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In this chapter, Keppel shows how to do trend analysis. Let's start by running the overall anova as shown in table 7-1 on page 143. We use the o. prefix before a because we will want to examine the trend coefficients. You can download the xi3 command by typing findit xi3 (see How can I use the findit command to search for programs and get additional help? for more information about using findit).
use http://www.ats.ucla.edu/stat/stata/examples/da/chap7, clear
xi3: regress numcorr o.a
o.a _Ia_1-4 (_Ia_4 for a==4 omitted)
Source | SS df MS Number of obs = 80
-------------+------------------------------ F( 3, 76) = 10.72
Model | 652.30 3 217.433333 Prob > F = 0.0000
Residual | 1541.90 76 20.2881579 R-squared = 0.2973
-------------+------------------------------ Adj R-squared = 0.2695
Total | 2194.20 79 27.7746835 Root MSE = 4.5042
------------------------------------------------------------------------------
numcorr | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Ia_1 | 1.788854 .5035891 3.55 0.001 .7858698 2.791839
_Ia_2 | -2.225 .5035891 -4.42 0.000 -3.227985 -1.222015
_Ia_3 | .0559017 .5035891 0.11 0.912 -.9470829 1.058886
_cons | 19.85 .5035891 39.42 0.000 18.84702 20.85298
------------------------------------------------------------------------------
We can use the test command below to get the overall test of the main effect of a.
test _Ia_1 _Ia_2 _Ia_3
( 1) _Ia_1 = 0.0
( 2) _Ia_2 = 0.0
( 3) _Ia_3 = 0.0
F( 3, 76) = 10.72
Prob > F = 0.0000
On page 145, Keppel shows a test of linear trend, and a test of quadratic trend on page 148, and a test of cubic trend on page 150. Because we use the o. prefix, we requested tests of orthogonal polynomials, meaning that the term _Ia_1 refers to the linear trend, _Ia_2 refers to the quadratic trend, and _Ia_3 refers to the cubic trend. The regression table above gives us the tests of all three trend components, but in terms of t-tests. Below we can use the test command to request F tests as shown in the book.
test _Ia_1
( 1) _Ia_1 = 0.0
F( 1, 76) = 12.62
Prob > F = 0.0007
test _Ia_2
( 1) _Ia_2 = 0.0
F( 1, 76) = 19.52
Prob > F = 0.0000
test _Ia_3
( 1) _Ia_3 = 0.0
F( 1, 76) = 0.01
Prob > F = 0.9119
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