2 Meaning of Quantitative Geography
Prof Bimal Kar
1. Introduction
Geography has undergone remarkable changes in the content, philosophical base and methodological treatment in the course of its development. Changing definition of the discipline and work done in the field give testimony to this fact. However, it does not mean that the basic definition of geography ‘study of the earth’ is presently out of context. Rather, as the study of geographical phenomena is based on observation of reality and concrete data, geography is always regarded as an empirical science. In the beginning of the 20th century when a division of the discipline into physical and human geographies took place, the main attention was focused towards the ‘study of man-environment relationship’ to bind tightly both the branches of geography. But the discipline geography continued to maintain idiographic tradition (descriptive) relying on the concept of ‘unique’ until the Second World War. It is worth mentioning that with the introduction of the idea of logical positivism supported by quantitative measures, the attention has farther shifted to nomothetic approach (analytical and law seeking) especially after the Second World War. It has been done so to provide a scientific basis to the discipline and to formulate theories, laws and models especially in the field of human geography. It was thought that application of quantitative techniques based on the idea of logical positivism would bring objectivity in the analysis of the pattern and processes of the human geographic phenomena. In this way, the revolutionary changes that emerged in the nature of geographical studies from regional-idiographic to systematic-nomothetic based on quantification, have been termed as the great ‘Quantitative Revolution in Geography’. This had finally laid the firm foundation of the Locational School in Geography in 1950s.
2. Basic Need of Quantification in Geography
Quantification and statistics are present, in some form or the other, in all branches of geography. Adequate understanding of the different aspects of the subject requires elementary knowledge of mathematics and statistics. Basically, application of various quantitative measures helps us to understand spatio-temporal patterns (i.e. spatial distribution, arrangement and organization) of various geographical phenomena, and their associated processes (i.e. causes of occurrence and changes) on the earth’s surface. For instance, we can statistically find the nature of distribution pattern and its degree of variation relating to phenomena like towns, schools, hospitals, rainfall, road networks, rice productivity, population density, etc being represented by points, lines and polygons. Similarly, the processes associated with the specific patterns and their changes over time and space can be found out through relationship analysis of the influencing factors. For instance, contribution of amount of rainfall as an influencing factor to rice productivity in a given region can be estimated through relationship analysis. In fact, the best way to understand a technique is to use it, and that the best way to appreciate the advantages and limitations of its use in geography is to apply it to solve the geographical problems.
It is thus clear that quantitative techniques are employed in geography for a very good reason. In fact, nothing is wrong with a qualitative statement, but it carries more weight if it is possible to make a statement quantitatively; that is, in a mathematical language rather than in words. Ideally, the aim of a geographical statement is to convey unbiased objective information. The advantage of a quantitative statement is its precision, which allows less room for subjective bias to enter into the construction and interpretation of the statement. Consequently, a quantitative statement is more amenable to verification, more easily compared with other statements, and generally more suitable for testing hypotheses and developing theory by scientific methods. In this respect, the geographical statements are no different from those of any other sciences.
In view of such methodological developments in the field of geography since mid-1940s, the discipline of geography turned into spatial science. The following two definitions, among many others, also clearly justify the upliftment of geography as science.
(i) Geography is concerned to provide accurate, orderly, and rational description and interpretation of the variable character of the earth’s surface” (Richard Hartshorne, 1959).
(ii) “Geography can be regarded as a science concerned with the rational development, and testing of theories that explain and predict the spatial distribution and location of various characteristics on the surface of the earth” (Maurice H.Yeates, 1968).
Learning Outcome
One can understand the distribution patterns of various geographical phenomena like rainfall, income, land, settlements, industries, transport networks, agricultural productivity, socio-economic development level on one hand and physical attributes of landscape in both spatial and temporal contexts using various appropriate statistical techniques ranging from simple measures of central tendency and dispersion to various statistical indices like location quotient, nearest neighbour statistics, Lorenz curve and Gini’s coefficient, urban primacy, transport connectivity and centrality, etc. Inferential parameters like chi-square, t, Z, F, etc. used for testing the validity of various model-based statistical results are part of scientific reasoning in geography. The analysis of distance decay pattern, rank-size relationship, and the multivariate techniques used for the analysis of various geographical phenomena such as to the aggregation of attributes for calculation of the level of socio economic development, level of agricultural production/ productivity, the composite scores to find location strength of various activities and its hierarchies are the part of spatial analysis of geographical phenomena. Two important issues associated with such aspects of discussion impose two important questions, “how are various spatial attributes distributed?” and “are places different in a homogeneous phenomenon present there in an area?” These issues are taken up here with forwarding some of the examples from geographic attributes with the relevance of quantitative analysis.
Example-1 : Centrality and Dispersion of a Distribution
The following illustrative discussion would help understand the role of quantification in geographical studies. First of all, let us take an example of the distribution of annual rainfall (in cm) in three different places for the last 15 years.
Place A: 232, 218, 247, 192, 216, 231, 199, 185, 223, 151, 184, 195, 207, 239, 157
Place B: 187, 199, 207, 212, 177, 217, 204, 185, 193, 230, 223, 198, 227, 216, 201
Place C: 121, 147, 189, 180, 185, 159, 168, 177, 194, 140, 149, 163, 205, 219, 189
The first two sets (related to Places A and B) of the above data reveal that the amount of annual rainfall in place A varies from a low as of 151cm to a high range of upto 247cm, and in place B, it ranges from 177cm to 230cm. But when asked about where rainfall is more, we calculate the mean value called a summary measure belonging to simple descriptive statistics. Accordingly, the averages of annual rainfall at place A as well as at Place B are calculated to be 205.07cm and 205.07cm annually which are same at both the places. But, the nature of occurrence or distribution of rainfall during the period of last 15 years has not been the same in both these two places. It can be understood through another quantitative measurement called dispersion, more specifically called ‘standard deviation’ which are calculated 27.46cm and 15.29cm for the variation of 15 years for the places A and B respectively.
As and when we consider the rainfall for Place C ,the mean rainfall of this place is found to be 172.33cm, which is much lower than the mean rainfall of the places A and B. On the other hand, the nature of variation of rainfall in place C as indicated by standard deviation is found to be 25.38cm. Now, although the standard deviation of rainfall for place A (27.46cm) is greater than the corresponding value for place C (25.38cm), the degree of variability of annual rainfall is higher for the place C. It shows that the values of a parameter of various distributions may be same but their dispersion parameters may vary which gives scientific clues of phenomenal characteristics.
Example-2: Point Patterning
Let us take the case of spatial distribution of market centres (point pattern) in an area (Figure- 1). How are the market centres numbering 24 distributed over space in a given area?
Figure-1: Distribution of Market Centres
Broadly speaking, if the market centres are assumed as points over space, the pattern of point-distribution in an area can be analysed by using a technique called nearest neighbour technique. It discriminate pattern from closeness of points to unification. There are two methods to analyse the distribution pattern of given points: first forwarded by Clark and Evan ( 1954) that is based on ‘distance criterion’ of point pattern and second is ‘space-dependent criterion’ when patterns are considered as part of the space and total space of study area is divided in to suitable number of grids/squares to calculate the density of points to decide the feature of point distribution. Note that Nearest Neighbour analysis is distance- dependent and Chi Square analysis is space- dependent. One can use the technique as per the purpose of the study.
Example-3: Comparison of Distribution Pattern
Let us take another case of spatial distribution patterns of settlements (point pattern) in two different areas for comparison (Figure-2). In general, it is not so difficult to know whether a distribution pattern is uniform, random or uneven, or clustered without any computation.
But, in reality it is hardly possible to get perfectly uniform or clustered distribution because of involvement of two distinct but opposite processes in the location distribution of activities as one is related to ‘concentration’ and another is ‘repulsion’. First attracts the settlements and develop the closeness of settlements. Rather second process disperses the forces of activities over space and forms unification in the distribution pattern. It is therefore necessary to know exactly the pattern of distribution more particularly by comparison of spatial processes
Figure-2: Comparison of Distribution of Settlements in an Area
For instance, the distribution pattern of settlements in both the two areas, viz. Area ‘X’ and Area ‘Y’ as given in Figure- 2 is uneven or random. But, the degree of randomness or unevenness can be determined only by using an appropriate statistical technique either chi square statistics or nearest neighbour statistics ore even spatial mean centre statistics. In the case of chi square statistic, zero or near zero value indicates uniform distribution, and higher the value, higher is the degree of unevenness in the distribution. On the other hand, randomness index value (nearest neighbour analysis) of 1 or around 1 is indicative of random distribution, and the value approaching zero is indicative of approaching clustered distribution, and approaching 2.15 is indicative of uniform distribution. In case, one who applies spatial mean centre technique in point- distribution, it is obvious to say that if around 68% of points lie within a radius of 1 standard distance around the mean centre, the distribution is called normal. Thus, application of appropriate statistical techniques as mentioned above is the point of discussion for geographical studies.
Example-4: Connectivity and Network
Transport connectivity of places (indicated by nodes) in the form of line pattern analysis can be done using some graph-theoretic measures like connectivity index, centrality index, etc. In network analysis all the important places are termed as nodes or vertices (it includes important place, transport intersection and terminus) and the linkages connecting the places are called edges or arcs. Further, in network analysis the number of arcs to be traversed between two places (origin and destination nodes) is considered distance between them. The degree of connectivity depends on the number of linkages for given number of nodes. It means higher the number of arcs for a fixed number of nodes, more is the degree of connectivity. This can be judged through connectivity indices like beta, alpha and gamma. While beta index, being the ratio between number of arcs and number of nodes, gives the overall degree of connectivity of a network (with value ranging from 0 to above 1), the alpha and gamma indices give the extent of circuit development and extent of arc development respectively for a given number of nodes in a network (with value ranging from 0 to 1).
Figure-3: Connectivity Pattern of Transport Network
For instance, the degree of connectivity, or extent of circuit and arc development, in the networks of both the areas, viz. Area ‘A’ and Area ‘B’, is not the same (Figure- 3). In terms of beta index, the degree of connectivity is higher in Place A (Beta=1.38) than Place B (Beta=1.12). But, in respect of alpha index, the degree of circuit development is as high as 0.26 (i.e. 26%) in Area A as against 0.11 (i.e. 11%) in Area B. Again, in respect of gamma index, the extent of arc development is 0.52 (i.e. 52%) in Area A as compared to 0.43 (i.e. 43%) in Area B. Besides these, centrality of each and every node in the network (i.e. relative accessibility) can be measured with the help of associated number and shimbel index. In fact, the node which has more direct connections or linkages with other nodes is considered more accessible. Further, detour index (ratio of the actual distance between two places and the corresponding straight distance) can also be used to know the relative accessibility of different places in any network system of an area.
Example-5: Trends of Geographic Attributes and their fluctuations
Trend analysis that shows change in any attribute over a period of time, is studied through different time series techniques, viz. semi-average, moving average, least squares, etc. The least squares method of linear trend analysis of food grains production, etc not only helps in understanding the overall trend but also phenomenal prediction. For example, the trend of foodgrains production, rainfall, temperature, price of different commodities, export, import and so on are the results of various factors and forces that are analysed through fluctuation of the value of an attribute from its trend. The effects of climate in the pre-liberalisation period and the effects of techno-economic factors during economic liberalization period of the nineties are obvious on the trend of food grain production in the North India(Figure- 4). Its deviation from straight line trend can be measured by fitting the straight line equation in agiven set of production data. However, for population trend analysis, the non-linear or exponential methods can be useful for fitting overall trend and also in population prediction.
Figure-4: Food grains Production Trend in Northern India ( 1980-81 to 2000-01)
More complex problems of phenomenal association and attributes’ comparisons are greatly dependent on various parametric tests like regression and correlation coefficients. In fact, the measures of association help to understand the nature and extent of various geographical phenomena in spatial context and extent of similarities and dissimilarities between different places. Some cases are given below for clear understanding and proper depiction.
Example-6: Phenomenal Relationships and their Measurements
The nature of bi-variate linear relationship is shown in the form of regression or best fit line. Here, a causal linear relationship between dependent and independent variables as positive relationship between rainfall and rice productivity, and negative linear relationship between female literacy and birth rate are shown (Figure- 5). It also helps in projecting rice yield and birth rate for any given value of rainfall or female literacy rate respectively. Further, the nature and extent of the relationship between two meaningfully associated variables, viz. rainfall and rice yield, or female literacy and birth rate, can be found out through coefficient of correlation (r). Its value ranges from -1 (perfect negative) to +1 (perfect positive) through 0 (no correlation).
Figure-5: Bi- variate Relationships of Rice yield and Birth Rate with their independent Variables
Such objective decisions are taken only by measuring the association between two attributes in which one is dependent attribute (rice yield in the present case) and another is independent (called explanatory, in this case rainfall). These measurements are basically related to the theory of causality when cause- effect relationship is established to infer the result. Another example of the same type is forwarded here to analyse the spatial gradient of population density.
Example-7: Generalisation of Spatial Features
Spatial gradient of population density in a city area, that shows population density subject to distance from city centre is measured by using straight line equation to provide a general feature of population trend within the city. It is generatised in the form of ‘distance-decay rule’. This rule is applicable for the distribution of population in the cities, but varies its nature from linear to non- linear. Distance decay of two cities are show in the diagram that compares the gradients of distance decay (Figure-6). The non-linear or exponential negative relationship between distance from city centre and population density is the question of data transformation. It can be made linear through semi-logarithmic transformation, i.e. distance in arithmetic scale and population density in logarithmic scale, and as such it would help understand the nature of urban development, spatially balanced or not, in different cities. Besides, this population density gradient reflects the spatial limit of a city. Similarly, non-linear rank-size rule also helps us understand the nature of urban development of any urban system and its change over time.
Figure-6: spatial gradient of City Population Density
The above are a few examples of understanding various spatial phenomena through the meaningful applications of various statistical techniques, and these prove the usefulness of such techniques in geographical study. But, like any other techniques, the quantitative techniques do have their inherent limitations also.
4. Limitations
It needs to be kept in mind that the superiority of a quantitative statement over a qualitative one cannot always be taken for granted. Quantitative techniques, like any other, can be misused also. A quantitative statement is superior only when two conditions are met, that are validity of a technique used for and accuracy of the results inferred from. For any statement to be valid, it must express the true meaning of what does it represent. For example, if the aim is to compare the ‘standard of living’ in different countries of the world, then one quantitative measure available for most countries is the ‘per capita income’. It is not important whether ‘income per capita’ is a valid measure of ‘standard of living’. In the minds of many, ‘standard of living’ has, for example, very little to explain with income in money term. In any case, the availability of data, the ease of measurement, the simplicity of quantitative measures, and related features of quantification should not always and any everywhere be comfortable for more important notion of appropriateness and validity. Just precisely, quantitative statement may not be valid, so it may not be accurate. However, precision (exactness) alone does not necessarily ensure accuracy (correctness), although lack of precision prevents the highest accuracy, and other things being equal, a precise statement is more likely to be accurate. A simple example of an inaccurate but precise statement is one based on measurements with a faulty instrument. However, objective measurements of phenomena provide the clues which lead us towards correct and accurate explanations provided we use appropriate quantitative techniques for synthesisation of statistical observations
5. Summary
One should always remember that quantification is rarely an end itself, but is an integral part of the method by which reliable knowledge is accumulated. It acts as an important tool for processing and analysing data. Any science proceeds by a cycle of observations and hypotheses (a proposition for searching truth) from which scientific orders emerge, while the observed facts are given meaning within a conceptual framework. Observations are not made without the benefit of experience or existing hypotheses, and hypotheses are not derived entirely in isolation from the real world. Moreover, the hypotheses are always subject to improvement. In testing the validity of any proposed hypothesis, the role of quantification becomes important. Application of appropriate quantitative technique also helps in description and prediction of the pattern of various geographical phenomena. However, a scientific approach supported by meaningful quantitative measurements is not the only basis for understanding the truth, but it provides us the basis of the ‘most consistent, coherent and empirically justified body of information’. However, the complexities of geographical phenomena on space and in time (particularly on human issues of the subject) are often very difficult to tackle quantitatively. This is another limitation of quantification in human geographical study. In view of this, quantification in human geography is also often confronted with strong criticism. Hence, one should be clear about the advantages and limitations of each and every quantitative measure and its appropriateness before application in any study. The mishandling and inappropriate use of such tools may lead to erroneous results. At present, the debate in geography is not merely whether statistics and mathematics should be applied, but how they can be best used in the accumulation of reliable knowledge.
It is thus no denying the fact that quantification, and as such application of various meaningful statistical and mathematical techniques has proved to be very useful in solving many geographical problems, be it simple or complex, in proper perspective. It also helps to analyse any geographical phenomenon following either inductive route (to develop theory, model or generalization in a given context) or deductive route (to test the validity of an existing theory or model in a given context). Such process basically involves observing and recording facts in quantitative form; and processing, analyzing, comparing and classifying these facts using appropriate quantitative measures to draw more acceptable conclusions. In fact, quantitative techniques are used as necessary tools for explanation and decision-making.