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#Spss 16 for dummies how to#

The regression coefficients, however, are different.įigure 5 displays the grand mean, the group means and the group effect sizes (i.e. The first Summary and ANOVA tables are identical to the results from the previous analysis, and so once again we see that the results are the same as for the ANOVA. The results of the regression analysis are given on the right side of Figure 4. Also β 1 = μ 1 – β 0 and β 2 = μ 2 – β 0, and so β 1 = the population Flavor 1 mean less the population grand mean and β 2 = the population Flavor 2 mean less the population grand mean. Simplifying, this means once again that the null hypothesis is equivalent to: Since for the Flavor 3 group, t 1 = -1 and t 2 = -1 The null hypothesis and linear regression model are as before. The data now can be expressed as in the table on the left of Figure 4.įigure 4 – Alternative coding for data in Example 1

In general, If there are k groups then the jth dummy variable t j = 1 if the jth group, t k = -1 if the kth group and = 0 otherwise. T 2 = 1 if flavoring 2 is used = -1 if flavoring 3 is used = 0 otherwise T 1 = 1 if flavoring 1 is used = -1 if flavoring 3 is used = 0 otherwise This is consistent with what we noted above when relating the population group means to the population coefficients, namely µ 3 = β 0, µ 1 = β 0 + β 1 and µ 2 = β 0 + β 2.Įxample 1 ( alternative approach): An alternative coding for Example 1 is as follows

The coefficient b 2 for variable t 2 = mean of the Flavor 2 group – mean of the Flavor 3 group = 11.5 – 14 = -2.5.

The coefficient b 1 for variable t 1 = mean of the Flavor 1 group – mean of the Flavor 3 group = 12 – 14 = -2.

The intercept b 0 = mean of the Flavor 3 group = 14.

Note the following about the regression coefficients: Note that the F value 0.66316 is the same as that in the regression analysis. We now compare the regression results from Figure 2 with the ANOVA on the same data found in Figure 3. The results of the regression analysis are displayed in Figure 2.įigure 2 – Regression analysis for data in Example 1 Simplifying, this means that the null hypothesis is equivalent to: Thus the null hypothesis given above is equivalent to Since for the Flavor 3 group, t 1 = 0 and t 2 = 0 Since for the Flavor 2 group, t 1 = 0 and t 2 = 1 Since for the Flavor 1 group, t 1 = 1 and t 2 = 0 Where x j = the score for Flavor group j. Note that in general, if the original data has k values the model will require k – 1 dummy variables. T 2 = 1 if flavoring 2 is used = 0 otherwise T 1 = 1 if flavoring 1 is used = 0 otherwise First, we define the following two dummy variables and map the original data into the model on the right side of Figure 1. Instead of doing the analysis using ANOVA as we did there, this time we will use regression analysis instead. In this example, we have reduced the sample size from Example 1 of Basic Concepts for ANOVA to better illustrate the key concepts. Our objective is to determine whether there is a significant difference between the three flavorings.

#Spss 16 for dummies how to#

See Three Factor ANOVA using Regression for information about how to apply these techniques to factorial ANOVA with more than two factors.Įxample 1: Repeat the analysis from Example 1 of Basic Concepts for ANOVA with the sample data in the table on the left of Figure 1 using multiple regression. We now illustrate more complex examples and show how to perform Two Factor ANOVA using multiple regression. As seen in Linear Regression Models for Comparing Means, categorical variables can often be used in regression analysis by first replacing categorical variables by a dummy variable (also called a tag variable).