9.6.2: Effects of a New Special Formula Fertilizer on Potato Growth
- Page ID
- 64648
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Previously we considered a study that explored the potential of three fertilizers that were designed to enhance the yield and quality of potato crops in a region of China (Xu et al. 2025). These fertilizers were compared to using no fertilizer and to using a conventional fertilizer on the crops using many measures of plant growth and yield. Some of these measures are technical in nature, so we will consider only a few selected measures. All the measures are based on computing the mean of the measures over the observed plants grown using each of the treatments.
For most of the measures the means are reported through graphs in the original paper. For our purposes here we will report numerical averages that have been approximated from the graphs. Table 9.10 shows these values for the measures of plant growth and yield. The first measure we consider is the mean plant height at the final growing stage of the crop, called the starch accumulation stage. From Table 9.10 we can observe that the mean plant height for plants with no fertilizer was 55.5cm while plants treated with the common fertilizer had a mean height of 63.3cm. Therefore, the use of the common fertilizer appears to increase the mean plant height in this stage. The three new fertilizers produced mean plant heights of 68.9cm, 72.5cm, and 71.3cm, respectively. All of these plants are larger than what was observed for the common fertilizer, but there is not much difference between the three mean values. From these results it appears that any of the specially formulated fertilizers are effective in increasing the mean plant height over using the common fertilizer or no fertilizer.
Table 9.10 Mean values for the measures of growth and yield of potato plants using different fertilizers (Xu et al. 2025). None indicates that no fertilizer was used. Common indicates that a common fertilizer was used. New 1, New 2, and New 3 indicate the three new formulations of fertilizer.
|
Measurement |
None |
Common |
New 1 |
New 2 |
New 3 |
|
Plant Height (cm) |
55.5 |
63.3 |
68.9 |
71.3 |
72.5 |
|
Stem Diameter (mm) |
15.8 |
18.2 |
19.0 |
20.7 |
18.5 |
|
Dry Weight (g) |
33.4 |
35.4 |
38.9 |
43.6 |
41.1 |
|
Yield (t per ha) |
26.8 |
44.0 |
46.8 |
59.4 |
55.4 |
The second measure we consider is the mean stem diameter at the final growing stage, which, from Table 9.10, we see for plants with no fertilizer was 15.8mm, while plants treated with the common fertilizer was 18.2mm. Therefore, the use of the common fertilizer appears to increase the mean stem diameter. The three new fertilizers produced mean stem diameters of 19.0mm, 20.7mm, and 18.5mm, respectively. Once again, all of these plants are larger than what was observed for the common fertilizer, but there is not much difference between the three mean values. From these results it appears that any of the specially formulated fertilizers are effective in increasing the mean stem diameter over using the common fertilizer or no fertilizer, though it is notable that the second fertilizer once again produces the largest mean value.
The third measure is the dry weight of the plant. The weight measure corresponds to the part of the plant that is above ground. From Table 9.10 we can observe that the mean dry weight for plants with no fertilizer was 33.4g while plants treated with the common fertilizer had a mean dry weight of 35.4g. Therefore, the use of the common fertilizer appears to increase the mean dry weight, but not to a great extent. The three new fertilizers produced dry weights of 38.9g, 43.6g, and 41.1g, respectively. Once again, all of these are larger than what was observed for the common fertilizer, but there is not much difference between these three mean values. From these results it appears that any of the specially formulated fertilizers are effective in increasing the mean dry weight over using the common fertilizer or no fertilizer, though it is notable that the second fertilizer once again produces the largest mean value, as with the two previous measures.
The last measure we will consider here is the yield measured in tons of potatoes per hectare. Plants treated with no fertilizer had a yield of 26.8 tons per hectare while the plants treated with the common fertilizer had a yield of 44.0 tons per hectare, clearly indicating that the common fertilizer increases yield considerably over not using any fertilizer. The three new fertilizers had yields of 46.8 tons per hectare, 59.4 tons per hectare, and 55.4 tons per hectare, respectively. Once again, the new fertilizers have improved yields over the common fertilizer, and the second new fertilizer shows the most improvement.
The second specialized fertilizer appears to be the best, as it outperforms all the other options for all the measures. As we shall see later in the book, one must be careful when making this type of conclusion, as many of the means are rather close. One key concept we considered earlier is the fact that the means computed here are estimating some conceptual idea about the average performance of each of the fertilizers. These estimates will have errors associated with them, and those errors must be accounted for when comparing means.