1
An environmental biologist wants to investigate the effect of two metals on algae growth. For the experiment she intends to use a factorial design using zinc and cadmium each at three levels (none, low concentration and high concentration). It is thought that there may be an interaction between the two metals in their effect on algae growth.
She can only set up a maximum of 32 growth tubes on each run of the experiment as this is the maximum that can be obtained from one initial culture of algae prior to the addition of the metals. Each run requires that the growth be monitored over 5 days.
Past experience suggests that a minimum of 8 replicates of each treatment will be needed.
(i)How many ‘treatments’ are being tested?
(ii)Why should she NOT treat this experiment as two separate experiments – one looking at the zinc at the three levels in the absence of cadmium and the other looking at the three levels of cadmium in the absence of zinc?
(iii)How should she organise the experiment to minimise problems with differences between the runs given that the algae vary somewhat from one initial culture to another?
2
A piece of ground 80m by 80m is available for a wheat trial to test 4 varieties of wheat. The recommended size for each plot for such a trial is 40m by 10m. It is suggested to you that a randomised block design is needed.
(i)Explain in general terms what is meant by a randomised block design and its purpose.
(ii)Draw a diagram showing how you would organise the plots for this experiment indicating the blocks.
(iii)How would you allocate the varieties (V1, V2, V3 and V4) to the plots?
3
Satisfactory experimental designs require that the experiment is replicated and that there is some randomisation. Explain the meaning of these terms.
The effect on heart rate of a certain drug in combination with exercise is to be measured.
Measurement of the heart rate will be needed for individuals who have…
(i)taken the drug and rested for 30 minutes
(ii)taken the drug and exercised moderately for 30 minutes
In addition it will be necessary to obtain control measurements for resting without the drug and for exercising without the drug.
Eight individuals are willing to take part in the experiment.
Give a suitable design for this experiment making clear where the replication and randomisation is incorporated.
4
(i)Explain the terms randomisation and replication and the reasons why they are necessary in a designed experiment.
(ii)There are 40 subjects available to test four treatments but each subject can only be used once. Explain carefully how you would assign the subjects to the four treatment groups.
5
A medical study of ease of use of single shot emergency injection packs looked at four types. Six nurses were asked to test the four packs to see how fast they could get the pack open and an injection given (using a dummy as a subject). The order of testing was randomised. The times obtained were as follows:
Times (secs)Nurse / 1 / 2 / 3 / 4 / 5 / 6
Standard / 35.6 / 31.3 / 36.2 / 31.1 / 39.4 / 34.7
Vari-Jet / 17.3 / 16.4 / 18.1 / 17.8 / 18.8 / 17.0
Unimatic / 24.4 / 22.4 / 22.8 / 21.5 / 23.3 / 21.8
Tubex / 25.0 / 26.0 / 25.3 / 24.0 / 24.2 / 26.2
a)The above experiment has a randomised block design. Which is the blocking factor and which is the treatment factor in the above experiment?
b)If this experiment had been done as a completely randomised design, how would it have been organised?
c)What is the purpose of using a randomised block design in preference to a completely randomised design?
d)Write down the sources of variation and degrees of freedom for the above experiment as they would be written in an ANOVA table. No other parts of the table are required.
6
Some cough medicines give a warning on the bottle about the use of machinery after taking the medicine as it can cause drowsiness. A group of students Anne, Barry, Caroline, Dave, Emma and Finn have been set the task of testing two such medicines X and Y to see whether either reduce reaction times and whether X and Y differ in their effect on reaction time. The method to be used is as follows. A star will be flashed on to a TV screen and the subject must then press a buzzer. The time between these events will be used as reaction time. One student will need to activate the star but the subsequent measurement is automatic.
The students are planning their experiment for which three weekly practicals are available. The drug needs to be taken an hour before testing and its effect can last up to three hours.
Caroline: We all take X this week and then measure ourselves and we do Y next week.
Emma: That’s no good, we need to know what our reaction times are normally.
Barry: OK so we all take nothing this week , then next week you all take X and I measure and the week after you all take Y and I measure.
Dave: That’s not fair. I want a turn at deciding when to set the star
Barry: OK, me this week then you next week and me for the last week
Anne : That is stupid. We will then have some people doing all three tests and some only one and no base measure for Barry. I can see no reason why any of us cannot set the star even if we have taken cough mixture. The reaction time is between the star and the buzzer not our initiating the star. We can all do all three tests and we need to organise it as a randomised block and we should do replicate tests each time and average the results.
(i)What does Anne mean? How should it be done as a randomised block? Why is this a good idea?
At this stage Finn wanders in. In a superior tone he says ‘What you actually need is to use two Latin squares.’
(ii)Is he correct that this could be done? What advantage might this have over a randomised block?
7
An experimenter wanted to test the effect of two diets (A and B) on the blood pressure of participants. This experiment would also need a control measurement of blood pressure when no change in diet was made.
The first suggested approach under consideration is as follows:
Try to find 30 willing subjects. Divide them at random into three groups.
Group 1: Blood pressure is measured after a period of 30 minutes resting.
Group 2: Follow diet A for one month, then measure blood pressure after a period of 30 minutes resting.
Group 3: Follow diet B for one month, then measure blood pressure after a period of 30 minutes resting.
A friend then suggests that a better approach would be to use a randomised block experiment using ten subjects only.
a)How would this proposed experiment be organised as a randomised block? What is the ‘block’? Where does the ‘randomising’ occur and how would you do this?
b)Considering the strengths and weaknesses of both approaches, explain which approach you believe is better.
8
a)Explain the terms randomisation and replication and the reasons why they are necessary in a designed experiment.
b)Twenty (20) subjects have been randomly selected from a large population and are available to test four treatments. Due to participants’ time constraints each subject can only be used once. How would you assign the subjects to the four treatment groups?
c)A colleague suggests that it would be better to use only 10 of the subjects who are willing to undergo all four treatments, so enabling a blocked design experiment. Do you agree with him? Support your answer.
9
a)Explain the difference between a one-way ANOVA and a randomised block design. Include the model and an explanation of the differences in the models in your answer.
b)Explain why it is preferable to use a randomised block design in preference to a one-way ANOVA if it is possible.
c)Give an example of a situation where it may not be possible to use a randomised block design and thus you would have to opt for a one-way ANOVA design instead.
a)groups under (i) a completely randomised design and (ii) a randomised block design?
10
a)Explain the difference between a ‘treatment factor’ and a ‘blocking factor’. What is the purpose of using a randomised block design for an experiment rather than a completely randomised design?
b)Suppose we want to test three step exercise routines measuring ‘VO2max’ and other lung function measures. We have a class of 30 students available for the test having excluded asthmatics etc. We have three practicals on successive weeks and it would be possible to test up to 10 subjects per practical session.
State how the experiment would be organised:
- as a completely randomised design;
- as a randomised block design.
State which you would prefer giving reasons.