Traditionally, science was focused on the development of effective and reliable methods of the analysis which could help researchers arrive to reliable results of their studies and, therefore, make their findings scientifically valid and trustworthy. At the same time, the development of science was accompanied by the wider introduction of new methods of the research which could vary dramatically depending on preferences of researchers. In the course of time, two major approaches to scientific researches were developed: qualitative and quantitative. Qualitative methods of the analysis are predominantly oriented on the qualification of subject of the research and identifying the reliability of the research in terms of quality. However, the qualitative approach is not absolutely objective. In stark contrast, often qualitative methods prove to be highly subjective and, hence, their reliability may be put under a question (Hagen, 2003). In such a situation quantitative methods may be particularly helpful since, unlike qualitative methods, they are focused on the research of quantitative characteristics of subjects related to the research. This means that quantitative methods provide a researcher with ample opportunities to conduct a study objectively, on the basis of the quantitative, but not qualitative analysis. Thus, the development of research methods is focused on two major directions quantitative and qualitative methods. In fact, both quantitative and qualitative methods have their own strength and weaknesses. This is why it is necessary to analyze them in the context of the practical application of these research methods in order to find out the extent to which they are effective and in which areas these methods can be applied. Also, it is important to underline that the contemporary science tend to the wider application of both qualitative and quantitative methods of research to make the outcomes of researches and their findings more accurate and objective (Litwack, 1993). At the same time, quantitative methods may be successfully applied in human services where they can contribute to the research of the most significant and socially important problems as well as indicate to possible ways of their solution. In this respect, it is possible to apply quantitative methods in demographic researches in order to find basic trends in the population, its needs and problems. For instance, today, problems of the aging population are growing more and more important because of the increasing share of the aging population (Volti, 2005). Therefore, it is very important to research their actual state, including their health state and health services available, the economic status and needs of elderly people. etc.
At this point, quantitative methods may be extremely helpful.
The reliability and validity of a research is highly dependent on the methods applied in the process of the research and analysis. In order to conduct a reliable research, it is necessary to define the basic methods that will be used and strategies of the research. Among the variety of research methods, it is possible to select positivist approach since this research philosophy is based on the use of the accurate scientific approach and it does not admit the possibility of some subjective influences on the research and its outcomes (Hesselbein et al., 1997). To put it more precisely, positivism implies that the entire research is based on the use of approaches and data that can be scientifically proved and stand on a reliable scientific ground. In such a way, this research philosophy minimizes the risk of using of uncertain approaches or methods that could put under a question the results of the entire research.
One of the most widely spread quantitative methods in map comparisons are unidirectional andÂ intransitive; that is, Map 1 may fit better when compared with Map 2 as a reference than Map2 fits using Map 1 as a reference. The selection of a base or reference map to which another is compared determines the direction of the comparison. If the number of categories in the maps being compared differs widely, the coarser map usually will exhibit a better comparison with the finer one as a reference than vice versa. Coarseness depends on the average size and number of the patches in each category, and may or may not be reflected in the number of categories in the map. The comparison direction that produces the best degree of fit is the one that we intuitively consider to be the level of concordance between the maps. Our conceptual model for comparison of categories is based on the degree of spatial overlap (Fig. 1) (Hagen, 2003). Two categories from two different maps are judged to be a good fit if their degree of spatial overlap is nearly complete (Fig. 1, right side). At this extreme, the two categories have a large degree of positive spatial correlation. This establishes a strong identity between these two categories, which can then be said to express the same feature in the two maps. Similarly, two categories are judged to be a poor fit if they share very little area of spatial overlap (Fig. 1, left side). Little spatial concordance means that these categories are not identical, and therefore describe separate features. An ideal GOF model will be especially responsive to incremental increases at high overlap, since this extra sensitivity will discriminate excellent fit from good fit, while distinguishing both from poor fits. The GOF algorithm can be applied equally well to whole map categories, individual patches, or even to vector polygons (although only application to entire map categories is described here). The comparison is restricted to the extent that both maps overlap spatially, and begins by selecting a category from the map which is being compared (Map 1, Fig. 2). All categories from the reference map (Map 2) having any degree of spatial overlap with this category are identified. The map comparison GOF algorithm is based on two values: (1) the proportion of the intersecting area to the total area of the intersecting category from Map 2, and (2) the proportion of the intersecting area to the total area of the category from Map 1 (Heilbroner and Milberg, 2000).
Unidirectional Map Comparisons
The first term gives the proportion of ”˜”˜insideness” that the reference category shares with the tested category, and itself represents a GOF term. The second term weights this degree of fit by the fractional share of the Map 1 category’s area that is intersected. Without such area weighting, the presence of many large, intersecting categories, each of which might share only a small spatial intersection with the category being tested, would result in a high degree of fit.
Summation of the product of ”˜”˜insideness” and the area weighting term over all intersecting categories provides a GOF score for this Map 1 category (Hargrove and Hoffman, 1999).
Fig. 1 Conceptual basis for comparing two categorical maps. The conceptual degree of fit is shown for two categories from separate maps as their spatial overlap is increased. When spatial overlap is maximized, the goodness of fit is high, and an identity between the map categories is suggested (Heilbroner and Milberg, 2000). When there is little spatial overlap, goodness of fit is low, and identity is unlikely. An ideal GOF model will be especially responsive to incremental increases at high overlap, since this extra sensitivity will discriminate excellent fit from good fit, while distinguishing both from poor fits Quantitative comparison of categorical maps unitless. Expressed as a percentage, the GOF measure is standardized, and can be compared across categories and maps (Kahneman, 1982).
Any Map 1 category that can be exactly comprised of a set of Map 2 categories will show a perfect fit with this measure (Fig. 3a). The ”˜”˜insideness” of all completely contained categories is 1, and the weighting factor is the proportion of the area that they represent, which must sum to 1 for a perfect fit (Hargrove and Hoffman, 1999).
Fig. 2 Goodness-of-fit (GOF) algorithm used with Mapcurves. A polygon or category is isolated from the map being compared (Map 1, brown), and all intersecting polygons or categories from the reference map (Map 2, red) are identified. For each of these, the proportion of their total area contained within the intersection is calculated as an indication of ”˜”˜insideness.” The degree of ”˜”˜insideness” is tempered by weighting it by the proportion of total area that the intersection represents of the category or polygon being compared (Hargrove and Hoffman, 1999). The sum of the product of each insideness term weighted by its proportion of overlap with the tested polygon gives a GOF term that is unitless, and is scaled so that GOF scores can be compared across multiple categories or polygons (Hargrove and Hoffman, 1999) intersecting reference polygons than the one shown in Fig. 3c, and this is intuitive, since there is more common overlap in the former. GOF is tested for each of the categories in Map 1 to estimate the directional fit of Map 1 compared to reference Map 2. GOF is calculated.
Fig. 3 Examples of goodness-of-fit (GOF) scores used with Mapcurves. a No matter what the spatial configuration or type of division, sets of polygons or categories in one map that exactly constitute a polygon or category in another map will show perfect GOF. All wholly included polygons have maximum ”˜”˜insideness” and, when multiplied by the area of overlap and summed, equal a perfect score, irrespective of the number of intersecting components (Hargrove and Hoffman, 1999). This design allows GOF of maps created by ”˜”˜splitters” and those created by ”˜”˜lumpers” to be compared regardless of the level of division that has been used. Outer boundaries of these groupings should coincide exactly, but have been depicted as adjacent for clarity. Examples shown in b and c indicate how this GOF changes for polygons sharing different degrees of spatial overlap with polygons from a reference map. The polygon shown in b has a higher GOF score than the one shown in c, as intuitively expected (Hargrove and Hoffman, 1999).
Quantitative comparison of categorical maps.
Fig. 4 Comparison of a First Pair of Test Maps using Mapcurves. Maps A and B are being compared, and maps in each row are derived from these. The middle maps in each row (Maps C and D) are reclassified by the translation table that maximizes the resemblance to the reference map by changing the label of the entire category and applying the reference map’s color table. The rightmost maps in each row (Maps E and F) show the goodness-of-fit (GOF) for each category. White is the highest GOF, and black is the lowest. Mapcurves resulting from both possible comparison directions are shown below (Hargrove and Hoffman, 2004). The uppermost Mapcurve reflects the comparison of Map B to Map A as a reference, and this is the best fit (GOF score = 0.6470). The lower Mapcurve shows the opposite comparison (Map B score = 0.4621), and is disregarded. These relative scores indicate a slightly greater degree of resemblance of Map D to Map A relative to the resemblance of Map C to Map B (Hargrove and Hoffman, 2003).
Intransitive Map Comparisons
Intransitive map comparisons may be successfully used as another quantitative researhc method which can be complementary to unidirectional map comparisons. At the same time, intransitive map comparisons have their own unique characteristic which make them different from unidirectional map comparisons.
Fig. 5 Comparison of a second pair of test maps using Mapcurves. Figure components as explained in Fig. 4. The identity of the first and second maps in each row indicates that each test map is already as much like the other as simple category reassignment can make it. The Mapcurves indicate that both maps have four categories (four possible tiers in the graphs), and actually cross over each other. Although nearly equal, Map A (GOF score = 0.4030) is a slightly better fit than Map B (GOF score = 0.4028), and is the uppermost Mapcurve. The Mapcurves and GOF score indicate that this pair of maps has a poorer GOF than the first test pair compared in Fig. 4 Langevoort, 1998).
Quantitative comparison of categorical maps separately for each category from Map 1 according to the algorithm shown in Fig. 2 (Hargrove and Hoffman, 2003). All categories in reference Map 2 sharing any spatial overlap are involved in the GOF summation for that Map 1 category.
Fig. 6 Comparison of Kuchler’s national vegetative types and vegetative forms maps. Figure components as explained in Fig. 4. Although not clear from simple inspection, Kuchler’s Types map (Map B) is a subdivision of his Forms map (Map A). This is shown by the fact that the reclassified Types map (Map D) exactly matches the original Forms map (Map A), and also by the fact that the goodness-of-fit (GOF) for all categories in the Forms map is perfect (Map E, empty state borders shown to outline the all white map). The Mapcurves also reflect this exact nesting; the comparison of the coarse map to the fine map as reference is a perfect fit (GOF score = 1.0, horizontal Mapcurve across top of graph). The fine map to coarse map comparison is poorer (bottom Mapcurve, GOF score = 0.2479).
This is intuitive, since it will always be more difficult to make a coarse map look like a finer one (Hargrove and Hoffman, 2003).
Fig. 7 Altered Version of Kuchler’s national vegetation types map to show effect on mapcurves. Figure components as explained in Fig. 4. Two of the 118 categories in Kuchler’s vegetation types map were eliminated by combining them with neighboring categories, in order to slightly degrade the perfect nested hierarchical fit, and the Mapcurves analysis from Fig. 6 was repeated. The GOF score of Map A is now reduced to 0.9899, and the uppermost Mapcurve now deviates from perfect horizontal by descending in four discrete steps (Litwack, 1993). These four steps correspond to the four categories that were altered in the map (two combined with two others). The GOF map (Map E) is no longer pure white, but shows the same four altered categories in shades of light gray. The GOF score for Map B increases slightly to 0.2496, bringing the two Mapcurves slightly closer together since the difference in their number of categories has been slightly reduced. Altering one map results in slight changes to both Mapcurves (Heilbroner and Milberg, 2000).
Conversely, calculating the fit of each category from Map 2 using Map 1 as a reference provides the quantitative comparison in the opposite direction. Translation tables are produced that show the best possible recoding of categories in one map to maximize the fit to the other map (Hargrove and Hoffman, 2003).
Fig. 8 Comparison of Hargrove/Hoffman statistical ecoregions, with 25 ecoregion divisions, with Kuchler’s national vegetation types map using Mapcurves. Figure components as explained in Fig. 4. The Hargrove/Hoffman 25 ecoregion map (Map A) has the best fit (GOF = 0.3442) using the Kuchler map as reference. Reclass Map D shows the best comparison with original Map A. Major rivers and wetlands are responsible for biggest differences between the maps, along with the mountainous regions of the western US (Map E). With a GOF score of 0.4578, the 10 ecoregion Hargrove/Hoffman map is an even better fit than the 25 ecoregion version shown here, and corresponds more closely with Kuchler Types than the second pair of test maps do with each other (GOF score = 0.4029) (Hargrove and Hoffman, 2004).
Different translation tables exist for each direction of the pairwise comparison. Using the translation tables, categories in each map can be reclassified such that one map resembles the other map as much as possible when entire categories are re-assigned. Each category can also be colored by the goodness-of-fit score to show parts of the map where agreement with the reference map is relatively good or poor. In this way, each map in a pairwise comparison can be reclassified to show the spatial locations of categories where fit is good and categories where fit is poor. 2.3 Mapcurves A Mapcurve is a GOF power curve showing the decline in percentage of map categories on the y-axis that still satisfy an increasing GOF threshold on the x-axis (Figs. 4, 5, 6, 7, 8, bottom) (Heilbroner and Milberg, 2000). A cumulative frequency distribution is plotted from each directional comparison showing the percentage of categories in one or multiple maps that meets or exceeds a particular sliding threshold of GOF. As the GOF threshold is increased, a smaller percentage of map categories satisfy or surpass that level of fit. All Mapcurves start at the top left corner of the graph, since in all map comparisons, 100%of the intersecting categories have a 0%or greater match (Fig. 4) (Hargrove and Hoffman, 2003). The Mapcurve resulting from a perfect match is a straight horizontal line along the top of the graph. Each Mapcurve is monotonically decreasing. If a Mapcurve intersects the right edge of the graph, this point indicates the percentage of overlapping categories within the comparison map that wholly contain categories within the reference map. Thus, a perfect fit Mapcurve running along the top of the graph indicates that 100% of comparison map categories completely contain reference map categories. The poorest possible fit would be indicated by a steep, rapid plunge to the x-axis (Heilbroner and Milberg, 2000).
The area under the Mapcurve can be used as a single index for the GOF of the entire map to the reference map.
Mapcurves that are higher and integrate more area indicate better matches between maps. Since they are plotted on standardized axes, all Mapcurves are comparable, and reveal which map comparisons represent closer matches. A flat Mapcurve across the top of the graph resulting from a perfect comparison represents an integrated area of 1.0, which is 100 Â· 100% (Heilbroner and Milberg, 2000). Two Mapcurves are produced from each pairwise map comparison (one for each direction). Whichever of these Mapcurves integrates more area indicates the comparison of the coarser map to the finer map as a reference, and is the relevant optimal direction of comparison. The other Mapcurve of the pair can be ignored. The direction of the most favorable comparison usually switches as the number of categories in one map exceeds those in the other, although artificial maps can be designed for which this is not the case (Litwack, 1993).
The most favorable direction of comparison cannot easily be determined before the full Mapcurves analysis is performed. Two sets of test maps were compared, as well as other well-known vegetation and ecoregion maps, in order to explore and demonstrate the behavior of Mapcurves. While several of these comparisons have expected outcomes, some do not. Finally, Mapcurves were used to rank pairwise comparisons (Langevoort, 1998).
Among a number of popular landcover and ecoregion maps, including some comparisons anticipated to display a poor GOF. Figure 4a and b show the first pair of maps to be compared, each with the same random color table assignment (although this does not imply correspondence). Each map in the same row of Fig. 4 stems from one of the original maps. Map A has seven categories, while Map B has only five. Map C shows Map A reclassified to match Map B as well as possible, and assigned Map B’s color table. Similarly, Map D shows the best reclassification of Map B to match Map A. The pair of Mapcurves resulting from the two directions of this comparison are shown at the bottom of Fig. 4 (Langevoort, 1998). The higher of the two Mapcurves represents the comparison of Map B to Map A as a reference, and this is the most favorable comparison direction. Five descending steps can be seen in this Mapcurve, corresponding to the five categories in Map B (the lower Mapcurve has seven potential descending steps).
Map B’s score when compared to Map A, calculated by integrating the area under the higher Mapcurve, is 0.6470 (Langevoort, 1998). Therefore, the best comparison is reclassified Map D with Map A. Map F shows Map B with each category colored by its GOF with Map A (lighter colors indicate a better fit). In Map F, GOF is shown for whole categories, not individual patches. The GOF for particular patches may be good, but the category is assigned a single GOF value and gray scale that represents the fit across the entire map. It is not necessary to draw Map E, since this represents the poorer comparison direction (Schein, 1999).
The second pair of maps to be compared, their derivatives, and Mapcurves are shown in Fig. 5. That the first and second maps shown in each row are identical indicates that each Test Map is already as much like the other as simple category reassignment can make it. The GOF scores for these maps are nearly equivocal, but Map A has a slightly higher GOF of 0.4029, making the reclassified Map C and Map B comparison slightly better (Hesselbein et al., 1997).
The Mapcurves show that both maps have four categories, and the curves actually cross over each other. Comparison of their GOF scores shows that the second pair of maps is a much poorer fit with each other than the firstpair.
Mapcurves may be used to compare Kuchler’s Vegetation Forms and Kuchler’s Vegetation Types maps, from coverages digitized at the United States Environmental Protection Agency from the 1979 Physiographic Regions Map produced by the Bureau of Land Management, which added 10 physiognomic types to Kuchler’s 1964 United States Geological Survey (USGS) Potential Natural Vegetation map (Kuchler 1964) differs from the 1985 USGS map revised by Kuchler and others, Kuchler (1993)]. Each of these maps has a resolution of 5 km2. Although not obvious by simple inspection, Kuchler’s Vegetation Typesmap (118 categories, Fig. 6 Map B) is a subdivided version of his Vegetation Forms map (29 categories, Fig. 6 Map A). The Mapcurves method immediately shows this to be the case, since the comparison is perfect (upper flathorizontal line, Fig. 6 bottom), and the Map A GOF score is 1.0. The reclassified Map D is identical with Map A, and, when colored by GOF, all categories in Map E are white (empty state boundaries are shown in Fig. 6e to outline the perfect fit of the all-white map). The flat horizontal Mapcurve represents the coarser Map A compared to the finer Map B as a reference. The lower Mapcurve (fine to coarse as reference) intersects the right edge of the graph, indicating that about 2% of the categories in the fine map completely contain categories in the coarse map. Indeed, category 48, California steppe, is identical with category 9 from Map A, California grassland. Similarly, category 52 from Map B, Alpine meadows and barren, is identical with category 11 from Map A, Alpine meadow. Since these two categories are not subdivided, 1.7% of the categories (2 of 118) are completely contained (Hesselbein et al., 1997). As a demonstration and test, we altered Kuchler’s finer Vegetation Types map by combining two small spatially contiguous categories with their neighboring categories. In this new test map, we eliminated the sandhills in Nebraska (category 89) by combining it with Oak/hickory/pine (category 111), and we re-labeled the Blackbelt in Mississippi and Alabama (category 75) to now become Grama/Buffalo grass (category 65) (Heilbroner and Milberg, 2000). These changes were designed to slightly degrade the perfectly nested, hierarchical fit of these two maps.
The Mapcurves comparison of this new map with Kuchler’s original Vegetation Forms map is shown in Fig. 7. As before, reclassified Map D is the best comparison with Kuchler’s original Forms Map A, but now the two changes in Nebraska and Mississippi can be seen. The altered Map B’s GOF score is now 0.9899. The GOF Map E shows four categories in light gray, the two combined categories and the two categories with which they were combined. The uppermost Mapcurve (Fig. 7, bottom) now deviates from the perfect horizontal fit shown in Fig. 6 (Heilbroner and Milberg, 2000). At the upper right, the altered Mapcurve descends four steps, corresponding to the two categories that were blended with two others. Both Mapcurves were altered by the changes to the finer map only, although the change in the lower curve is subtle due to the large number of categories in the finer map. The gap separating the two Mapcurves narrows as the difference between the number of categories in the two maps decreases.
Hargrove and Hoffman (1999) have experimented with ecoregionalizations created using Multivariate Geographic Clustering (MGC). MGC uses non-hierarchical multivariate clustering, employing the iterative k-means algorithm of Hartigan (1975) to produce national ecoregions statistically at a resolution of 1 km2, based on a number of abiotic environmental variables. Normalized variable values from each map raster Quantitative comparison of categorical maps cell are used as coordinates to plot each map cell in a data space with as many axes as there are multivariate environmental descriptors. Similarity is inversely related to separation distance in this data space. The MGC process iterates on a parallel supercomputer until it converges on a particular classification structure.
The user can specify the number of clustered ecoregions which result from the process, making it possible to divide the map into a few large, coarselydefined ecoregions or a larger number of small, finely-resolved ones. All large ecoregions produced by MGC have a similar upper limit on within-group variance. This control on heterogeneity across ecoregions prevents delineation of highly variable regions in the same map with ones that are more homogeneous
Hargrove and Hoffman (2004) have produced as many as 5,000 US ecoregions on the basis of 25 environmental factors, including elevation, mean and extremes of annual temperature, mean monthly precipitation, soil nitrogen, organic matter, and water capacity, frost-free days, soil bulk density and depth, and solar aspect and insolation.
Ecoregions created with MGC are useful for characterizing regional borders (Hargrove and Hoffman 1999), predicting species ranges (Hargrove and Hoffman 2003), statistically designing large networks of sensors or samples (Hargrove et al. 2003; Hargrove and Hoffman 2004b; White et al. 2005) and detecting trends in other complex multivariate phenomena, such as simulation output from global circulation models (Heilbroner and Milberg, 2000).
Because maps generated by MGC represent a way to vary the number of division categories present in the map, they offer a unique chance to test the Mapcurve comparison method. A series of national ecoregions can be produced at different levels of division, from fine to coarse, all based on the same set of multivariate environmental descriptors.
Because MGC is non-hierarchical, all borders between ecoregions are re-drawn for each separate level of division.
Hargrove/Hoffman map containing 25 ecoregions was compared and createdÂ Â using our MSTC process based on the 25 environmental variables described above, with Kuchler’s Vegetation Types map (Fig. 8a, b). With the finer Kuchler Vegetation Types map serving as the reference, the Hargrove/Hoffman 25 ecoregions map has the higher map score of 0.3442. Reclassed Map D is the best version for comparison with Map A (Heilbroner and Milberg, 2000).
When the Hargrove/Hoffman map is colored by GOF to Kuchler’s Vegetation Types (Fig. 8, Map E), major river systems are darkly highlighted as strong differences. Wetlands and swamps also differ between the two maps, and the Everglades, the Okefenokee, the Dismal Swamp, and the Mississippi Delta show as poor GOF, since Kuchler’s Vegetation Types map does not contain river or wetland features. Other differences exist between these two maps, particularly in the highly dissected Pacific Northwest (PNW). At this level of ecoregion division, the MGC method does not subdivide the PNW, while the Kuchler Types map does. Nevertheless, a Hargrove/Hoffman 10 ecoregion map is an even better fit with Kuchler Vegetation Types, having a Mapcurves score of 0.4578 (Hesselbein et al., 1996).
GOF maps like Map E in Fig. 8 are not area-weighted in any way. Instead, the map GOF score is obtained as the mean of the single gray level W.W. Hargrove et al. taken from each category in the map (Hesselbein et al., 1997).
Thus, a category covering a large portion of the map could have a poor GOF and be dark, but, if sufficient numbers of other categories with high GOF exist, the GOF score for the map could be high. Mapcurves are based on the proportion of the map’s categories exceeding a particular GOF threshold.
The application of map comparisons to the research of problems of the aging population
The use of different types of map comparisons methods can contribute consistently to the profound research of problems of the aging population. To put it more precisely, map comparisons can provide researchers with an opportunity to identify major trends among the aging population inhabiting different areas and reveal similarities and differences between the subject populations in the researched areas (Volti, 2005). For instance, it can be the statistical information on the major health problems elderly people suffer from or the level of funding of healthcare services in different areas and its impact on the quality of health of the gaining population. In fact, the low quantity of appeals of elderly people to healthcare services can be viewed as an indicator of a relatively good quality of health care services. For the same purpose it is possible to compare maps containing information on the life expectancy in different areas. In such a way, it will be possible to identify areas with a longer life expectancy that will indicate to the higher quality of healthcare services and standards of living at large. For instance, it is possible to compare the aging population in rural and highly urbanized areas. The difference is likely to be significant and map comparisons can reveal major differences and, therefore, major advantages and disadvantages elderly people can have in different areas, namely in rural and urban areas (Volti, 2005).
In such a context, the use of map comparisons methods seems to be quite efficient, but, on the other hand, it is necessary to remember about considerable drawbacks of these quantitative methods. In spite of the importance of quantitative data, for instance data on the amount of appeals of elderly people to healthcare services or the life expectancy, the comparisons of these data do not fully reflect the actual situation and the quality of healthcare services and the quality of life of the elderly population. The quantity of appeals does not necessarily mean the quality of healthcare services or standards of living of the aging population (Gitlow, 1997). For instance, the aging people may have insignificant health problems, such as cold, which may need a frequent assistance of healthcare professionals, while more serious diseases, such as cancer, may be less frequent but lead to more serious outcomes.
Consequently, in qualitative terms the quantitative methods are not effective and, what is more, they do not fully reflect the actual situation.
In conclusion, it should be said that basically, quantitative methods of the research may be applied in cases when precise information and outcomes of the research is needed. At the same time, quantitative methods do now allow evaluating the quality of the research and research’s subjects since basically quantitative methods are focused on the analysis of statistical information collected in the process of the research, which do not fully reflect subjective factor that influence the research in the real life. In actuality, the use of quantitative methods of research, being quite effective, is often insufficient for a profound and reliable research. This is why often quantitative methods of the research need to be complemented by qualitative methods. In such a way, contemporary researchers tend to mix both quantitative and qualitative methods of the research in order to achieve more reliable and accurate results of their researches.Â Consequently, it is very important for a researcher to be able to use both quantitative and qualitative methods.