Page 186 - Applied Statistics Using SPSS, STATISTICA, MATLAB and R

166 4 Parametric Tests of Hypotheses

As mentioned in Commands 4.5 be sure to check the No intercept box in
STATISTICA (Options tab) and uncheck Include intercept in model
in SPSS (General Linear Model, Model tab). In STATISTICA the
Sigma-restricted box must also be unchecked; the model will then be the
Type III orthogonal model.
The meanings of most arguments and return values of anova2 MATLAB
command are the same as in Commands 4.5. The argument reps indicates the
number of observations per cell. For instance, the two-way ANOVA analysis of
Example 4.19 would be performed in MATLAB using a matrix x containing
exactly the data shown in Figure 4.18a, with the command:

» anova2(x,4)

The same results shown in Table 4.21 are obtained.
Let us now illustrate how to use the R anova function in order to perform two-
way ANOVA tests. For this purpose we assume that a data frame with the data of
Example 4.19 has been created with the column names f1 , f2 and X as in the left
picture of Figure 4.18. The first thing to do (as we did in Commands 4.5) is to
convert f1 and f2 into factors with:

> f1f <- factor(f1,labels = c(“1”, 2”, 3”))
“
“
> f2f <- factor(f2,labels = c(“1”, 2”))
“

We now obtain the two-way ANOVA similar to Table 4.21 using:

> anova(lm(X~f1f*f2f))

A model without interaction effects can be obtained with anova( lm(X~
f1f+f2f)) (for details see the help on lm )

Exercises

4.1 Consider the meteorological dataset used in Example 4.1. Test whether 1980 and 1982
were atypical years with respect to the average maximum temperature. Use the same
test value as in Example 4.1.

4.2 Show that the alternative hypothesis µ T 81 = 39 8 . for Example 4.3 has a high power.
Determine the smallest deviation from the test value that provides at least a 90%
protection against Type II Errors.

4.3 Perform the computations of the powers and critical region thresholds for the one-sided
test examples used to illustrate the RS and AS situations in section 4.2.

4.4 Compute the power curve corresponding to Example 4.3 and compare it with the curve
obtained with STATISTICA or SPSS. Determine for which deviation of the null
hypothesis “typical” temperature one obtains a reasonable protection (power > 80%)
against alternative hypothesis.