Dec 6 2006 Lab 9 Econ240A 1 One Way and Two Way Analysis of Variance L Phillips I One Way Analysis of Variance A Excel Open the data file xm15 01 that has data on weekly apple juice sales organized by advertising strategy 1 convenience city 1 2 quality city 2 3 price city 3 Go to the Tools menu select Data Analysis and in the dialog box select Anova Single Factor and hit OK In the next dialog box for input range type in A1 C21 or select those cells Check the box labels in the first row For output Options select new worksheet ply In the top panel under averages note the sample means for convenience quality and price This is the data reported in Table 2 of the Lecture 15 notes In the bottom panel is the table of ANOVA reported in Table 4 of these lecture notes B Eviews One Way ANOVA as Hypothesis Testing Open the Eviews file apple juice sales in Eviews Select salesaj convenience quality price and go to the menu and select view open selected one window open group Note that the sales data is stacked in a column of sixty observations where the first twenty are for city one convenience the second twenty are for city two quality and the last twenty are for city 3 price Convenience is a dummy variable with ones for the first twenty observations and zeros for the last 40 Quality is a dummy variable with zeros for the first and last twenty observations and ones for observations 21 40 Price is a dummy variable with zeros for the first forty observations and ones for the last twenty Close this workfile window and select salesaj Go to the menu and select view open selected one window In the work file window for apple juice sales that opens go to the menu and select view tests for descriptive stats equality tests by classification Dec 6 2006 Lab 9 Econ240A 2 One Way and Two Way Analysis of Variance L Phillips In the dialog window that opens up in the series group for classify box type in convenience quality price with a space between them and hit OK Note in the top panel the F statistic 3 23 with 2 degrees of freedom in the numerator and 57 in the denominator In the second panel is the table of ANOVA the same as in Table 4 of the Lecture notes 15 The last panel shows the means for convenience quality and price as well as other statistics as reproduced in Table 2 of these lecture notes C Eviews Using Regression for One Way ANOVA Use this file for apple juice sales to run a regression of salesaj convenience quality price with no intercept The regression results are reproduced as Table 5 of Lecture notes 15 Note that the estimated coefficients on the three dummy or indicator variables are the mean sales of apple juice for the corresponding three cities The F statistic for the regression is 3 23 and the sum of squared residuals 506983 5 is the same as the unexplained sum of squares in Table 4 of the lecture notes The standard deviation of the dependent variable 97 81474 squared and multiplied by 59 is the total sum of squares 564496 reported in Table 4 The difference between this total and the unexplained is the explained sum of squares So a table of ANOVA can be reproduced from this regression Go to the view menu and select actual fitted residual graph Note the variation of actual sales around fitted sales the mean level for convenience then quality then price which is the residual and an indication of the unexplained variance To test the null hypothesis that the three means are equal use the view menu to go to representations and observe that the three coefficients on the three dummy variables are denoted as C 1 C 2 and C 3 Use the view menu to go Dec 6 2006 Lab 9 Econ240A 3 One Way and Two Way Analysis of Variance L Phillips to coefficient tests Wald coefficient restrictions In the Wald Test box that appears type in C 1 C 2 C 3 and hit OK Note that the F statistic is 3 23 the same as for the regression and for the ratio of the explained mean square to the unexplained mean square in Table 4 of Lecture notes 15 In this regression the expected value of sales conditional on the dummy variables is E salesaj convenience 1 quality 0 price 0 convenience 1 E salesaj convenience 0 quality 1 price 0 quality 2 E salesaj convenience 0 quality 0 price 1 price 3 And the estimated parameters C 1 C 2 and C 3 are the corresponding estimated sample means as we saw from the regression We could estimate the regression with a constant term and two of the dummy variables say for convenience and quality Salesaj a bc convenience bq quality e 4 In this case the expected value of sales conditional on the values of the dummy variables including the intercept is E salesaj a 1 convenience 0 quality 0 a 5 E salesaj a 1 convenience 1 quality 0 a bc 6 E salesaj a 1 convenience 0 quality 1 a bq 7 As can be seen from running this regression the estimated intercept is the sample mean for price the dummy variable that was omitted as implied by the indicator variables for convenience and quality being zero so E salesaj a 1 convenience 0 quality 0 a price 8 E salesaj a 1 convenience 1 quality 0 a bc convenience 9 E salesaj a 1 convenience 0 quality 1 a bq quality 10 Thus subtracting Eq 8 from Eq 9 Dec 6 2006 Lab 9 Econ240A 4 One Way and Two Way Analysis of Variance convenience price bc L Phillips 11 and similarly subtracting Eq 8 from Eq 10 quality price bq 12 so in this regression specification the coefficients on the dummy variables capture the difference in mean sales between the subgroup corresponding to that dummy variable and the mean sales for the subgroup for the omitted variable Looking at the estimated regression for Eq 4 there is no significant difference in sales between quality and price and or between convenience and price However the biggest difference between means is between quality and convenience Note that the F statistic for the regression 3 23 is significant showing that at least two means differ Repeat the regression for Salesaj a bq quality bp price e 13 Note that the coefficient on quality is significant indicating a significant difference in mean sales between quality and convenience II Two Way Analysis of Variance A Excel Open the data file xm15 03a in Excel First we will conduct one way analysis of variance Go to the Tools menu select Data Analysis and in the dialog box select Anova Single Factor and hit OK In the next dialog box for input range type in A1 F11 or select those cells Check the box labels in the first row For output Options select new …
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