 This is single factor ANOVA done using Excel. Single factor refers to just a single variable. This is a typical problem. The data table shows the energy consumed in millions of BTU in one year for a random sample of households from four regions in the United States. At alpha equal 0.05, can you conclude that the main energy consumption of at least one region is different from the others? Perform a one-way ANOVA test, and we assume the population variances are equal, and the populations are normally distributed. For the ANOVA, our null is always that the means are equal. Mean one equal mean two equal mean three equal mean four. And the alternative is always that at least one mean is different. The ANOVA will not directly tell us which mean is different if it's significant. We'll have to do a post-talk, a subsequent test to find out that. Excel, with the data analysis tool pack, does give you a tool for conducting the single factor ANOVA. But it stops short of running the post-talk, the second part of the test, to tell us which groups are different if indeed the ANOVA is significant. Remember in the ANOVA, if the ANOVA is significant, that means we reject the null that all of the means are equal, and that at least one mean is different. In your assignment package, you will find a spreadsheet that looks a little like this. What you will need to do will be to find your data and enter it in this part of the table. And then you need to run the ANOVA and this red cell becomes very important. Let me show you how to run the data analysis ANOVA. Click on data, data analysis, bring up the dialogue, and find the ANOVA single factor. Click on that, click okay. And we bring up this part of the dialogue and we clear out what we have there. We want to put the input range in this window for the ANOVA, you need to have all of your regions in this case adjacent. You can't have any gaps between your data. So here I'm going to select that range, it's grouped by columns it is, and then the labels are in the first row, which it is, my alpha is .05, and here's where that red cell comes in. You want to make sure that's cleaned out, put your cursor in there, and then click on the red cell so that the ANOVA is printed out in exactly the right spot so that the rest of the test works. I'm going to click okay, and you can see we get the ANOVA output here. We get the summary of the data, the counts, the averages, the variance. This is the ANOVA itself. You can see that we've got a p-value that is less than .05, which means we reject the null, and that tells us at least one of these means up here is statistically different. And the reason you can't just look at them and tell which one's different is because of the large variances. Once we've done that, the rest of the table, the second part of the test, it's called a Tukey Kramer, is completed for you except for this one blue cell, which is the Q-statistic, and I'll show you how you get that now. In this other data section of the Tukey Kramer, you see that we have our alpha there, .04, we've got a cell that's labeled numerator degrees of freedom, which is four, denominator degrees of freedom, 16. We use that information, those three pieces, and we'll go into a Q-statistic table, which is provided for you. This one is for the .05 alpha, and the columns are labeled number of groups, which is number of treatments. In our case, that's the number of regions, so we've got four. And from the table, we can see the denominator of degrees of freedom is 16. So we go down here for 16, look over in the four column, and we see 4046 would be our Q factor. You take that information, and I'm going to type it in there, .046, hit enter, and this part of the table updates. You can see that the calculations show in the results here that group one and two are not different, group three and four are not different, but one and three, one and four, two and three, and two and four are all different. So we had more than just one being different. We had quite a few differences there. So that's how you're going to do your ANOVA problem. You'll have different data, but you'll have a screen similar to that, a worksheet similar to this, I should say. And just be very careful to make sure you put it in that red cell when you say where on the worksheet you want your ANOVA to print out.