An experiment was conducted to investigate how the thickness

An experiment was conducted to investigate how the thickness of electrolytic deposition varies with the position of the rod and the vertical height on the rod at which the deposition is measured. Five nickel rods, 1mm in diameter, were put in a metallic clamp and immersed in a suspension of aluminum oxide. Voltage of 100 volts was applied for a few seconds between the rods (which had negative charge) and the conducting vessel containing the suspension. As a result, oxide particles (which had positive charge) were deposited on the nickel rods. The thickness of the deposition was measure din micrometers and the data collected from the fully randomized execution are provided in the table below. Calculate and report each of the effects for the height levels and for the positions. Conduct the appropriate statistical analyses and report the conclusions offered. Be sure to include supporting computational results.

Solution

Anova table will be set up to obtain the impact of height levels and positions on the thickness of the deposition.

> hpt <- read.csv(\"clipboard\",sep=\"\\t\")
> head(hpt)
Height Position Thickness
1 H1 P1 125
2 H1 P2 130
3 H1 P3 128
4 H1 P4 134
5 H1 P5 143
6 H2 P1 126
> sapply(hpt,class)
Height Position Thickness
\"factor\" \"factor\" \"integer\"
> thickness_aov <- aov(Thickness~Height+Position,data=hpt)
> summary(thickness_aov)
Df Sum Sq Mean Sq F value Pr(>F)
Height 2 1290 645 4.418 0.051 .
Position 4 600 150 1.027 0.449
Residuals 8 1168 146   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

The associated p-values indicate that while the position is insignificant variabel in explaining the thickness of the deposition, the height is significant.