\u00b9\u00ba 7KH 6XPPDU 6WDWLVWLFV The summary statistics for the grades of each row are

¹º 7kh 6xppdu 6wdwlvwlfv the summary statistics for

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´¹º 7KH 6XPPDU\ 6WDWLVWLFV The summary statistics for the grades of each row are shown in the table below Row Front Middle Back Sample size 7 9 8 Mean 75.71 67.11 53.50 St. Dev 17.63 10.95 8.96 Variance 310.90 119.86 80.29 ´¹± :H 6WDFN 2XU 'DWD LQ 6WDWD ´¹²
6WDWD 2XWSXW . oneway score block,tabulate | Summary of score block | Mean Std. Dev. Freq. ------------+------------------------------------ 1 | 75.714286 17.632492 7 2 | 67.111111 10.94811 9 3 | 53.5 8.9602296 8 ------------+------------------------------------ Total | 65.083333 15.162645 24 Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups 1901.51587 2 950.757937 5.90 0.0093 Within groups 3386.31746 21 161.253212 ------------------------------------------------------------------------ Total 5287.83333 23 229.905797 Bartlett's test for equal variances: chi2(2) = 3.1149 Prob>chi2 = 0.211 ´¹³ 7ULFN» &UHDWLQJ 'XPP\ 9DULDEOHV From stacked data we can create dummy variables in Stata as follows: ´¹´ tabulate block,generate(dum) block | Freq. Percent Cum. ------------+----------------------------------- 1 | 7 29.17 29.17 2 | 9 37.50 66.67 3 | 8 33.33 100.00 ------------+----------------------------------- Total | 24 100.00 1RZ $129$ YLD 5HJUHVVLRQ Same output as before (but of course): ´¹µ . regress front dum2 dum3 Source | SS df MS Number of obs = 24 -------------+---------------------------------- F(2, 21) = 5.90 Model | 1901.51587 2 950.757937 Prob > F = 0.0093 Residual | 3386.31746 21 161.253212 R-squared = 0.3596 -------------+---------------------------------- Adj R-squared = 0.2986 Total | 5287.83333 23 229.905797 Root MSE = 12.699 ------------------------------------------------------------------------------ front | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- dum2 | -8.603175 6.399468 -1.34 0.193 -21.9116 4.705249 dum3 | -22.21429 6.572125 -3.38 0.003 -35.88177 -8.546804 _cons | 75.71429 4.799601 15.78 0.000 65.73297 85.6956 ------------------------------------------------------------------------------ $129$ SRSXODU UHVHDUFK WRRO A famous Harvard Law Study ´¹¶ 7KH 'DWD 500 1,000 1,500 2,000 2,500 Profit 4 3 2 1 graph hbox profit, over(racegen) ´¹· 6WDWD 2XWSXW . oneway discount group,tabulate | Summary of discount group | Mean Std. Dev. Freq. ------------+------------------------------------ 1 | 829.8 226.72331 15 2 | 1554.5 241.52364 4 3 | 792.2 157.14706 5 4 | 2021.4286 180.56288 7 ------------+------------------------------------ Total | 1186.3226 556.66773 31 Analysis of Variance Source SS df MS F Prob > F ------------------------------------------------------------------------ Between groups 8107320.86 3 2702440.29 61.36 0.0000 Within groups 1189047.91 27 44038.8116 ------------------------------------------------------------------------ Total 9296368.77 30 309878.959 Bartlett's test for equal variances: chi2(3) = 1.0207 Prob>chi2 = 0.796 . ´¹¸
Things you should know ANOVA is a useful procedure for testing the equality of 3 or more means. It assumes the population variances are all the same; if this isn’t the case there are nonparametric methods that can be used. If you reject the null hypothesis, it doesn’t imply all the means are unequal; just that there is some difference between them. Most importantly, it can easily be done using dummy variables in regression. ´¹¹ µºº Stat 104: Quantitative Methods for Economists Class 41: Course Review µº± ^Ž / ƐĂƚ ƚŚĞƌĞ ĨŽƌ ƚŚĞ ĞŶƚŝƌĞ ƐĞŵĞƐƚĞƌ ƚŚŝŶŬŝŶŐ ͞ǁŚĂƚ Ă ŚŽƌƌŝďůĞ /ŶƚƌŽĚƵĐƚŝŽŶ ƚŽ ^ƉĂŶŝƐŚ ±ůĂƐƐ͘͟ µº² )DOODFLHV DQG 7UDSV Before we review the main ideas from the course, it will beneficial to review some of the essential ideas from the course. We call them Fallacies and Traps. µº³ )DOODFLHV DQG 7UDSV Lying with Graphs (please don’t do it) µº´
3RSXODWLRQ DV 6DPSOH A small company wishes to investigate the ages of its workers. It has collected data from all 92 workers, and finds an average age of 42 with a

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