & Sons Ltd.
SPSS 18 = r (Likelihood to Date, Physical Attractiveness) © 2009 John Wiley & Sons Ltd.
Model Significance H 0 : 0 = 1 =... = m = 0 (all parameters are zero) H 1 : Not H 0 19 © 2009 John Wiley & Sons Ltd.
Model Significance H 0 : 0 = 1 =... = m = 0 (all parameters are zero) H 1 : Not H 0 Test statistic ( k = # of variables excl. intercept) F = (SS Reg / k ) ~ F k, n-1- k (SS e /( n – 1 – k) SS Reg = explained variation by regression SS e = unexplained variation by regression 20 © 2009 John Wiley & Sons Ltd.
SPSS 21 © 2009 John Wiley & Sons Ltd.
Parameter significance Testing that a specific parameter is significant (i.e., j 0) H 0 : j = 0 H 1 : j 0 Test-statistic: t = b j /SE j ~ t n-k-1 with b j = the estimated coefficient for j SE j = the standard error of b j 22 © 2009 John Wiley & Sons Ltd.
SPSS cont’d 23 © 2009 John Wiley & Sons Ltd.
Conceptual Model 24 Physical Attractiveness Likelihood to Date + © 2009 John Wiley & Sons Ltd.
Multiple Regression Analysis We use more than one (metric or non-metric) independent variable to explain variance in a (metric) dependent variable. 25 © 2009 John Wiley & Sons Ltd.
Conceptual Model 26 Perceived Intelligence Physical Attractiveness + + Likelihood to Date © 2009 John Wiley & Sons Ltd.
© 2009 John Wiley & Sons Ltd. 27
Conceptual Model 28 Perceived Intelligence Physical Attractiveness Likelihood to Date Gender © 2009 John Wiley & Sons Ltd.
Moderators Moderator is qualitative (e.g., gender, race, class) or quantitative (e.g., level of reward) that affects the direction and/or strength of the relation between dependent and independent variable Analytical representation Y = ß 0 + ß 1 X 1 + ß 2 X 2 + ß 3 X 1 X 2 with Y = DV X 1 = IV X 2 = Moderator 29 © 2009 John Wiley & Sons Ltd.
© 2009 John Wiley & Sons Ltd Moderators
interaction significant effect on dep. var. © 2009 John Wiley & Sons Ltd Moderators
Conceptual Model 32 Perceived Intelligence Physical Attractiveness Communality of Interests Likelihood to Date Gender Perceived Fit © 2009 John Wiley & Sons Ltd.
Mediating/intervening variable Accounts for the relation between the independent and dependent variable Analytical representation 1.Y = ß 0 + ß 1 X => ß 1 is significant 2.M = ß 2 + ß 3 X => ß 3 is significant 3.Y = ß 4 + ß 5 X + ß 6 M => ß 5 is not significant => ß 6 is significant 33 WithY = DV X = IV M = mediator © 2009 John Wiley & Sons Ltd.
Step 1 34 © 2009 John Wiley & Sons Ltd.
Step 1 cont’d 35 significant effect on dep. var. © 2009 John Wiley & Sons Ltd.
Step 2 36 © 2009 John Wiley & Sons Ltd.
Step 2 cont’d 37 significant effect on mediator © 2009 John Wiley & Sons Ltd.
Step 3 38 © 2009 John Wiley & Sons Ltd.
Step 3 cont’d 39 significant effect of mediator on dep. var. insignificant effect of indep. var on dep. Var. © 2009 John Wiley & Sons Ltd.