Question

Using R, conduct an ANOVA to see if there are differences in weight between two groups of monkeys. What is null hypothesis conclusion with evidence.

Conduct a post-hoc MCP (use TukeyHSD) to see which means are different. What do the outputs lwr and upr mean?

The numbers are

monkey group 1= 9.7, 9.2, 9.5, 9.5, 10.9, 9.8, 8.7, 7.9, 9.8, 9, 10.5, 8.9, 10, 8.9, 6.8, 9.3, 8.2, 8.5, 9.4, 10.5

Monkey group 2= 8.1, 7.8, 7.6, 9.9, 8.1, 9.1, 8.8, 10.4, 8.6, 6.9, 9.1, 6.7, 7.3, 7.8, 9.6, 8.7, 5.5, 9.5, 8.2, 7.8

Answer 1

Hypothesis =

H₀ = There is no Significance differences in weight between two groups of monkeys.

H₁ = There is Significance differences in weight between two groups of monkeys.

> m1=c(9.7, 9.2, 9.5, 9.5, 10.9, 9.8, 8.7, 7.9, 9.8, 9, 10.5, 8.9, 10, 8.9, 6.8, 9.3, 8.2, 8.5, 9.4, 10.5)

> m2=c(8.1, 7.8, 7.6, 9.9, 8.1, 9.1, 8.8, 10.4, 8.6, 6.9, 9.1, 6.7, 7.3, 7.8, 9.6, 8.7, 5.5, 9.5, 8.2, 7.8)

> an=aov(m1~m2)

> an

Call:

   aov(formula = m1 ~ m2)

Terms:

                       m2 Residuals

Sum of Squares   0.363025 17.106975

Deg. of Freedom         1        18

Residual standard error: 0.9748782

Estimated effects may be unbalanced

> summary(an)

            Df   Sum Sq   MeanSq   F value  Pr(>F)

m2           1   0.363    0.3630   0.382    0.544

Residuals   18   17.107   0.9504

Here from ANOVA Table we can say that probably looks like “a One-way ANOVA showed a non-significant effect of monkey 1 on Monkey 2 , F(1,18)=0.382, p>.01”

In other words, we can accept the null hypothesis that, there is no Significance differences in weight between two groups of monkeys.

to perform TUKEY HSD we need factors between each group.