Estimate Difference of Means from Raw Data

How To... > Work with Statistical Objects > Estimate Parameters and Compute Confidence Intervals > Estimate Difference of Means from Raw Data

1.	Create a new estimate by dragging one from the shelf or choosing Object \| New \| Interval Estimate.

From the pop-up menu in the estimate’s upper-right corner, choose Difference of Means. You have two groups and something you’ve measured. You want to know the confidence interval for the difference of means of the two groups. We’ll use an example to illustrate this. Suppose we are doing an experiment with plants and fertilizer. Some of the plants get the fertilizer and some don’t.

There are two ways to use this estimate, depending on how the data are structured.

The preferred way of structuring data is shown below. Each case is a plant, and the attribute Group tells whether or not the plant got fertilizer. To assign attributes to the estimate object, the Group attribute, being categorical, goes to the second line of the attribute pane, and the Height attribute goes to the first line. This is all shown below. (Notice that the estimate is in terse mode.)

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The less preferred way of structuring data is to use one attribute for the values of one group and a second attribute for the values of the other group. Notice that this means that a single case in the collection doesn’t really make any sense. The case represents a pair of plants, but there isn’t any good reason for a particular pair to be assigned to the same case. You can drag either attribute to either line in the estimate object; the difference will be the first attribute minus the second.

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By default, Fathom calculates the difference in means using unpooled variances. Click on the phrase “unpooled variances” for a pop-up menu that allows you to switch between unpooled variances and pooled variance. Use pooled variance when you have reason to believe that the standard deviation of the values is the same for both groups. Unpooled variances use weaker assumptions and produce somewhat larger intervals than does pooled variance.

You can change the confidence level by double-clicking it and typing a different value or by assigning it a formula.