vested

RShiny application implementing virtual experiments for teaching experimental design

Link to vested here

Students are typically introduced to experimental design via textbook examples; statistical analysis is carried out on already collected, wrangled, and cleaned data. A virtual setting is a cost- and hassle-free way to emulate a real-world experiment. The vested Rshiny application implements three virtual experiments: Country Pumpkin, Chook eggsperiment, and Head Tomato

The Country Pumpkin experiment

Background given

Two farmers, Esther and Gwenllian, grow pumpkins in Pukekohe for the farmer's market. After several years, Esther clearly gets higher yields than Gwenllian. But why? Several factors—variety, heat, and light—differ in cultivation methods. Farmer Esther is conservative; she uses natural heating, ambient lighting, and a variety of pumpkin called Kumi Kumi, whilst Gwenllian uses supplementary heating, controlled lighting, and a variety called Buttercup. Can you design a two-stage experiment and, based on the results, decide which combination of the three factors of heat, light, and variety give the highest pumpkin yield?

Due to funding cuts, you only have a small greenhouse to carry out this experiment. The greenhouse has six north facing plots and six south-facing. Your colleague tells you that from previous experiments in the greenhouse there are known to be a substantial difference in yields between the two sides of the greenhouse.

Example questions to ask

• What treatments do you plan to apply to each plot in the first-stage, and why?
• How did the results from the first-stage inform your choices in the second?
• Which combination, of heat, light, and variety, do you believe gives the maximal yield?

References

Pollock, K., Ross-Parker, H., & Mead, R. (1979). A Sequence of Games Useful in Teaching Experimental Design to Agriculture Students. The American Statistician, 33(2), 70--76.

The Chook eggsperiment

Background given

You have been employed by the University's Poultry Research Farm to look into how pullets respond to the amount of copper added to basic diets of either wheat or maize. You need to determine the optimum amount of copper to add to their diets to improve their growth rate.

You are told that 150 units of copper added to either diet seems to improve growth. It is also known that there is a level of copper beyond which toxic effects will reduce the growth rate. So what is the optimum amount to add?

At your disposal, you have 32 cages that each contain 16 chicks. In addition to the amount of copper in their diet, other factors may influence the growth rate of chicks (e.g., brooder, tier position within the henhouse, etc.). You should take these into consideration whilst designing your experiment.

Example questions to ask

• What quantity of copper must be added to a maize diet to give maximum growth rate?
• What quantity of copper must be added to a wheat diet to give maximum growth rate?
• What is the increase in growth rate obtained for a maize diet with the best quantity of copper compared with no copper?
• What is the increase in growth rate obtained for a wheat diet with the best quantity of copper compared with no copper?
• Which diet responds more to copper? (i.e., which diet gives the larger increase in growth rate when copper is added at its best level, compared with no added copper?)

References

Pollock, K., Ross-Parker, H., & Mead, R. (1979). A Sequence of Games Useful in Teaching Experimental Design to Agriculture Students. The American Statistician, 33(2), 70--76.

Mead, R., & Freeman, K. (1973). An Experiment Game. Journal of the Royal Statistical Society. Series C (Applied Statistics), 22(1), 1--6.

The Head Tomato experiment

Background given

Your family owns a tomato farm and has done for generations. Yields are down, money's tight, and the farm is at risk of bankruptcy. However, there is rumour of some fertilizer recipe handed down from your great-great-grandmother that will maximise the yield of tomatoes. But, the exact recipe has been lost. You know the recipe involves horse manure, but have no clue as to the optimal amount? To save your family's farm you must find the optimal dose of fertiliser that produces the maximum average biomass of tomatoes.

The greenhouse you will use to answer this question is bordered left and right with heating strips and is lighted by artificial light: the floor pattern illustrates the light intensity pattern that will be experienced by the plants. You are already aware that heat and light affect plant growth. Design an experiment to find the optimal dose of manure in the fertiliser to maximise tomato yield. Your father has given you twelve trays of twelve seedlings you can use in your experiment (you do not have to use them all). You have four different recipes to test.

Example questions to ask

• How did you incorporate the three key principles of experimental design into your experiment?
• What are the optimal conditions for tomato yield?

References

Darius, P., Portier, K., & Schrevens, E. (2007). Virtual Experiments and Their Use in Teaching Experimental Design. International Statistical Review / Revue Internationale De Statistique, 75(3), 281--294.