Heart rates were monitored (10) for six tree shrews (Tupaia glis) during three different stages of sleep: LSWS (light slow-wave sleep), DSWS (deep slow-wave sleep), and REM (rapid-eye-movement sleep).

(a) Do the analysis of variance to test the equality of the heart rates during these three phases of sleep. Let α = 0.05.
(b) Because of the marked physiological difference between REM sleep and LSWS and DSWS sleep, it was decided before the data were collected to test the REM rate against the average of the other two. Test the appropriate subhypothesis with a contrast. Use the 0.05 level of significance. Also, find a second contrast orthogonal to the first and verify that the sum of the sum of squares for the two contrasts equals SSTR.

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Heart Rates (beats 5 seconds Tree Shrew LSWS DSWS REM 14.1 11.7 15.7 26.0 21.1 21.5 20.9 19.7 18.3 19.0 18.2 17.0 26.1 23.2 22.5 20.5 20.7 18.9