A research team monitored the heart rates for six randomly selected 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). The authors wish to account for any differences between the tree shrews and stages of sleep.

HeartRates	The heart rates of the tree shrew
Shrews	The specific tree shrews (labelled as 1, 2, 3, 4, 5 and 6)
Sleep	The stages of sleep (labelled as LSWS, DSWS, REM)

Analyse the data, stating the null and alternative hypothesis for each test, and check assumptions. In your answer:

Write down the mathematical model for this situation, defining all appropriate parameters

State the appropriate hypotheses

Compute an appropriate ANOVA table

Check assumptions

e. State your conclusions about the effect of Shrews and Sleep on HeartRates. These conclusions are only required to be at the qualitative level and can be based off the outcomes of the hypothesis tests and the preliminary plots in b. You do not need to statistically examine the multiple comparisons.

Data:

HeartRates Shrews Sleep 14 1 LSWS 12 1 DSWS 16 1 REM 26 2 LSWS 21 2 DSWS 22 2 REM 21 3 LSWS 20 3 DSWS 18 3 REM 19 4 LSWS

18 4 DSWS 17 4 REM 26 5 LSWS 23 5 DSWS 22 5 REM 20 6 LSWS 21 6 DSWS 19 6 REM

Preliminary plots:

Heart Rates 12 14 16 18 20 22 24 26 1 + 2 N 3 w Shrews Boxplot of Heart Rates vs Shrews 4 5 on 9 o Boxplot of Heart Rates vs Sleep Heart Rates 12 14 16 18 20 22 24 26 g DSWS LSWS REM Sleep Heart Rates 12 14 16 18 20 22 24 26 1 + 2 N 3 w Shrews Boxplot of Heart Rates vs Shrews 4 5 on 9 o Boxplot of Heart Rates vs Sleep Heart Rates 12 14 16 18 20 22 24 26 g DSWS LSWS REM Sleep