First Difference Method Research Articles

Performances of different yield-detrending methods in assessing the impacts of agricultural drought and flooding: A case study in the middle-and-lower reach of the Yangtze River, China

In evaluating the impacts of drought and flooding disasters on crop yields, accurately calculating meteorological yield (i.e., detrended yield) is an important procedure. The present work aimed to compare various yield-detrending methods in terms of characterizing the regression relationships between meteorological yield and the intensities of drought and flooding. Taking the middle-and-lower reach of the Yangtze River (MLRYR) as the study region, the intensities of drought and flooding during the growing seasons of four study crops (cotton, oilseed rape, wheat, and maize) were quantified using the standardized precipitation evapotranspiration index. Nine popular yield-detrending methods and the first-difference method were employed to determine meteorological yields. The results indicated that the examined methods consistently identified the cases with very significant yield-reducing impacts of drought and flooding. The first-difference method identified 58 significant regression relationships, outperforming the yield-detrending methods (identifying 39–44 significant regression relationships). The 20-yr moving average and the linear fitting methods performed best at the provincial level, while the cubic smoothing spline and the quadratic polynomial fitting methods performed best at the district level. Based on these best-performing methods, the average method was proposed and exhibited wider applicability and better performance than the individual methods. In terms of meteorological yield losses, cotton was the most affected crop (35% of all districts experienced severe cotton yield loss) and Anhui was the most affected region (with an average crop yield loss of 14.06%). The yield-reducing impact of flooding was significant in 41 districts; in comparison, the impact of drought was significant only in 7 districts. Additionally, oilseed rape was the crop most affected by drought and flooding. These results can provide guidance for assessing agricultural drought and flooding disasters under climate change.

Changes in vegetation in China's drylands are closely related to afforestation compared with climate change

The response of vegetation to climate change and human activities has attracted considerable attention. However, quantitative studies on the effects of climate change and human activities on dryland vegetation in different seasons remain unclear. This study investigated the impacts of precipitation, temperature, soil water storage (SWS) (top [0–7 cm], shallow [7–28 cm], and middle [28–100 cm] layers), vapor pressure deficit (VPD), and afforestation on vegetation as well as their relative contribution rates during the rainy season ([RS], June to September), dry season ([DS], November to April), transition season ([TS], May and October), and all year period (AY) in China's drylands from 2001 to 2020 using the first-difference method. Areas with precipitation and SWS showing significant positive correlation with dryland vegetation (p < 0.05) were found to be larger in RS than in DS and TS, and the positive effect of SWS increased with soil depth in the 0–28 cm interval. Increasing VPD induced a significant negative effect on vgetation during RS but it was not predominant in DS and TS. Afforestation showed an extremely significant positive correlated with dryland vegetation across >60 % of China's dryland areas (p < 0.01), but this improvement was found to be limited to regions with the highest afforestation area. Moreover, dryland vegetation dynamics were driven by afforestation in all seasons, with contribution rates of 64.23 %–71.46 %. The effects of SWS and VPD on vegetation driven by precipitation and temperature exceeded the direct effects of precipitation and temperature. Among climatic factors, VPD showed a major regulating effect on dryland vegetation at the top and shallow soil layers in almost all seasons, whereas the relative contribution rate of SWS increased with soil layer. The findings can provide a scientific reference for the sustainable development and protection of drylands under global warming.

Soil moisture content-based analysis of terrestrial ecosystems in China: Water use efficiency of vegetation systems

Water is a prerequisite for the formation of earth-biochemical-ecological systems. Differences in the spatial and temporal distribution of water resources are important factors in the formation of differences in the distribution of vegetation in terrestrial ecosystems and are key to the differences in vegetation productivity. Vegetation water use efficiency is calculated by the total amount of fixed biogenic carbon per unit mass of water consumed in photosynthesis and can be used to assess the intensity and capacity of an ecosystem to use water biomass. Based on remote satellite sensing data, this study proposes a new water use efficiency assessment model. The model was validated using flux site data, and we analyzed the relative contribution of climate factors to soil moisture use efficiency using a first-difference method. The results revealed the following: (1) The soil moisture use efficiencies (SUE) of remote sensing data inversions that were evaluated using flux site data based on correlation coefficients and Nash coefficients showed high reliability, and only the NMG (Inner Mongolia) station showed low correlation among the nine sites. (2) Among the nine agricultural sub-regions in China, only the SUE of the Qinghai-Tibet Plateau region showed a decreasing trend (−1.08 g C/m−2 kg H2O yr), while all other regions showed an increasing trend. (3) The highest vegetation soil moisture use efficiency (1.83 g C/m−2 kg H2O) was found in ferralisols, while the lowest vegetation SUE (0.17 g C/m−2 kg H2O) was found in arid soils. The SUE of different vegetation types showed the characteristics of forest > scrub > cultivated vegetation > wetland > grassland. (4) The relative contribution of gross primary productivity (GPP) to the change in SUE was 37.53%, while the relative contribution of soil moisture content to the change in SUE was −26.71%. Among the five climatic factors, temperature was the most dominant factor affecting the change in SUE, followed by precipitation, net radiation, leaf area index, and potential evapotranspiration. Revealing the relationship between terrestrial ecosystem GPP, soil moisture content, and their responses to climate factors is a prerequisite for understanding the adaptation strategies of regional terrestrial ecosystems to global climate change, which can help to inform decision-making for the sustainable development of ecosystems.

Does decentralisation turn minority parties into secessionists? Insights from Eastern and Western Europe

Whereas Western European governments have devolved political authority to minority regions, governments in Eastern Europe have shied away from using decentralisation to accommodate national minorities. This article assesses how these differences affect the secessionism of minority parties. The theoretical section argues that both programmatic accommodation (i.e. when governments adopt positions in favour of decentralisation) and institutional accommodation (i.e. when governments create regions that correspond to the settlement areas of minority groups and transfer authority to the regional level) increase the likelihood that minority parties will adopt secessionist positions. Regression analyses of 83 European minority parties show that a higher level of programmatic and institutional accommodation is indeed associated with a higher likelihood of secessionism. However, increases in programmatic accommodation between 2011 and 2017 in fact decrease the likelihood that minority parties turn secessionist when using the method of first differences. Future research should therefore collect panel data on minority parties’ positions.

Modelling the impacts of climate change and crop management measures on soybean phenology in China

Climate change and crop management measures affect crop growth. But their combined and relative impacts on soybean phenology are still not clear. Based on the first-difference method, we discriminated and quantified the impacts of climate change and crop management measures on soybean phenology using observational data from 51 agro-meteorological stations in China’s major soybean planting areas from 1992 to 2011. Results showed that (1) vegetative, reproductive and whole growth periods of northern spring soybean were shortened whereas those of summer soybean were prolonged. Reproductive and whole growth periods of southern spring soybean were also prolonged. (2) Climate change independently prolonged the vegetative growth periods of northern spring soybean, summer soybean, and southern spring soybean by 0.3, 0.52, and 0.3 days/decade, respectively, and shortened the whole growth periods by 1.43, 0.74, and 6.3 days/decade, respectively. Increasing temperature advanced the soybean phenology and shortened key growth stages. (3) Crop management measures contributed more to the observed trends of phenology and growth stages than climate change. Temperature and sunshine duration dominated the impact of climate change on soybean phenology and growth stages. (4) Shifting sowing date and selecting soybean cultivars with high temperature resistance, high thermal requirements and long growth periods are effective strategies to adapt to climate change. The findings could contribute to providing appropriate adaptation and mitigation strategies to facilitate sustainable soybean production.

Asymmetric Fixed-effects Models for Panel Data

Standard fixed-effects methods presume that effects of variables are symmetric: The effect of increasing a variable is the same as the effect of decreasing that variable but in the opposite direction. This is implausible for many social phenomena. York and Light showed how to estimate asymmetric models by estimating first-difference regressions in which the difference scores for the predictors are decomposed into positive and negative changes. In this article, I show that there are several aspects of their method that need improvement. I also develop a data-generating model that justifies the first-difference method but can be applied in more general settings. In particular, it can be used to construct asymmetric logistic regression models.

Healthcare-Seeking Behavior and Out-of-Pocket Payments in Rural Bangladesh: A Cross-Sectional Analysis

This study investigates the determinants of patient’s choice of treatment (i.e., modern vs. alternative healthcare) using Bangladesh’s Household Income and Expenditure Survey (HIES) dataset for exploring their healthcare-seeking behavior and the extent of out-of-pocket (OOP) payment due to illnesses. It explores this issues using the descriptive statistics, bivariate analysis like analysis of variance (ANOVA) and Chi-square test as well as econometric modeling (probit regression model on modern healthcare utilization for the full sample as well as for each quintile). All these help to identify the determinants of healthcare-seeking behavior in rural Bangladesh and how these vary across the quintiles of expenditure on food consumption. This study finds that higher percentage of healthcare-seeking patients receives alternative healthcare because of the lower cost and easier access compared to modern healthcare. The marginal effects of the predisposing factors like patient’s age, parent’s literacy, mother’s age, house with separate dining room, access to electricity and mobile are significantly positive, which means these are more likely to influence modern healthcare utilization. In contrast, the marginal effects of the enabling factors like income, landholdings, access to social benefit are positive, but insignificant. Therefore, predisposing factors rather than enabling factors play crucial role in determining choice of modern treatment in rural Bangladesh. In addition, variations in the marginal effects exist across different groups based on regression by quintile. Finally, sickness prevalence as well as modern healthcare utilization also varies across geographic regions. The average OOP payment is higher for modern healthcare compared to alternative one and it remains true after disaggregation of OOP expenditure. Disease-specific OOP using first-difference method is also positive for all diseases (i.e., OOP expenditure for modern healthcare> OOP expenditure for alternative healthcare) and most of the first-difference estimates are statistically significant. Similar tendencies are also observed in case of applying distributional analysis using quintiles. All these are important for formulating a national health policy for the rural people in Bangladesh. At last, a special attention to expanding utilization of modern healthcare is required for young mothers, elderly household head and the patients belong to minority group in rural Bangladesh.

Associations of Emergency Department Length of Stay With Publicly Reported Quality-of-care Measures.

The Institute of Medicine identified emergency department (ED) crowding as a critical threat to patient safety. We assess the association between changes in publicly reported ED length of stay (LOS) and changes in quality-of-care measures in a national cohort of hospitals. Longitudinal analysis of 2012 and 2013 data from the American Hospital Association (AHA) Survey, Center for Medicare and Medicaid Services (CMS) Cost Reports, and CMS Hospital Compare. We included hospitals reporting Hospital Compare timeliness measure of LOS for admitted patients. We used AHA and CMS data to incorporate hospital predictors of interest. We used the method of first differences to test for relationships in the change over time between timeliness measures and six hospital-level measures. The cohort consisted of 2,619 hospitals. Each additional hour of ED LOS was associated with a 0.7% decrease in proportion of patients giving a top satisfaction rating, a 0.7% decrease in proportion of patients who would "definitely recommend" the hospital, and a 6-minute increase in time to pain management for long bone fracture (p<0.01 for all). A 1-hour increase in ED LOS is associated with a 44% increase in the odds of having an increase in left without being seen (95% confidence interval=25% to 68%). ED LOS was not associated with hospital readmissions (p=0.14) or time to percutaneous coronary intervention (p=0.14). In this longitudinal study of hospitals across the United States, improvements in ED timeliness measures are associated with improvements in the patient experience.

Social capital and homophily both matter for labor market outcomes – evidence from replication and extension

Social resource theory has been challenged, as the effects of contact resources on job outcomes may be spurious given the presence of homophily. We review the Mouw–Lin debate and propose that occupational homophily moderates the role of contact resources in the labor market and that effects of resources depend on labor market institutions. We analyze data from the US, East Germany before 1989, and post-reform China, combining the first-difference method and Heckman selection procedure to deal with endogeneity. Empirical findings from different labor market contexts demonstrate that: (1) contact resources have a causal and positive role in job outcomes; (2) in a market economy, the role of resources is more salient if they provide within-occupation job-leads; (3) under state job-assignment systems occupational homophily does not pay off; and (4) job-search ties can take the form of heterophilous selection.

Fertilization regulates the response of wheat yield to interannual temperature variation in North China

Aims Understanding the effect of long-term fertilization on the sensitivity of grain yield to temperature changes is critical for accurately assessing the impact of global warming on crop production. In this study, we aim to assess the impacts of temperature changes on grain yields of winter wheat (Triticum aestivum L.) under different fertilization treatments in a long-term manipulative experiment in North China. Methods We measured grain yields of winter wheat under four fertilization treatments at the Yucheng Comprehensive Experimental Station each year from 1993 to 2012. We also measured air temperature at 0200, 0800, 1400 and 2000 h each day since 1 January 1980. We then used the first-difference method and simple linear regression models to examine the relationship of crop yield changes to mean air temperature, mean daytime and nighttime air temperature in crop growing seasons. Important Findings We found that increases in mean daily temperature, mean daytime temperature and mean nighttime temperature each had a positive impact on the grain yield of winter wheat. Grain yield increased by 16.7-85.6% for winter wheat in response to a 1 degrees C increase in growing season mean daily temperature. Winter wheat yield was more sensitive to variations of nighttime temperature than to that of daytime temperature. The observed temperature impacts also varied across different fertilization treatments. Balanced fertilization significantly enhanced grain yields for winter wheat under a warming climate. Wheat plots treated with nitrogen and phosphorous balanced fertilization (NPK- and NP-treated plots) were more responsive to temperature changes than those without. This report provides direct evidence of how temperature change impacts grain yields under different fertilization treatments, which is useful for crop management in a changing global climate.

Teacher Characteristics and Student Achievements in TIMSS - Findings Gained from Applying the 'First-Difference' Method to TIMSS-2007 Data

The advantage of Trends in International Mathematics and Science Study is that not only does it perform a direct cognitive assessment of students concerning these students' teachers, but also their education, work experience and the instructional strategies used in their classes. In order to estimate teachers’ characteristics effects on a student’s achievements and overcome the limits of the TIMSS' correlational design, we have employed the first-difference method. Teachers’ characteristics effects have also been measured with the usual regression method. The effects discovered varied from one subject field to another, and there has been a difference between the results gained by using the first-difference method and OLS regression analysis model. The first-difference method has revealed a negative effect of reproductive tasks and group work in math class, whereas comprehension tasks and tasks for developing meta-cognitive skills have shown a positive effect. On the contrary, reproductive tasks for science classes have had a positive effect while comprehension tasks and tasks for developing meta-cognitive skills have had either none or negative effects. Apart from this, a teacher's experience has had a significant effect on natural science subjects as opposed to mathematics. The possible interpretations of these results are discussed in this paper.

INNOVATIVE BUT INSUFFICIENT? A RESPONSE TO GRAHAM'S COMMENTARY ON ‘ALCOHOL, SUPPRESSED ANGER AND VIOLENCE’

We wish to thank Kate Graham for her comments [1] on our paper [2] and to respond to the issues that she raised. To recapitulate, by applying the first-difference (FD) method we submitted the alcohol–violence association to a more stringent test for causality than those used in previous survey research. Thus, using two-wave panel data from a general population study of young people, we estimated how changes in the frequency of violence correlated with changes in drinking. Further, we examined whether this correlation was contingent upon suppressed anger. The results indicated that alcohol may indeed be related causally to violence, but that the effect of drinking was confined to individuals who tend to withhold their angry feelings. Graham describes our study as innovative, but she also questions our statistical approach as well as our conclusion regarding the moderating role of suppressed anger. The major advantage of the FD-method is that it eliminates the effects of time-invariant confounders, but as Graham rightly points out, this method also has some important limitations. However, most of these limitations work in the direction of increasing the risk of type 2 error (rejecting a true hypothesis), which must be weighed against the reduced risk of type 1 error (not rejecting a false hypothesis). In his instructive methodology book, Firebaugh [3] notes that the first-difference method is conspicuously under-utilized in social science and pleads for a wider use of it. In response to some more technical queries, we wish to clarify that the log-transformation of our measures on alcohol use and violent behaviour was performed to linearize the associations between the two. There are certainly other transformations that could do this job, but logging has the advantage that it yields a highly intelligible effect measure (elasticity). Further, with regard to the items used to assess suppressed anger, Graham asks why we used factor scores rather than a sum score. Our answer is simple: factor scores are advantageous because each item contributes to the scale in proportion to its relation to the underlying dimension. Moreover, the fine-grained scale of the factor scores made it possible to divide our sample into three equal-sized groups, whereas the coarse summed scale yielded groups that differed substantially in numbers. It may also be noted that we used a sum score in the first version of our paper, yielding an identical pattern of findings to that observed when factor scores were applied instead. Graham also asks why Pearson's r was used to estimate cross-sectional correlations while the associations between the change scores were reported as elasticities. However, we did in fact also report cross-sectional elasticities (in addition to the Pearson's r), noting that these were twice the size of the elasticities based on change scores. According to Graham, the suppressed anger explanation that we propose may not apply to alcohol-related violence among young people. Referring to qualitative studies of bar-room aggression, she suggests that violent behaviour in relation to drinking may occur because it is considered normative among young males—not because withheld feelings of anger are more likely to be behaviourally expressed under the influence of alcohol. Indeed, for some subgroups of young males, this may well be the case. However, our study was based on a general population sample and we did not focus specifically on male-to-male aggression in the context of on-premise drinking. Moreover, only a tiny fraction of all drinking events (including those of young males) involves violence, and we examined whether alcohol in combination with the disposition to suppress anger could account for individual differences in aggressive behaviour. For both males and females, our hypothesis of a moderating role of this anger dimension was supported. Graham also suggests that the above-mentioned effect of suppressed anger may be due to other dimensions of anger or to an angry disposition more generally. However, we focused specifically upon suppressed anger because it was the theoretically more interesting one (e.g. fitting well into the disinhibition perspective), and allowed ourselves to do so because our analyses indicated that it was empirically distinctive from other indicators of anger. We still agree with Graham that a more convincing strategy would be to conduct comparable analyses for both suppressed and expressed anger. However, we do not agree that our findings are inconsistent with experimental research showing no moderating role of suppressed anger on the link between alcohol consumption and anger expression. Thus, the one and only study that Graham refers to in this context [4] used facial expression of anger as outcome measure, implying that its scope differed from that of our study. None.

From Pubs to Scrubs: Alcohol Misuse and Health Care Use

To analyze the relationships between alcohol misuse and two types of acute health care use-hospital admissions and emergency room (ER) episodes. The first (2001/2002) and second (2004/2005) waves of the National Epidemiological Survey of Alcohol and Related Conditions (NESARC). Longitudinal study using a group of adults (18-60 years in Wave 1, N=23,079). Gender-stratified regression analysis adjusted for a range of covariates associated with health care use. First-difference methods corrected for potential omitted variable bias. The target population of the NESARC was the civilian noninstitutionalized population aged 18 and older residing in the United States and the District of Columbia. The survey response rate was 81 percent in Wave 1 (N=43,093) and 65 percent in Wave 2 (N=34,653). Frequent drinking to intoxication was positively associated with hospital admissions for both men and women and increased the likelihood of using ER services for women. Alcohol dependence and/or abuse was related to higher use of ER services for both genders and increased hospitalizations for men. These findings provide updated and nationally representative estimates of the relationships between alcohol misuse and health care use, and they underscore the potential implications of alcohol misuse on health care expenditures.

A comparative study of point-to-point algorithms for matching spectra

Matching spectra is necessary for database searches, assessing the source of an unknown sample, structure elucidation, and classification of spectra. A direct method of matching is to compare, point by point, two digitized spectra, the outcome being a parameter that quantifies the degree of similarity or dissimilarity between the spectra. Examples studied here are correlation coefficient squared and Euclidean cosine squared, both applied to the raw spectra and first-difference values of absorbance. It is shown that spectra do not fulfill the requirements for a normal statistical interpretation of the correlation coefficient; in particular, they are not normally distributed variables. It is therefore not correct to use a Student's t-test to calculate the probability of the null hypothesis that two spectra are not correlated on the basis of a correlation coefficient between them. We have investigated the effect on the similarity indices of systematically changing the mean and standard deviation of a single Gaussian peak relative to a reference Gaussian peak, of changing one peak, and of changing many peaks, in a simulated 10-peak spectrum. Squared Euclidean cosine is least sensitive to changes and the first-difference methods are most sensitive to changes in mean and standard deviation of peaks. A shift of the center of a peak has a greater effect on the indices than increases in peak width, but a decrease in peak width does lead to significant changes in the indices. We recommend that if these indices are to be used to match spectra, appropriate windows should be chosen to avoid dilution by regions with no significant change.

Anomalously large gradients in Version 1 of the “GEODATA 9 SECOND” Digital Elevation Model of Australia, and their effects on gravimetric terrain corrections

Large gradients, when calculated by a first-difference method, have been detected in Version 1 of the 9 arc-second National Digital Elevation Model (DEMv1) of Australia released by the Australian Surveying and Land Information Group. Gradient values implied by the mean elevations in the DEMv1 between adjacent grid cells of up to 74° have been observed, most notably in Australia's more mountainous regions in the east. Comparisons with topographic maps indicate that these are anomalous gradients in the DEMv1 that are not present in the mapped topography. It is recommended that the first-difference method is used to test DEMs before they are used to compute terrain corrections.

Optimization of quantitative electron energy loss spectroscopy in the low loss region: Phosphorus L-edge

The purpose of this study was to optimize quantitative electron energy loss spectroscopy (EELS) of elements that have characteristic edges in the low energy loss region and are components of organic matrices. The optimum parameters for phosphorus L 2,3-edge (at 135 eV) detection were determined by numerical analysis of computer-generated, Poisson-noisy spectra and by experimental measurements (at 80 keV) of films of the phosphoprotein, phosvitin. When the first, second and third valence electron/plasmon scatterings are included in the multiple least-squares (MLS) fit, the background subtraction of (first-difference) spectra is significantly more accurate than that obtained with the “inverse power law” method, even for a specimen thickness of only 0.25λ. Taking into account the effects of plural scattering, the optimal thickness for P quantitation is approximately 0.3λ. Signal-to-noise ( S / N) ratio decreases rapidly with thickness, and at 1.0λ, it is only about 60% of the optimum S / N. The combined effects of the statistical uncertainty of measurements and of the systematic error due to gain variations of the parallel detector were evaluated, and the relative sensitivities of the no-difference (raw spectrum), first-difference and second-difference methods were compared. For channel-to-channel gain variations greater than 0.1% and up to 0.8%, the first-difference method results in the lowest uncertainty of P measurements. In the absence of gain variations, direct fitting provides the greatest sensitivity (least uncertainty), whereas at larger gain variations it may be necessary to use the second-difference method. The optimum energy shift for collecting a first-difference spectrum, approximately 15 eV, did not show any great variation between 5 and 25 eV, and is, in general, specimen dependent. Quantitation with EELS showed excellent correlation with simultaneous electron probe X-ray microanalysis, but, for the detection of P in a 0.25λ thick specimen, EELS was approximately five to six times more sensitive than X-ray. The minimal detectable P concentration, with 0.5 nA beam current for 100 s in a 0.25λ thick specimen, was 8.4 mmol/kg (0.01 at%) at the 99% confidence level, equivalent to 34 phosphorus atoms for a 15 nm probe. This value is close to the theoretical prediction of 7.5 mmol/kg, and can be improved only by further reducing the gain variation and directly fitting the non-difference spectrum. Appropriate reduction of the gain variations to less than 0.1% would result in a further, approximately two-fold, improvement in the parallel EELS detection system. However, in order to obtain the optimal specimen thickness for phosphorus quantitation in cryosections, it will be necessary to use higher (approximately 200 keV) excitation voltages.

Comparing detrended UCR and NCS crime rates over time: 1973–1986

Previous comparisons of trends in UCR and NCS crime rates over time have found little convergence between these two series (Menard and Covey, 1988). When these series are detrended, however, either by using year as a control variable or by employing the method of first differences, the convergence between them is, in general, impressive. Thus, fluctuations in the UCR crime rates over time are paralleled by fluctuations in the NCS crime rates. If researchers detrend their data, as many time-series analysts do, then results based on UCR and NCS data are likely to be similar. This is encouraging news for those who use either set of data in time series-analyses.

Panel data and models of change: A comparison of first difference and conventional two-wave models

The method of first differences as an approach to modeling change is described and it is compared to more conventional two-wave panel models. Substantial advantages are found to the first-difference approach, especially if there are unmeasured, unchanging predictor variables in the model. It is also argued that there are substantial problems in the interpretation of results from the conventional two-wave models. Some of the analytic results are illustrated with a number of applications to the area of stressful life events.

The NEC μPD7720 Digital Signal Processor — A Laboratory-Based Case Study

The concepts of single-chip digital signal processing are presented via a student-oriented tutorial/laboratory case study. This involves the design of a highpass digital filter using the first-difference design method and its implementation using the NEC μPD7720 Signal Processor.

Components of the hypsometric curve of the Earth

The method of first and second differences often permits the separation of zigzag curves (on probability paper) into two or more Gaussian components. Where the procedure can be employed, it yields means and percentages. By this method the hypsometric curve of the earth can be made to produce four components, having means at −5.2 km, −4.85 km, 0.3 km, and 0.35 km. Not all curves permit analysis of this type. For those that do, the procedure is partly subjective.