[FREE EBOOK]Statistical Analysis: Microsoft Excel 2013 by Conrad Carlberg

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Author:Conrad Carlberg [Carlberg, Conrad]
Language: eng
Format: azw3, epub , pdf
Publisher: Pearson Education
Published: 2019-04-04T04:00:00+00:00

Now, the critical value of t that divides the alpha area from the rest of the area under the control group’s distribution of sample means has 5% of the area to its left, not 95% as in the prior example. You can find out what the t-value is by using this formula:

=T.INV(.05,18)

The alpha rate is the same in both examples, and both examples use a directional hypothesis. The degrees of freedom is the same in both cases. The sole difference is the direction of the alternative hypothesis; in Figure 9.3 you expect the experimental group’s mean to be lower, not higher, than that of the control group.

One way to deal with this situation is as shown in Figure 9.3. The area that represents alpha is placed in the left tail of the control group’s distribution, bordered by the critical value that separates the 5% alpha area from the remaining 95% of the area under the curve. When you want 5% of the area to appear to the left of the critical value, you use 0.05 as the first argument to T.INV(). When you want 95% of the area to appear to the left of the critical value, use 95% as the first argument. T.INV() responds with the critical value that you specify with the probability you’re interested in, along with the degrees of freedom that defines the shape of the curve.

The t-distribution has a mean of zero and it is symmetric (although, as Chapter 8 discussed, its shape is not the same as that of the normal distribution). Earlier in this section you saw that the formula =T.INV(0.95,18) returns 1.73. Because the t-distribution has a zero mean and is symmetric, the formula

=T.INV(0.05,18)

returns –1.73. Either 1.73 or –1.73 is a critical value for a directional t-test with an alpha of 5% and 18 degrees of freedom.

I included Figure 9.3 (and the related discussion of the placement of the area that represents alpha) primarily to provide a better picture of where and how your hypotheses affect the placement of alpha. This chapter gets more deeply into that matter when it takes up nondirectional hypotheses.

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