A researcher wishes to compare the effects of 2 fertilizers on the yield of a soybean crop. She has 20 plots of land available and she decides to use a paired experiment — using 10 pairs of plots. Thus, she will:
a. Use a table of random numbers to divide the 20 plots into 10 pairs and then, for each pair, flip a coin to assign the fertilizers to the 2 plots.
b. Subjectively divide the 20 plots into 10 pairs (making the plots within a block as similar as possible) and then, for each pair, flip a coin to assign the fertilizers to the 2 plots.
c. Use a table of random numbers to divide the 20 plots into 10 pairs and then use the table of random numbers a second time to decide upon the fertilizer to be applied to each pair.
d. Flip a coin to divide the 20 plots into 10 pairs and then, for each pair, use a table of random numbers to assign the fertilizers to the 2 plots.
e. Use a table of random numbers to assign the 2 fertilizers to the 20 plots and then use the table of random numbers a second time to place the plots into 10 pairs.
I am wondering how one could use anything but a binary choice on the pairing, answer b appears a good choice to me.
The correct answer is:
c. Use a table of random numbers to divide the 20 plots into 10 pairs and then use the table of random numbers a second time to decide upon the fertilizer to be applied to each pair.
The researcher wants to compare the effects of 2 fertilizers on the yield of a soybean crop using a paired experiment. This means that each pair of plots will be treated with a different fertilizer. To assign the fertilizers to the plots, the researcher needs to ensure that the assignment is done randomly to eliminate any bias.
Looking at the options provided:
a. Using a table of random numbers to divide the 20 plots into 10 pairs and then flipping a coin to assign the fertilizers to the plots within each pair is a valid approach. However, it is important to note that the coin flip should be unbiased, such as by using a fair coin.
b. Subjectively dividing the 20 plots into 10 pairs and then flipping a coin to assign the fertilizers would introduce bias, as the researcher may unknowingly create pairs that are not truly random.
c. Using a table of random numbers to divide the 20 plots into 10 pairs and then using the table of random numbers a second time to decide upon the fertilizer for each pair is unnecessary. The first random assignment of pairs already ensures randomness, and using the second random assignment for the fertilizer would be redundant.
d. Flipping a coin to divide the 20 plots into 10 pairs and then using a table of random numbers to assign the fertilizers to the plots within each pair is similar to option a but reverses the order of randomness. It is still a valid approach as long as the coin flip is unbiased.
e. Using a table of random numbers to assign the 2 fertilizers to the 20 plots and then using the table of random numbers a second time to place the plots into 10 pairs is not appropriate for a paired experiment. This approach would assign fertilizers randomly to individual plots, without considering the pairing structure.
Based on the above information, option a (using a table of random numbers to divide the 20 plots into 10 pairs and then flipping a coin to assign the fertilizers to the plots within each pair) would be the most appropriate method for the researcher to use.