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(Five parts; 12 marks in total): A study was conducted to test the effect of fertilizer...

  1. (Five parts; 12 marks in total): A study was conducted to test the effect of fertilizer and irrigation on tomato crop yield. Two types of fertilizers (Fertilizer A and Fertilizer B) and five levels of irrigation (100, 150, 200, 250, and 300 mm) were applied. For each combination of these factors, 5 replicate plots of tomatoes of the same variety were grown, making a total of 50 plots. The plots in the field were assigned randomly and independently to the combinations of treatments. When the crop matured, the yield of tomatoes in each plot was recorded in kg/m2.

    (a) (1 mark) Identify the study units.
    (b) (3 marks) What is/are the explanatory variable(s) or factor(s)? State the type of data scale used (e.g.,

    categorical, ordinal, etc.) for recording the explanatory variable(s).
    (c) (2 marks) What is/are the response variable(s)? State the type of data scale used (e.g., categorical,

    ordinal, etc.) for recording the response variable(s).
    (d) (2 marks) Is this an observational or experimental study? Very briefly explain your answer.
    (e) (4 marks) Based on this study, will it be possible to make either population inferences or causal

    inferences or both? Briefly explain your answer.

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Answer #1

(a) The study units= plot in the field

(b) Factors: There are two factors: 1. fertilizer 2. irrigation.

The type of data scale used for recording the fertilizer is nominal and the type of data scale used for recording the irrigation is ordinal.

(c) Response variable=The yield of tomatoes in each plot and it measured in ratio scale and unit is kg/m2.

(d) It is experimental study since here researcher introduces an intervention (i.e. two types of fertilizers and five levels of irrigation) and study the effects.

(e) Based on this study, it will be possible to make population inferences and causal inferences both.

This is a two way ANOVA with 5 observations in each cell. From the output, we can draw interaction plot, to see that whether there is any interaction between fertilizer and irrigation and using sample statistic and other relevant bar diagrams we can draw casual inference and through ANOVA test and t-tests (if required) we can draw population inference.

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