STA 3024 Test1 Spring, 2000 Name____________________________

Due: March 2

This is a Test. Do your own work. If you have any questions, ask ME.

(7) 1. Seven plots are randomly selected at a research station. On each plot, three species of grass are planted, the locations randomly selected within the plot. The response is the biomass grown after 5 months.

a) What design is this. RBD b) Give Source and d.f. in ANOVA table, using specific names and numbers. Species: 2 Plots: 6 Error: 12

c) Would you use this design if the seven plots were located in seven different states? Why or why not? No, because the blocks might be so different that a treatment x block interaction might occur, contrary to an assumption of the RBD.

  1. 2. Give an example from your field of a factorial design with two factors. Identify the response, factors, levels, experimental units. Make sure it is an experiment, not an observational study. Remember to allow for replication.
  1. 3. Give an example from your field (identify response, factor) in which it would be difficult to do an experimental study. State and advantage and a disadvantage of observational studies, compared to experimental studies. Adv: can be more realistic and won't violate ethical principles; Dis: difficult to prove cause-effect relationship, since "treatments" are just attributes of the observed units.
  1. 4. Give two possible benefits obtained by transforming the response variable. Describe the difference between assumptions and hypotheses in statistics. Get better agreement with assumptions. Assumptions are the statistical conditions needed for the statistical inferences to be exactly correct.

Hypotheses are statements about the unknown parameters which are to be supported or contradicted by the statistical inference.
  1. 5. Suppose you have a CRD with four treatments, six replications per treatment. a)Give the source and d.f. in the ANOVA table. b) Give two hypotheses you can test using Tukey’s procedure. c) How many experimental units do you need? d) How will you decide which experimental units get assigned to the four treatments? Justify your answer.

a) Treatments 3 b) m 1 = m 2 and m 1 = m 3, where m I is the mean for treatment i.

Error 20 c) 6x4 = 24. d) randomly assign replicates to treatments, in order to guard against bias caused by variable experimental units.
  1. 6. In a RBD, the following was printed out: Source SS d.f. MS

Treatments 500 4 150

Blocks 700 7 100

Residual 700 28 25

The treatments were five levels of temperature and the response was the % of turtle eggs which hatched females. The blocks were locations at which the experiment was done.

State the hypothesis tested in this design. The mean % female eggs is the same at all five temperatures. Obtain an F ratio and the p-value. F = 150/25 = 6; p < 0.01.

What can you tell your boss at this point? The mean % female eggs is not the same at all temperatures.

Calculate the Estimated Relative Efficiency of this RBD relative to a CRD. ERE = 1.54.

Interpret this efficiency estimate in non-technical terms for a person who says, "What does this number mean?" You would need roughly 54% more observations when using a CRD to get the same precision as this RBD.

  1. 7. Draw a normal plot (label axes) which suggests that the experimenter should try a log transformation. Plot curves smoothly to the right in the upper part. Axes are labeled normal scores (vert) and residual (horiz)

Draw a plot of residuals which suggests that the errors are correlated (label axes.) The residual are plotted in order of time. A systematic pattern appears over at least part of the data, e.g. a trend, bowl, or snake. The vertical axis is labeled Residual; the horizontal, Order of observations.