Question

Mussel settlment patterns on algae. Mussel larvae are in great abundance in the drift material that washes up on Ninety Mile Beach in New Zealand. These larvae tend to settle on algae. Environmentalists at the University of Auckland investigated the impact of algae type on the abundance of mussel larvae in drift material (Malacologia, February 8, 2002). Drift material from three different wash-up events on Ninety Mile Beach were collected;for each wash-up,the algae was separated into four strata: coarse-branching, medium-branching, fine-branching, and hydroid algae. Two samples were randomly selected for each of the3×4=12event/strata combinations, and the mussel density (percent per square centimeter) was measured for each. The data was analyzed as a complete 3×4 factorial design. The ANOVA summary table is shown below. (a) Identify the factors (and levels) in this experiment. (b) How many treatments are included in the experiment? (c) How many replications are included in the experiment? (d) What is the total sample size for the experiment? (e) What is the response variable measured? (f) Which ANOVA F-test should be conducted first? Conduct this test(atα = .05)and interpret the results. (g) If appropriate, conduct the F-tests (at α = .05)for the main effects .Interpret the results.

A second course in statistics Regression Analysis 7th addition

Answer 1

As Table Is Not mentioned I took It By By own..

You Could Solve the Answer Likewise

Part a)

There are 3 factors in this experiment which are the 3 different wash up events.

Each factor has 4 levels - coarse-branching, medium branching, fine branching, and hydroid algae

Part b)

12 treatments are included in this experiment.

As there are 3X4=12 event/strata combinations

Part c)

There are 2 replications for each treatment in this experiment

Since Two samples were randomly selected for each of the 3X4=12 event/strata combinations.

Part d)

Thus, the total sample size for this experiment

Is 12 * 2 = 24

Part e)

The response variable measured is

mussel density (percent per square centimeter)

Part f)

First, the ANOVA F test to test the effect of interaction effect of wash up event and strata should be conducted.

The F statistic to test this interaction effect is 1.91 and the p-value of this test is greater than 0.05

Hence at level of significance equal to 0.05, we fail to reject the null hypothesis and thus we conclude that

There is no interaction effect of wash up event and stratum type on the mussel density (percent per square centimeter).

Part G)

Now, conducting the F tests for the main effects:

The p-value of the F test for the main effect due to wash up event is greater than 0.05

Thus, at level of significance 0.05 we fail to reject the null hypothesis and thus we conclude that the

mussel density (percent per square centimeter) is equal for the different wash up events.

The p-value of the F test for the main effect due to strata is greater than 0.05

Thus, at level of significance 0.05 we fail to reject the null hypothesis and thus we conclude that the

mussel density (percent per square centimeter) is equal for the different strata.