Question

We want to assess whether there is a difference in the impact that the predatory larvae of three damselfly species (Enallagma, Lestes and Pyrrhosoma) have on the abundance of midge larvae in a pond.

We plan to conduct an experiment in which small (1 m2m2) nylon mesh cages are set up in the pond. All damselfly larvae will be removed from the cages and each cage will then be stocked with 20 individuals of one of the species. After 3 weeks we will sample the cages and count the density of midge larvae in each. We have 12 cages altogether, so four replicates of each of the three species can be established.

We have two options:

• Use a CRD and distribute the cages at random, or
• Adopt an RCBD by grouping the cages into clusters of three, placing each cluster at a randomly chosen location, and assigning the three species to cages at random within each cluster.

Answer the following two questions.

1. Which design do you think is more reasonable and what else information do you need to justify your choice?
2. If one choose RCBD for this experiment, and collect the data ("T1_Damsefly.csv"). Analyze the data and provide your interpretation or conclusions.

T1_damsefly
Midge	Block	Species
304	A	Enallagma
464	A	Lestes
320	A	Pyrrhosoma
578	B	Enallagma
509	B	Lestes
458	B	Pyrrhosoma
680	C	Enallagma
740	C	Lestes
630	C	Pyrrhosoma
356	D	Enallagma
390	D	Lestes
350	D	Pyrrhosoma

Answer 1

1.

It is mentioned that there are 12 cages, and the difference (if any) among 3 damselfly species (Enallagma, Lestes, and Pyrrhosoma) are to be studied, so that individuals from each species can be allocated to 4 (= 12/3) cages.

Although in the data set, Clocks A, B, C, and D are given, nothing is mentioned that would indicate that blocking is at all necessary. From the information provided, it appears that A, B, C, and D are merely used to identify the replicates. There is nothing to suggest that the cages, or the environmental conditions are heterogeneous and thus need to be divided into 4 homogeneous subgroups or blocks.

It is not desirable to increase complications of the analysis by unnecessarily introducing a blocking variable.

Hence, it is reasonable to use CRD (completely randomized design). However, before ignoring the blocking variable completely, it is desirable to confirm whether the cages and other environmental conditions are homogeneous, so that there is no need of a blocking variable. If there is some heterogeneity in the study conditions that supports blocking, then an RCBD is to be used.

2.

We have used Excel to analyse the data in an RCBD (randomized complete block design).

First, we have entered the data in the following manner:

Note that the rows represent the treatments (3 different species) and the column represent the 4 blocks.

Go to Data > Data Analysis > Anova: Two-Factor Without Replication [since each treatment appears in each block exactly once] > OK.

Enter Input Range as $A$1:$E$4, tick on Labels, enter Alpha as 0.05 and click OK.

The following output is obtained:

The null hypothesis for the block (Column) effect would be of the form “there is no difference in the block effects”, and the alternative hypothesis would be of the form “there is significant difference in the block effects”.

The null hypothesis for the treatment (Row) effects would be of the form “there is no difference in the impact that the predatory larvae of three damselfly species have on the abundance of midge larvae in a pond”. The alternative hypothesis would be of the form “there is significant difference in the impact that the predatory larvae of three damselfly species have on the abundance of midge larvae in a pond”.

The decision rule for a hypothesis testing problem using p-value is: Reject the null hypothesis if P-value ≤ α. Otherwise, fail to reject the null hypothesis.

In the above ANOVA table, the P-value for the “Columns”, that is, block effects is 0.000630585, which is less than most of the commonly used significance levels, such as, 0.001, 0.01, 0.025, 0.05, 0.10, etc. Hence, there is sufficient evidence to indicate a difference among the block, which indicates that it is reasonable to use RCBD in this case, instead of CRD.

The P-value for the “Rows”, that is, treatment effects is 0.124668717, which is greater than all of the commonly used significance levels. Hence, there is no evidence to indicate a significant difference in the impact that the predatory larvae of three damselfly species have on the abundance of midge larvae in a pond.