• Communications for Statistical Applications and Methods
• /
• v.28 no.3
• /
• pp.295-305
• /
• 2021

Most graphical representation methods for two-dimensional contingency tables are based on the frequencies, probabilities, association measures, and goodness-of-fit statistics. In this work, a method is proposed to represent the correlation coefficients for each of the two selected levels of the row and column variables. Using the correlation coefficients, one can obtain the vector-matrix that represents the angle corresponding to each cell. Thus, these vectors are represented as a unit circle with angles. This is called a CC plot, which is a correlation plot for a contingency table. When the CC plot is used with other graphical methods as well as statistical models, more advanced analyses including the relationship among the cells of the row or column variables could be derived.

• The Korean Journal of Ecology
• /
• v.9 no.3
• /
• pp.161-184
• /
• 1986

An experiment was made in order to analyze the growth characteristics and productivity of Zoysia japonica under control, mowing and TIBA treatment conditions at the experimental farm of Kyung Hee univ. from May 26 to Oct. 1 in 1985. The field was planned by the randomized block design method and each treatment was given to three plots (2${\times}$2, 4${\times}$4 and 10${\times}$10 cm) and was replicated three times. Each plot was 1$m^2$ for Zoysia japonica. The sampling of each plot was taken once a week after sowing. In order to know the dry matter of total standing crops, kept 9$0^{\circ}C$ and weighted each organ of the plants. Total leaf area of a plant was measured by drawing method. The author adopted the growth analysis of English School. The increasing rates of numbers of leaf and stem were remarkably high in each plot between 10th and 12th weak after sowing and it was highest in TIBA treated plot. The increasin rate of leaf area in each plot was remarkably high beween 10th and 12th week and the maximum value of leaf area was 274.00c$m^2$ in TIBA treated plot of 100 plants/$m^2$. The increasing rate of standing crop was remarkably high between 10th and 12th week and the high increasing tendency in TIBA plot resulted from TIBA. The positive correlationship was founded between standing crop and leaf area. The evaporation rather than temperature acted as a main factor of negative correlation with standing crop during the experiment period. Solar radiation had a high positive correlation in the lower density of plot. C/F ratio was low, during the growth period, from 10th to 12th week after sowing and was low in the higher density under each treated plot. T/R ratio was not constant during the sampling period but was high in the lower density. The increasing rates of RGR and NAR were high between 11th and 12th week after sowing. Leaf area ratio was high in higher density in each plot and not constant in all treated plot.

• The Bulletin of The Korean Astronomical Society
• /
• v.39 no.1
• /
• pp.59.2-59.2
• /
• 2014

Radiative transfer models in a spherical, turbulent interstellar medium (ISM), in which the photon source is situated at the center, are calculated to investigate the correlation between the scattered light and the dust column density. The medium is modeled using fractional Brownian motion structures that are appropriate for turbulent ISM. The correlation plot between the scattered light and optical depth shows substantial scatter and deviation from simple proportionality. It was also found that the overall density contrast is smoothed out in scattered light. In other words, there is an enhancement of the dust-scattered flux in low-density regions, while the scattered flux is suppressed in high-density regions. The correlation becomes less significant as the scattering becomes closer to being isotropic and the medium becomes more turbulent. Therefore, the scattered light observed in near-infrared wavelengths would show much weaker correlation than the observations in optical and ultraviolet wavelengths. We also find that the correlation plot between scattered lights at two different wavelengths shows a tighter correlation than that of the scattered light versus the optical depth.

• Journal of Korea Water Resources Association
• /
• v.47 no.2
• /
• pp.161-170
• /
• 2014

It is important to estimate an appropriate quantile for design of hydraulic structure. For this purpose, it is necessary to find the appropriate probability distribution which can represent the sample data well. Probability plot correlation coefficient test as one of goodness-of-fit test, is recently developed and has been known as a simple and powerful method. In this study, probability plot correlation coefficient test statistics using the plotting position considering the coefficients of skewness for the GEV distribution is derived, and represented by the regression equation. Monte-Carlo method is also performed to compare the rejection power between each method. As the results, the probability plot correlation coefficient test which is derived in this study is better than the others. In particular, when sample size is small and distribution has the shape parameter, rejection power of probability plot correlation coefficient test considering the coefficients of skewness is bigger than the others.

• Applied Biological Chemistry
• /
• v.16 no.2
• /
• pp.99-111
• /
• 1973

Percentage recovery or fertilizer nitrogen, phosphorus and potassium by rice plant(Oriza sativa L.) were investigated at 8, 10, 12, 14 kg/10a of N, 6 kg of $P_2O_5$ and 8 kg of $K_2O$ application level in 1967 (51 places) and 1968 (32 places). Two types of nutrient contribution for the yield, that is, P type in which phosphorus firstly increases silicate uptake and secondly silicate increases nitrogen uptake, and K type in which potassium firstly increases P uptake and secondly P increases nitrogen uptake were postulated according to the following results from the correlation analyses (linear) between percentage recovery of fertilizer nutrient and grain or dry matter yields and nutrient uptake. 1. Percentage frequency of minus or zero recovery occurrence was 4% in nitrogen, 48% in phosphorus and 38% in potassium. The frequency distribution of percentage recovery appeared as a normal distribution curve with maximum at 30 to 40 recovery class in nitrogen, but appeared as a show distribution with maximum at below zero class in phosphorus and potassium. 2. Percentage recovery (including only above zero) was 33 in N (above 10kg/10a), 27 in P, 40 in K in 1967 and 40 in N, 20 in P, 46 in Kin 1968. Mean percentage recovery of two years including zero for zero or below zero was 33 in N, 13 in P and 27 in K. 3. Standard deviation of percentage recovery was greater than percentage recovery in P and K and annual variation of CV (coefficient of variation) was greatest in P. 4. The frequency of significant correlation between percentage recovery and grain or dry matter yield was highest in N and lowest in P. Percentage recovery of nitrogen at 10 kg level has significant correlation only with percentage recovery of P in 1967 and only with that of potassium in 1968. 5. The correlation between percentage recovery and dry matter yield of all treatments showed only significant in P in 1967, and only significant in K in 1968, Negative correlation coefficients between percentage recovery and grain or dry matter yield of no or minus fertilizer plots were shown only in K in 1967 and only in P in 1968 indicating that phosphorus fertilizer gave a distinct positive role in 1967 but somewhat' negative role in 1968 while potassium fertilizer worked positively in 1968 but somewhat negatively in 1967. 6. The correlation between percentage recovery of nutrient and grain yield showed similar tendency as with dry matter yield but lower coefficients. Thus the role of nutrients was more precisely expressed through dry matter yield. 7. Percentage recovery of N very frequently had significant correlation with nitrogen uptake of nitrogen applied plot, and significant negative correlation with nitrogen uptake of minus nitrogen plot, and less frequently had significant correlation with P, K and Si uptake of nitrogen applied plot. 8. Percentage recovery of P had significant correlation with Si uptake of all treatments and with N uptake of all treatments except minus phosphorus plot in 1967 indicating that phosphorus application firstly increases Si uptake and secondly silicate increases nitrogen uptake. Percentage recovery of P also frequently had significant correlation with P or K uptake of nitrogen applied plot. 9. Percentage recovery of K had significant correlation with P uptake of all treatments, N uptake of all treatments except minus phosphorus plot, and significant negative correlation with K uptake of minus K plot and with Si uptake of no fertilizer plot or the highest N applied plot in 1968, and negative correlation coefficient with P uptake of no fertilizer or minus nutrient plot in 1967. Percentage recovery of K had higher correlation coefficients with dry matter yield or grain yield than with K uptake. The above facts suggest that K application firstly increases P uptake and secondly phosphorus increases nitrogen uptake for dry matter yied. 10. Percentage recovery of N had significant higher correlation coefficient with grain yield or dry matter yield of minus K plot than with those of minus phosphorus plot, and had higher with those of fertilizer plot than with those of minus K plot. Similar tendency was observed between N uptake and percentage recovery of N among the above treatments. Percentage recovery of K had negative correlation coefficient with grain or-dry matter yield of no fertilizer plot or minus nutrient plot. These facts reveal that phosphorus increases nitrogen uptake and when phosphorus or nitrogen is insufficient potassium competatively inhibits nitrogen uptake. 11. Percentage recovery of N, Pand K had significant negative correlation with relative dry matter yield of minus phosphorus plot (yield of minus plot x 100/yield of complete plot; in 1967 and with relative grain yield of minus K plot in 1968. These results suggest that phosphorus affects tillering or vegetative phase more while potassium affects grain formation or Reproductive phase more, and that clearly show the annual difference of P and K fertilizer effect according to the weather. 12. The correlation between percentage recovery of fertilizer and the relative yield of minus nutrient plat or that of no fertilizer plot to that of minus nutrient plot indicated that nitrogen is the most effective factor for the production even in the minus P or K plot. 13. From the above facts it could be concluded that about 40 to 50 percen of paddy fields do rot require P or K fertilizer and even in the case of need the application amount should be greatly different according to field and weather of the year, especially in phosphorus.

• Bulletin of the Korean Chemical Society
• /
• v.34 no.8
• /
• pp.2455-2460
• /
• 2013

Second-order rate constants ($k_N$) have been measured spectrophotometrically for the nucleophilic displacement reactions of 4-nitrophenyl X-substituted-cinnamates (4a-4e) and Y-substituted-phenyl cinnamates (5a-5e) with Z-substituted-phenoxide anions in 80 mol % $H_2O$/20 mol % DMSO at $25.0{\pm}0.1^{\circ}C$. The Hammett plot for the reactions of 4a-4e with 4-chlorophenoxide (4-$ClPhO^-$) consists of two intersecting straight lines, which might be taken as a change in the rate-determining step (RDS). However, it has been concluded that the nonlinear Hammett plot is not due to a change in the RDS but is caused by stabilization of the ground state of substrates possessing an electron-withdrawing group in the cinnamoyl moiety through resonance interactions, since the Yukawa-Tsuno plot exhibits an excellent linear correlation with ${\rho}X=0.89$ and r = 0.58. The Br${\o}$nsted-type plot for the reactions of 4-nitrophenyl cinnamate (4c) with Z-substituted-phenoxides is linear with ${\beta}_{nuc}=0.76$. The Br${\o}$nsted-type plot for the reactions of Y-substituted-phenyl cinnamates (5a-5d) with 4-chlorophenoxides (4-$ClPhO^-$) is also linear with ${\beta}_{lg}=-0.72$. The Hammett plot correlated with ${\sigma}^-$ constants for the reactions of 5a-5d results in a much better linear correlation than that correlated with ${\sigma}^o$ constants, indicating that a partial negative charge develops on the O atom of the leaving aryloxide. Thus, the reactions have been concluded to proceed through a concerted mechanism.

• Bulletin of the Korean Chemical Society
• /
• v.29 no.4
• /
• pp.767-771
• /
• 2008

Second-order rate constants have been measured spectrophotometrically for the Michael-type reaction of 1-(Xsubstituted phenyl)-2-propyn-1-ones (2a-f) with amines in $H_2O$ at 25.0 ${\pm}$ 0.1 ${^{\circ}C}$. A linear Brønsted-type plot is obtained with ${\beta}_{nuc}$ = 0.25 ${\pm}$ 0.02, a typical $\beta_{nuc}$ value for reactions which proceed through a stepwise mechanism with attack of amine on the electrophilic center being the rate-determining step. Secondary alicyclic amines are found to be more reactive than isobasic primary amines. The Hammett plot for the reactions of 2a-f with morpholine is not linear, i.e., the substrate with a strong electron-donating group (e.g., 4-MeO) exhibits a negative deviation from the Hammett plot. However, the Yukawa-Tsuno plot for the same reactions exhibits an excellent linear correlation with ρ = 0.62 and r = 0.82. Thus, it has been proposed that the nonlinear Hammett plot is not due to a change in the ra te-determining step but due to ground-state stabilization through resonance interactions.

• Communications for Statistical Applications and Methods
• /
• v.11 no.2
• /
• pp.345-353
• /
• 2004

Graphical methods for the specification of the curvature as a function of two predictors are animated to see the effect of an added variable to the model. Through a 3D animated plot it might be difficult to find a sequence of interpretable plots. But examples demonstrate that useful information can be obtained by using rotation technique in 3D plot. Besides 3D plots, an example of 2D animated plot applied to the case of high correlation between predictors and an added predictor is also given. It implies that speed of the convergence to a certain image in a dynamic plot may be understood as an influence of collinearity.

• Publications of The Korean Astronomical Society
• /
• v.21 no.2
• /
• pp.27-33
• /
• 2006

Infrared color-color diagram of 10 giant molecular clouds are examined to explore the dust property from the COBE Diffuse Infrared Background Experiment of the 100, 140, and $240{\mu}m$ emission. Four of them, Taurus, Mon OB1, Gem OB1, and Chameleon, show the anti-correlation in $R_{100/140}-R_{140/240}$ plot and the horizontal distribution in $R_{100/240}-R_{140/240}$ plot, which disagree with those of theoretical calculation. These could be explained by the depletion of $100{\mu}m$ and the excess of $140{\mu}m$ emission, though no existing dust model could support them. Mean color temperature of the anti-correlation region appears to be lower than that of the linear region, whose temperatures are 15.3, 17.0 K, respectively. And the linear region shows large dispersion in the plot of intensity relation. Both imply that a star formation would be more active, but not homogeneous, in the linear region compared to the anti-correlation region.

• Bulletin of the Korean Chemical Society
• /
• v.34 no.7
• /
• pp.2001-2005
• /
• 2013

The second-order rate constants ($k_{OH^-}$) for the reactions of Y-substituted-phenyl diphenylphosphinates (4a-4i) with $OH^-$ in $H_2O$ at $25.0{\pm}0.1^{\circ}C$ have been measured spectrophotometrically. Comparison of $k_{OH^-}$ with $k_{EtO^-}$ (the second-order rate constants for the corresponding reactions with $EtO^-$ in ethanol) has revealed that $EtO^-$ is less reactive than $OH^-$ although the former is ca. 3.4 $pK_a$ units more basic than the latter, indicating that the reactivity of these nucleophiles is not governed by their basicity alone. The Br${\o}$nsted-type plot for the reactions of 4a-4i with $OH^-$ is linear with ${\beta}_{lg}$ = -0.36. The Hammett plot correlated with ${\sigma}^-$ constants results in a slightly better correlation than that correlated with ${\sigma}^{\circ}$ constants but exhibits many scattered points. In contrast, the Yukawa-Tsuno plot for the same reactions exhibits an excellent linear correlation with ${\rho}$ = 0.95 and r = 0.55. The r value of 0.55 implies that a negative charge develops partially on the O atom of the leaving group. Thus, the reactions of 4a-4i with $OH^-$ have been concluded to proceed through a concerted mechanism.