# ANOVA Tests

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Can you please show me how to perform an ANOVA on the data below using Microsoft Excel. Then I need to understand how to interpret the results of your ANOVA and the significance of the results to the organization as a whole.

U.S. airlines carried 47.4 million domestic passengers in April, the U.S. Department of Transportation's Bureau of Transportation Statistics reported today in a release of preliminary data. Effective October 2002, commuter and small certificated carriers were required to begin reporting domestic enplaned data. The addition of this new data has a distorting effect on year-over-year domestic enplanement comparisons, but represents the new way that this data will be announced (affected data shown in bold).

The April 2003 data include 3,163,281 domestic enplanements that were reported by these relatively new reporting carriers. Thus, the same carrier year over year comparison in April 2003 would total 44,234,664 domestic enplanements this year or a 2.6 percent decrease compared to the prior year's April results.

Total domestic enplanements were 3.8 percent lower in April 2003 compared to March 2003 for all domestic flights operated by U.S. airlines. Month-to-month changes can be affected by seasonal factors.

Table 1. Industry Domestic Enplanements

Month 2001 2002 2003

January 44,107,354 38,557,439 43,067,895

February 43,177,091 38,644,426 40,981,396

March 53,054,589 48,501,883 49,292,829

April 50,791,568 45,437,147 47,397,945

May 51,119,648 47,114,281

June 53,471,052 49,188,600

July 55,802,826 51,155,839

August 56,404,948 51,226,483

September 30,546,412 40,223,878

October 40,290,718 48,273,424

November 40,691,635 44,226,121

December 40,901,001 49,864,516

YTDate 191,130,602 171,140,895 180,740,065

Annual 560,358,842 552,414,037

Source: T-100 Domestic Market

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The question here is to compare the population means of each year.

If there is significant difference between these averages, the addition of new data does have effect on the enplanement; if not, no significant effect.

Since there's a lack in data of May-December 2003, we only use the January - April samples.

The null hypothesis will be that all population means are equal, the alternative hypothesis is that at least one mean is different:

H0: D1=D2=D3 vs. H1: at least one D is different

(Please refer to the attached EXCEL file for calculation.)

The grand mean of a set of samples is the total of all the data values divided by the total sample size. Dgm=45250964

The total variation (not variance) is comprised the sum of the squares of the differences of each mean with the grand mean. There is the between group ...

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