An optimized approach for community detection of Uttar Pradesh state, India (Census 1991, 2001 & 2011)

The study on the gender ratio of overall population and of children in 0-6 age group for different districts of Uttar Pradesh state concentrates on the following: The data collected is evaluated for any pattern of sex ratio’s in terms of urban, rural segregation and to find whether the indices are different from district to district of Uttar Pradesh state so that precautionary measures can be taken care of to tackle this alarming situation in the state. For comparing sex ratios between pair of districts, it is tempting to arrange these (districts) in an increasing or decreasing order of sex ratio. But the reported sex ratios are not directly comparable since their “reliability” depends on the size of the population of the districts. Hence, a more reasonable index of dissimilarity between districts is the Chi-square measure computed under the hypothesis that the districts have the same sex ratio. The sex ratios/Chi-square values cannot be arranged on a linear interval scale and hence one has to think of an alternative more complex partial ordering among the districts to reflect a more meaningful structure that may be present in the data. Any ordering based on the results to be meaningful should be such that in the sequence, the difference between neighboring districts possible and the “effective difference” may be defined as the largest of these differences between successive pairs along the ordered set. Hence, ordering between every pair of districts must be such that this largest “gap” between consecutive pairs along the ordering should be as small as possible, that is among all possible sequences one can introduce between any specified district pairs. Hence, Minmaxion, an operation which enables one to find such “optimal approach distance” between every district pair, based on the Chi-square as an index or dissimilarity with respect to the sex ratios.

Introduction

As per the Census 2011, the overall sex ratio at the national level has increased by 7 points since the 2001 census to reach 940 females per 1000 males¸ this is lower than 1961 when the figure stood at 941 females per 1000 males. Despite introducing several laws on female foeticide and schemes to encourage the families to have a girl child, the sex ratio in India has gone down. The child sex ratio has gone to 914 females per 1000 males which is the lowest record since independence. These numbers clearly state that the Indian society still prefer boys over girls such that they could have a security for their future. The child sex ratio has gone down to 914 from 927 when the last census was taken. The monotonic decline in the sex ratio over the last decade, despite the improving socio economic characteristics reinforces the existence of gender discriminatory practices which starts even before birth; which requires the urgent attention of public policy, as improving literacy and economic value of women is necessary but not sufficient for enhancing the relative life chances of girl child (Srinivasan, 1994). However, this figure conceals the wide variation across the states in India and a distinct geographical pattern. The state of Mizoram has the highest child sex ratio with 971 females per 1000 males, while Meghalaya has 970 per 1000 males. Normally, the states like Punjab and Haryana have lower sex ratio, but in the recent years, an increasing trend has been seen in these states as compared with 2001 census. Haryana has 830 females while Punjab has 846 females per 1000 males.

The 2001 & 2011 census highlighted this issue by devoting a full section on child sex ratio. This distressing state of affairs raised voice of grave concern across all sections of society. It set into motion serious debates and resulted in a series of action on several fronts to curb the menace of female foeticide in certain parts of the country. In this direction, (Haragopal and Pandit, 2006) (Haragopal and Lakshman Rao, 2014) analyzed the data for Andhra Pradesh, Delhi, Punjab and Haryana states and found that there is a substantial drop of 0-6 female sex ratio. This was noticed by analyzing the data on village wise/district wise. With this experience we have analyzed the data on Uttar Pradesh state for the 1991, 2001 and 2011 censuses and present the results in the next sections.

The analysis of results in Uttar Pradesh district wise data revealed a significant insight into the problem at levels below the state at the national level particularly in certain parts of the country. The rural-urban differentials in the sex ratio in the age group 0-6 further sheds light on the spatial analysis of possible adverse impact on the female child due to the spread of the modernization and technological advancement in the villages and urban centers. The Uttar Pradesh state has 71 districts (Census 2011) and as per the data provided by the census. 1, it is observed that very few of the districts in the state have the 0-6 child sex ratio above 916. The number of districts seems to be dropping down and the state should recover comprehensively in the improvement of the Indices. The district level data on child sex ratio provides further insight into the pattern that exists at this level within a state. Keeping this point in view we have analyzed the district level data with urban and rural segregation and found that an alarming situation exists in the districts of Uttar Pradesh where a highest fall in the sex ratio is observed. On the whole the sex ratio at the district level is below the ideal of 1000. However, as will be seen later in many districts the variations in sex ratio is considerably being quite low in some districts and relatively very high in some other districts.

Child sex ratio district level analysis

Analysis for the present situation is as follows: In this section we present the data into a structured form as per the six characteristics in tables in each district for each of the subdistricts the sex ratio of all children, rural children and urban children as well as entire population including the children and rural and urban separately evaluated for the data. The associations of these characteristics are analyzed by Chisquare statistic for overall population for the data and the statistic values for 1991, 2001 and 2011 census data are 1881.9, 6458.9 and 5678. 3. From these values it can be concluded that there is a difference between overall male population and overall female population with respect to rural and urban areas for three census data respectively. Similarly, overall male 0-6 population and overall female 0-6 population with respect to rural and urban areas for 1991, 2001 and 2011 census data respectively. Chi-square values for overall 0-6 population for 1991, 2001 and 2011 census data are 16.9, 1277.1 and 629.0 respectively. From these values it can be concluded that there is a difference between overall male 0-6 population and overall female 0-6 population with respect to rural and urban areas for 1991, 2001 and 2011 census data respectively. Also, we have calculated the proportion of female and female 0-6 population for all the 71 districts and are given in Table 3, same calculations did for 1991 & 2001 also. From this we observed that there is no improvement in terms of female 0-6 population for the data and found that the difference between rural and urban areas and are misleading.

—	Male	Female	Male 0-6	Female 0-6
Total	0.5215	0.4785	0.5304	0.4696
Rural	0.5246	0.4754	0.5229	0.4771
Urban	0.5279	0.4721	0.5257	0.4743

Table text extracted from the original PDF; superscript letters are shown inline. The original table image is below.

View original table image

↗ Enlarge

Table 3Close ×

Proportion of female, female 0-6 of 71 districts for 2011

Open full-size image ↗

Original paper tableSource PDF · page 2 ↗

Analysis of Uttar Pradesh districts

With the above observations in sight we want to see that whether there is any difference within the 71 districts of the state and found that there is a difference within the districts for the six characteristics considered and these results are given in table 4 and found that most of the districts are different. Similarly we did for 1991 & 2001 hence, the interpretation for three censuses 1991, 2001 and 2011 we found that in case of proportion of female 0-6 population in the overall population for 1991 census data that there are 50 districts which are different. And for 2001 census data it was found that there are 60 districts which are different. While for 2011 census data it was found that there are 60 districts which are different. Over three decade 1991 to 2011, districts are increasing seem to have no improvement with respect to the proportion of female 0-6 in the overall population. Also, with respect to proportion of female 0-6 in the rural region for 1991 census data that there are 38 districts which differ. And for 2001 census data it was found that there are 47 districts which are different. While for 2011 census data it was found that there are 44 districts which are different. Over three decade from 1991 to 2011, districts are increasing seem to have no improvement with respect to the proportion of female 0-6 in the rural region. Also, with respect to proportion of female 0-6 in the urban region for 1991 census data that there are 57 districts which differ. And for 2001 census data it was found that there are 61 districts which are different. While for 2011 census data it was found that there are 57 districts which are different. Over three decade from 1991 to 2011, districts are increasing seem to have no improvement with respect to the proportion of female 0-6 in the urban region. Whereas, from three censuses 1991, 2001 and 2011 we found that in case of proportion of female population in the overall population for 1991 census data that 60 districts which are different. And for 2001 census data it was found that 70 districts which are different. While for 2011 census data it was found that there are 69 districts which are different. Over three decade 1991 to 2011, districts are increasing seem to have no improvement with respect to the proportion of female in the overall population. And three censuses 1991, 2001 and 2011 we found that in case of proportion of female population in the rural region for 1991 census data that there are all 53 districts which are different. And for 2001 census data it was found that there are 58 districts which are different. While for 2011 census data it was found that there are 58 districts which are different. Over three decade 1991 to 2011, districts are increasing seem to have no improvement with respect to the proportion of female in the rural region. And for three censuses 1991, 2001 and 2011 we found that in case of proportion of female population in the urban region for 1991 census data that there are 62 districts which are different. And for 2001 census data it was found that there are 56 districts which are different. While for 2011 census data it was found that there are 69 districts which are different. Over three decade 1991 to 2011, districts are increasing seem to have no improvement with respect to the proportion of female in the urban region. The major characteristic of female 0-6 population with respect to all regions of rural, urban and overall areas of these districts shows a major decline. From this observation we understand that the 0-6 child sex ratio is quite different in almost all the districts of Uttar Pradesh. This justification can be observed in the From this analysis we find that there is a change in the overall female and female 0-6 population in rural and urban areas for three Censuses (1991, 2001 and 2011). This inadequacy made us to study further the data for these three censuses, and in the next section we have studied how each district performs with each other districts is analyzed. Further, to know which district differs with respect to all the other districts is analyzed by considering the district data of 1991, 2001 and 2011 censuses. The Chisquare values have been calculated for the six characteristics of the population for 1991, 2001 and 2011 censuses separately and results are reported. From the total adult male and total adult female population for the 1991 census difference is observed in majority of the districts. Whereas, for some of the districts do not differ with another districts when compared with all the districts. Similarly the other five characteristics also calculated differ leaving very few districts not differing. The same procedure of chi-square is computed for the data on 2001 census for six characteristics, found that all the districts are different keeping some districts left with no difference. Similarly for the data on 2011 census for six characteristics, found that all the districts are different keeping some districts left with no difference. That is, this analysis shows that there is no improvement over these six characteristics from 1991 to 2011 census. In particular, we can understand that the 0-6 child sex ratio is quite different in almost all the districts of Uttar Pradesh. With this status of difference in all the districts of Uttar Pradesh for the six characteristics considered seem to have a mixed reaction. To see how the districts perform, entirely different or having some sort of similarities among these districts is studied by considering the clustering technique. From this big data analytics of Uttar Pradesh state we found that over 3 decades the indices seem to be in a very bad state and has to be improved immediately. After realizing the drastic changes in the data we want to study that whether these districts are similar or not with respect to 0-6 sex ratio etc is explored by the technique of clustering. Cluster analysis is computed for finding the district similarities for data with respect to six characteristics of the population separately and found that there is a difference within the districts and among the districts with respect to the six characteristics.

Districts	Proportion of females pop. in the pop.	Proportion of female 0-6 in the pop.	proportion of females in the rural region	proportion of female 0-6 in the rural region	proportion of females in the urban region	proportion of female 0-6 in the urban region
Saharanpur	562.6*	54.8*	6.5*	2.3	537.4*	39.1*
Muzaffar nagar	884.5*	297.7*	0.6	21.7*	695.8*	321.8*
Bijnor	0.4	110.4*	137.9*	8.7*	21.6*	67.0*
Rampur	76.7*	16.6*	94.2*	64.1*	10.8*	50.8*
Meerut	647.9*	223.5*	11.1*	111.9*	731.1*	418.7*
Ghaziabad	680.5*	215.9*	159.3*	200.1*	1427.6*	597.0*
Aligarh	1263.7*	126.9*	1.0	0.2	1044.8*	113.2*
Agra	2226.6*	252.3*	251.4*	66.3*	2683.9*	377.7*
Firozabad	1344.4*	58.8*	0.7	0.1	1066.2*	55.1*
Mathura	1751.4*	106.6*	193.2*	20.4*	1952.0*	136.9*
Mainpuri	859.5*	34.9*	22.0*	0.9	572.5*	30.6*
Buduan	2855.4*	16.1*	51.6*	23.5*	1968.3*	2.2
Etah	1072.9*	58.0*	0.6	0.8	856.8*	50.2*
Bareilly	1134.5*	2.6	0.9	24.0*	902.6*	0.1
Shahjahan pur	2117.2*	0.0	5.6*	0.0	1569.0*	0.1
Kheri	656.2*	45.6*	6.4*	8.2*	419.2*	67.2*
Sitapur	1361.7*	116.6*	70.0*	28.5*	837.9*	164.6*
Hardoi	3338.9*	12.1*	3.7	9.2*	2579.5*	2.4
Unnao	105.1*	31.8*	45.3*	6.1*	29.0*	41.6*
Lucknow	65.6*	32.0*	726.9*	38.4*	26.6*	24.3*
Rae Bareli	674.4*	60.0*	80.6*	5.9*	936.1*	81.7*
Farrukha bad	1011.3*	12.2*	15.0*	6.8*	891.8*	17.9*
Philibhit	285.3*	5.4*	0.9	1.0	197.5*	7.9*
Kanpur Dehat	1579.4*	3.5	0.9	1.4	1290.0*	2.5
Kanpur Nagar	1111.4*	31.9*	1252.7*	41.9*	3616.6*	140.4*
Jalaun	1368.1*	33.4*	16.5*	1.1	1191.8*	33.5*
Jhansi	223.3*	81.8*	16.3*	14.3*	307.4*	111.7*
Lalitpur	58.6*	5.3*	24.9*	7.4*	16.6*	12.1*
Hamirpur	1001.7*	9.2*	37.0*	4.5*	942.5*	12.6*
Banda	1605.3*	1.2	16.7*	2.0	1389.7*	0.0
Fatehpur	199.0*	0.9	11.0*	0.0	99.5*	2.5
Pratapgarh	5840.9*	15.2*	91.8*	6.0*	6466.7*	29.5*
Allhabad	14.2*	21.8*	486.7*	2.8	225.4*	24.0*
Bahraich	750.9*	156.5*	19.5*	16.1*	467.7*	204.3*
Gonda	22.8*	68.0*	8.7*	6.0*	82.9*	95.9*
Barabanki	43.0*	100.2*	12.2*	17.1*	5.3*	135.2*
Faizabad	1908.8*	75.2*	6.9*	4.9*	1707.0*	89.7*
Sultanpur	4754.6*	46.8*	41.6*	2.3	5306.6*	68.2*
Siddharth nagar	2496.4*	120.1*	87.3*	9.4*	2915.3*	155.1*
Mahraj ganj	487.0*	74.6*	66.3*	6.7*	726.5*	101.7*
Gorakhpur	1872.8*	4.5*	25.7*	1.2	1774.3*	7.6*
Deoria	8921.9*	48.8*	106.9*	8.0*	9126.8*	68.7*
Mau	2282.3*	11.8*	470.4*	107.2*	2732.2*	58.9*
Ballia	387.0*	3.6	35.7*	0.7	553.6*	0.6
Jaunpur	14295.1*	28.3*	158.5*	9.0*	14962.9*	49.7*
Ghazipur	1314.8*	0.8	28.7*	2.0	1593.6*	5.0*
Basti	1579.4*	62.6*	6.4*	1.8	1812.2*	82.2*
Azamgarh	13255.6*	32.6*	293.8*	20.4*	14140.5*	60.8*
Varanasi	123.9*	33.4*	13.3*	1.5	0.6	47.7*
Mirzapur	73.8*	0.6	33.1*	0.4	71.1*	0.0
Sonbhadra	41.4*	57.8*	54.6*	3.8	14.3*	47.9*
Kannauj	824.3*	2.9	7.3*	0.2	584.5*	1.5
Etawah	1176.4*	53.7*	0.6	2.0	889.8*	52.4*
Auraiya	1295.8*	5.2*	0.1	1.1	1014.5*	2.3
Mahoba	361.7*	6.6*	5.2*	0.4	317.2*	4.3*
Chitrakoot	436.2*	0.7	0.2	0.8	338.6*	1.3
Kaushambi	45.6*	23.4*	9.6*	5.0*	10.7*	35.7*
Ambedkar nagar	2489.8*	55.6*	179.1*	34.7*	2869.2*	90.4*
Shrawati	463.3*	26.8*	3.6	6.7*	333.1*	40.7*
Balrampur	66.8*	213.8*	26.8*	17.2*	144.5*	259.8*
Sant Kabir nagar	1550.8*	101.1*	20.0*	15.5*	1729.2*	131.5*

Table text extracted from the original PDF; superscript letters are shown inline. The original table image is below.

View original table image

↗ Enlarge

Table 4Close ×

Chi-square values for the proportion of overall female population, female 0-6 population of 71 districts with respect to rural, urban

Open full-size image ↗

Original paper tableSource PDF · page 3 ↗

Min Maxion Approach

In this section we have explored another technique to evaluate the data for the possible path with respect to the six characteristics for the all districts for the computed Chi-square values as distance matrix, which is non-metric matrix, for finding the possible meaningful district paths. The Chi-square values for rural 0-6 child male population and rural 0-6 child female population tabulated 2001& 2011 census data is taken as the distance matrix D, as an illustration to explain the Min Maxion technique. Then the Minmax Satiated Matrix S= D* of the distance matrix is computed. Next the Direct Link Matrix P is obtained from S. Lastly the Step Length Matrix L from the Direct Link Matrix P is computed. With the help of the 3 matrices the Minmaxion paths are listed below for all the Census data. Now, from these observations we formulate the paths for the state for the three decades for the characteristics as follows:

The path obtained is the optimal one in arranging them as changes of sex ratio. This path can help in trying to link the possible causes of difference in sex ratio with those factors which change in similar way among the districts. For example Education, Transportation facilities, Industrialization etc., thus, it is an exploratory tool which arranges districts according to gradual changes in sexratios and suggesting to explore whether any other characteristics (like Education, Welfare groups etc.,) about the districts show a similar ordering. Also, by comparing all these paths for all the characteristics it is observed that all the paths differ drastically with each other. Thus, the causes operating on the sex ratios may not be the same but differ from path to path for the data. For instance the overall male, female population path indicates that the indices for the district Auraiya to Banda is not much different while, when we compare district Auraiya to Jaunpur the indices is very different and the distance between these districts is large. Similar path evaluations by this method are explored and are tabulated below for the other characteristics. Which indicate that the distances between the districts are clearly observed. If we observe these paths in some characteristics some districts does not seen, indicates that they have the same distance are dropped from the list.

Path for overall male population and overall female population

Path for overall male population and overall female population

Figures and tables from the paper

Child sex ratio (0-6)	Number of Districts	—	—
	1991	2001	2011
880 & below	--	10	14
881-915	17	22	30
916-950	33	31	27
951-985	11	7	--
986 & above	1	--	--

Table text extracted from the original PDF; superscript letters are shown inline. The original table image is below.

View original table image

↗ Enlarge

Table 1Close ×

Distribution of districts by range of 0-6 child sex ratio of Uttar Pradesh state: 1991, 2001 & 2011

Open full-size image ↗

Original paper tableSource PDF · page 2 ↗

—	Population	Male	Female	Pop 0-6	Male 0-6	Female 0-6
Total	155317278	80992995	74324283	25040583	13135595	11904988
Rural	44495063	23487515	21007548	5750748	3049986	2700762
Urban	199812341	104480510	95331831	30791331	16185581	14605750

Table text extracted from the original PDF; superscript letters are shown inline. The original table image is below.

View original table image

↗ Enlarge

Table 2Close ×

Totals of 71 districts for each of six groups data

Open full-size image ↗

Original paper tableSource PDF · page 2 ↗

↗ Enlarge

Figure 1Close ×

(for 2011)

Open full-size image ↗

Original paper figureSource PDF · page 4 ↗

1. Agnihotri SB. Sex Ratio Patterns in the Indian Population: A Fresh Exploration. New Delhi, Sage Publications, 2000.
2. Haragopal VV, Pandit SNN. Analysis of Sex Ratio in Andhra Pradesh (Census 2001), Proc.A.P Akademi of Sciences, Hyderabad. 2006; 10(2):289-301.
3. Lakshman Rao K, Haragopal VV. Analysis of Sex Ratio in Punjab India (Census 2011) -A Demographic Study, Research Journal of Recent Sciences. ISSN 2277 -2502 2014; 3(ISC-2013):12-19.
4. Lakshman Rao K, Haragopal VV. Analysis of Sex Ratio in Haryana (Census 2011) -A Demographic Study, International Research Journal of Mathematics, Engineering & IT. ISSN 2349 -0322, 2014; 1(3):47-62.
5. Pandit SNN. Minaddition and an Algorithm to find most reliable paths in a network, I.R.E Transactions on Circuit Theory. 1961; CT-9:190-191.
6. Pandit SNN. A New Matrix Calculus, journal of the society of Industrial and Applied Mathematics. 1961; 9:632-639.
7. Registrar General of India, Census of India, 2011. www.censusindia.com
8. Srinivasan K. Sex Ratios -what they hide and what they Reveal Economic and Political Weekly. 1994; 30(51)323-334.