Two-Way ANOVA in Excel

Excel only caters for one- and two-way ANOVA. In two-way ANOVA there are two factors being considered. For example, we may be interested in the effect of changing the catalyst and the temperature in a synthesis. One factor is the catalyst (e.g., Zn or Li) and the other is temperature (e.g., 50, 70, or 90°C). In two-way ANOVA in Excel the distinction is made between measurements that are repeated and those for which only a single measurement is made, at each combination of factors. The layout for this example is given in table 4.5. 

The Excel output from the two-way ANOYA with replication has summary statistics of each factor with an ANOYA table that looks like spreadsheet 4.5. 

Unfortunately, the labels are used for the statistics but do not find their way to the ANOVA table. The word Sample refers to the factor in the rows (having levels 50°C, 70°C, and 90°C in the example), the columns are in Columns (Zn and Li), Interaction is as described above, and Within is the residual or within factor variance. The interpretation of the columns of the ANOVA table is exactly as described above for the one-way case. 

Determine whether there is any difference in the means with 95% probability with regards to either the two analysts or the two pipetting methods. 

The solution to this problem involves performing a two-factor ANOYA with replication. This will be demonstrated using Excel. First we plot the means and standard deviations to give a first impression of the data. With two factors there are two options for our plot. We can have the analyst as the v-variablc and plot the forward and reverse data on the graph, or vice versa with the direction as the v-variablc and the analysts on the graph. This is shown in figure 4.5. To perform the calculation  

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The idea behind ANOVA is that if two distributions with very different means are combined, the variance of the resulting distribution will be much greater than the variances of the two distributions. Here I describe one- and two-way ANOVA in Excel, See (Massart et al 1997, chapter 6) for a more comprehensive discussion of the use of ANOVA,... 

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