Question

using spss software and write your interpretationa nd conclusion

3. To test the hypothesis that all four types of plants reach the same maximum height, scientists selected six greenhouses. In each greenhouse, one of each of four types of plants was planted. The plant heights (in centimeters) are recorded as following: Greenhouse Plant type Plant type 2 Plant type 3 Plant type 4 14.7 13.5 12.8 19.8 16.7 17.7 18.2 20.3 15.5 21.9 19.8 21.0 21.4 22.1 20.8 16.4 15.4 14.8 4 15.6 13.7 16.4 14.6 4 3 4 14.6 12.9 (a) What type of experimental design is this? (b) Test the hypothesis that all four types of plants reach the same maximum height.

Answer 1

(a) The experiment design is Completely Randomized Design or CRD.

(b) The R-code for analysis is:

data <- c(19.8,16.7,17.7,18.2,20.3,15.5,21.9,19.8,21.0,21.4,22.1,20.8,16.4,15.4,14.8,15.6,16.4,14.6,14.7,13.5,12.8,13.7,14.6,12.9)
plant <- c(rep("type 1", 6),rep("type 2", 6),rep("type 2", 6),rep("type 3", 6))
aov(data~plant)
summary(aov(data~plant))
TukeyHSD(aov(data~plant))

Output:

> aov(data~plant)
Call:
aov(formula = data ~ plant)

Terms:
plant Residuals
Sum of Squares 93.3350 121.5233
Deg. of Freedom 2 21

Residual standard error: 2.405582
Estimated effects may be unbalanced
> summary(aov(data~plant))
Df Sum Sq Mean Sq F value Pr(>F)   
plant 2 93.34 46.67 8.064 0.00252 **
Residuals 21 121.52 5.79   
---
Signif. codes: 0 ‘*’ 0.001 ‘*’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1
> TukeyHSD(aov(data~plant))
Tukey multiple comparisons of means
95% family-wise confidence level

Fit: aov(formula = data ~ plant)

$plant
diff lwr upr p adj
type 2-type 1 0.3166667 -2.715053 3.3483860 0.9625785
type 3-type 1 -4.3333333 -7.834061 -0.8326053 0.0137461
type 3-type 2 -4.6500000 -7.681719 -1.6182806 0.0024700

Since the p-values for both the pairs including type 3 is less than 0.05, the plant of type 3 is significantly different from the other two types