Question

unit anova (biostatistics) using R

on the table below Oxygen consumption you will find the rate of oxygen consumption of two species of limpets (Acmaea scabra & A. digitalis) in three different concentrations of salt water. The variable is given as μl O2/mg units per dry weight at 22°C. The researcher would like to know whether the rate of oxygen consumption differs between both species and the different concentrations of salt water.

Coding in Oxygen consumption:

Species 1 = Acmaea scabra

Species 2 = A. digitalis

Concentration 1 = 100%

Oxygen consumption:

consumption	species	concentration
7.16	1	1
6.78	1	1
13.6	1	1
8.93	1	1
8.26	1	1
14	1	1
16.1	1	1
9.66	1	1
5.2	1	2
5.2	1	2
7.18	1	2
6.37	1	2
13.2	1	2
8.39	1	2
10.4	1	2
7.18	1	2
11.11	1	3
9.74	1	3
18.8	1	3
9.74	1	3
10.5	1	3
14.6	1	3
11.1	1	3
11.8	1	3
6.14	2	1
3.86	2	1
10.4	2	1
5.49	2	1
6.14	2	1
10	2	1
11.6	2	1
5.8	2	1
4.47	2	2
9.9	2	2
5.75	2	2
11.8	2	2
4.95	2	2
6.49	2	2
5.44	2	2
9.9	2	2
9.63	2	3
6.38	2	3
13.4	2	3
14.5	2	3
14.5	2	3
10.2	2	3
17.7	2	3
12.3	2	3

Answer 1

The r-codes are given below

data=read.csv(file.choose())

attach(data)

twanova<-aov(consumption~as.factor(species)*as.factor(concentration))

twanova

output
Two-Way ANOVA
	df	Sum of Squares	Mean Squares	F	Pr(>F)
species	1	16.638075	16.638075	1.74037878	0.19423806
concentration	2	181.32101667	90.66050833	9.48328607	0.00039931
species: concentration	2	23.9262	11.9631	1.25136624	0.29656157
Residuals	42	401.5213	9.56003095	NA	NA

TukeyHSD(twanova)

For species
Tukey's HSD
	diff	lwr	upr	p adj
2-1	-1.1775	-2.97876567	0.62376567	0.19423806

For concentartion
Tukey's HSD
	diff	lwr	upr	p adj
2-1	-1.38125	-4.03708104	1.27458104	0.42339233
3-1	3.255	0.59916896	5.91083104	0.01306912
3-2	4.63625	1.98041896	7.29208104	0.00034582

From the we conclude that there is significant differen in the concetration only because the p-value associatiated with is 0.0003 which is significant ans species are insignificant because p-value > 5% level of significance.

In concentration the diffrence in solt of 3-a and 3-2 is significant, because p- value associated with it is < 0.05 level of significance