Welcome back dear students. We are into the module 3 now and we shall talk about AttributeData Management and Data Exploration in this particular lecture.
So, the concepts that we are going to cover today is about Descriptive Statistics and we aregoing to talk about the Univariate Statistics, we are also going to talk about touch uponMultivariate Statistics, we would see what is Inferential Statistics, we shall also look into thetypes of Data Attributes and how the data is managed in GIS.
So, how we do the Attribute data entry, how we do the Database design, what is a Relationaldatabase and the I mean different types of data operations regarding joining of the tables. So,we shall look into these following concepts.
So, talking about Descriptive or Univariate statistics, it is used I mean for the ordinal variablesand the ratio variables and it cannot be used for nominal or categorical variables. We shall seewhat are these nominal and categorical variables. Some of you might be knowing about thesewho are into I mean data management and I mean database design and all these things.
So, it basically summarises the observation with descriptive statistics, it gives a summary ofthe observations and it is with reference to the distribution of a variable. So, whenever wehave variables and we have distributed data or discrete data, it is lumped or grouped into
different classes or grouped values and we have frequencies of occurrence for each of thesegroups which can be shown as histogram of the different classes.
Now, I mean the number of classes that we would categorise our data is determined as afunction of the number of observation and the range of the values. Now, talking about themeasures of central tendencies, we have three measures which you already know about. Thefirst one is known as Mean which is I mean the average of all the sets of observation.
So, if we have n number of observations, we sum up the I mean observations all the “n”observations and divide it by the number of observation to give us the mean which is denotedas mu. Now the next measure of central tendency is the Median which is the median middlevalue when all values are ordered if we I mean stack up the values from the smallest to thelargest.
So, you can find out the middle value and in case if you have even number of data sets, in thatcase what we do is we take the two middle values and I mean take mean of those. Now, youhave different types of algorithms in computer I mean software analysis. So, we can I meancategories the data or I mean save the data in a I mean smallest to largest I mean ordering. So,those different algorithms are available where in if we have a very large data set, it can beordered and then we can find out the median.
Now, mode is the most frequently occurring value in a data set. So, whatever data value is themost frequently occurring data value I mean that we take it as a mode. Now, if we haveoutliers in the data, if we have some data values which are extreme data values I mean whichis beyond the I mean central any of the central tendencies and which has very high values, soin those cases what happens this outliers will add up significantly to the mean. So, in a way themean gets I mean affected by this kind of outliers. So, mean median or mode value it reducesthe impact of the outliers.
So, I mean we talk about the descriptive statistics. So, we have three measures basically wetalk about the standard deviation where in we have the degree of the dispersion around themean and it is represented as sigma which is the difference of the square I mean of yourobserved values to the mean are divided by the total number of observations and it is taken asa square root.
We also have a term which is known as Variance which is I mean extensively used in GIS orotherwise in descriptive statistics. So, I mean it is the expectation of square deviation when thevariable is random with respect to its mean, now I mean it gives us a spread out of thoserandom numbers with respect to the average value with respect to the mean values. Talkingabout the coefficient of skewness when we are having a distribution a, when we are having ahistogram we can see that it could be in the form of a inverse bell curve.
So, this curve could be symmetrical in nature or it could be asymmetrical in nature. So, thecoefficient of skewness, it measures the lack of symmetry or the presence of symmetry in thedata distribution and it is measured using Pearson’s moment coefficient of skewness which isgiven by this particular equation shown here.
Now, going to Multivariate Statistics, generally I mean we are dealing with data which is notunivariate, but it is multivariate where in we have one dependent variable and we may havemultiple independent variable.
So, I mean your univariate statistics cannot be used to analyse such situation. So, I mean againwhen we like we were talking about univariate data in case of multivariate analysis as well Imean it is not possible for us to analyse the nominal or categorical variables, so we can as I
was telling that we can explore if there is a relationship between two or even more than twovariables.
So if you have two variables, then it would come as a scatter plot you can have abscissa andordinate x-axis and y-axis and the data plots would data values would be scattered in as paperpot, I mean diagram as I mean as dots in the x and the y axis. So, I mean if you have a threedimensional data set in which you may have one independent, dependent variable and twoindependent variable, in that case it would look like a cloud of points and similarly, if you havemore number of variables it becomes a figure becomes complicated.
So, I mean we can include more than one variable and but the advantage of this multivariatedata descriptive statistics is that we can simultaneously assess the interrelationship betweenmultiple number of variables. Now, to do this assessment what we do is, there are twomethods. We are talk about the correlation and we talk about regression.
So, in correlation and regression we nature I mean we explore the nature of relationshipsbetween the different variables and we try to assess a what is the strength of relationshipsbetween these variables. So, when we have these variables, what we can do is we can fit a lineto these data points and this line is the line of the best fit, that is the line which passes throughthis scatter plot is worked out. So, it is as close as possible to all the points and it represents Imean this particular line or the best fit line it represents the trend in the data.
So, suppose we have this data points and we I mean try to create this data points scatter plotsin this particular x, y and z values two variables which is y and z. So I mean if we try to do abest fit plot, then what happens is you can find out the distances and these distances would beminimised, these distances from this points would be minimised, so that the this is the best fitline.
Now, if we see the equation of the best fit line, it is in the form of y equals mx plus c where inwe have the slope and we have the I mean intersect. So, this in this particular equation that is zi equals to I mean beta subscript 0 plus beta subscript 1 y i in this beta 0 represents the slopeand the beta 1 represents the intercept coefficients. So, we see this particular equation in thisyour z i is equal to beta 0 beta subscript 0 plus beta subscript 1 yi.
This is the equation of this particular line which is the line of best fit in which it is as close aspossible to the to all the points. So, we shall see how we minimise this distance from all thesepoints. So, in this case this is of the form of y equals to mx plus c. So, we see the betasubscript 0 and beta subscript 1 are the intercept and the slope coefficients.
Now, we had talked about the I mean the best fit line. So, this is the regression equation. Thisequation that we had talked about is the regression equation. Now talking about the slope ofthis particular line that is the beta 1 it is I mean calculated using this particular equation I meanit gives you the ratio of the rise along the x to the ratio of rise along the y axis. So, in this caseit is given by this particular equation. So, similarly we can work out the calculate the interceptby this equation. Again it is I mean subtracting your z mean minus beta 1 into y mean.
Talking about the correlation coefficient which gives us the strength and the nature of therelationship between the variables, so it gives us the degree to which the scatter points arearound the regression line. So, it is a ratio again and it is worked out using this particularequation and we can see that the r that is the correlation coefficient, it ranges from minus 1 topositive 1 value.
Now, when we have positive values of r, it indicates a positive correlation and when we havenegative r values as negative, it indicates we have negative correlation. Now, the coefficient ofdetermination that is also known as r square or in some cases you will see there are values ofadjusted r square, it would give the indication of the goodness of the fit. Now, it is the squareof the correlation coefficient that we had seen earlier and it I mean gives us the percentagevariation in the data that is explained by the line of the best fit.
Now, talking about inferential statistics when we have a population huge population, wecannot do a sampling of the entire population. So what we can do is, we can take a sample ofthe population and that sample has to be significant. So what we do in inferential statistics, wetried to see or do the testing of significance. So, this testing of significance is between thedifferent groups that is the we try to measure the degree of difference between the differentsamples in the population. Now, this inferential statistics it helps us to consider the likelihoodof statement about a given parameter.
So, when we are talking about a hypothesis before doing a research, so we bank upon thisinferential statistics to see whether the hypothesis is correct or it is incorrect. So, we talkabout two cases in terms of hypothesis 1 is the null hypothesis and one is the Alternatehypothesis. So when we do this inferential statistics, we can conclude that the if there issignificant difference between the two groups I mean between the statistical parameters of the
two groups that is the mean or the standard deviation if the two groups were significantlydifferent for the population.
So it gives us the null hypothesis and the other one is your alternate hypothesis that is whenthe significant there is a significant difference in the population, it gives the alternatehypothesis and we also have the significance level which is denoted as alpha and it is definedas the probability that null hypothesis is correct and if it is statistically significant I mean it isunlikely that the observation or the sample would have occurred by chance.
So, this is how we use the I mean or we can use your univariate statistics, multivariatestatistics or inferential statistics. So, we have several other matrix in inferential statistics. Firstis the standard error where in we try to measure the confidence interval which is the I meanwhich gives us the sample mean and the population mean difference. So, if this error is small
that means the there is greater confidence that the two means are closer to each other. Now,the standard error is the ratio of standard deviation to the square root of the number of theobservations in the sample.
We also have a measure which is known as t-statistic which assesses the difference betweenthe two sample means. It is calculated using this particular equation which is r into root over nminus 2 divided by 1 minus r square. Now, we also analyse we can also analyse the variationwithin the data columns and between the data columns. So, it can be done using this particularmethod which is known as ANOVA which is analysis of variance.
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So, apart from this we can also I mean find out how your spatial data and aspatial data aredifferent from each other. So, if we run the statistical inferences on spatial data, we can seethat there is a difference between the spatial data sets and the aspatial data sets does. It should
be treated differently, in a way that your the premise when we are dealing with aspatial data,any sort of statistical analysis that we had talked about whether it is univariate, multivariatestatistics in that case the assumption is that there is independence in the observation of thesamples that is the value of an observation is not affected by the other observations in thegiven data set.
But when we are talking about spatial data analysis in real world, we would see thatobservations in the spatial variables in the spatial domain, they are often similar to theneighbouring values. So in a way when we are to analyse the spatial data, we should have adifferent approach, a distinctly different approach than the approach that we use for a spatialdata analysis.
Now, talking about Data Management we can define the each field in the data table where inwe give the field name, we can specify the field length which is the number of digits to bereserved for a field. We can also give the data type whether that data is integer, it is float or itis a text information, whether it is a date or a currency information and we can also give thenumber of decimal digits in case the data is a float data type.
So, I mean we when we are doing this analysis, initially we can start with flat files. So I meanwhen we have more amount of data, then we can get into a relational database. If we have ahuge data set, we can create a relational database and we can it becomes easier to handle insuch a case when we are using the relational database management for handling huge amountof data.
So talking about the different types of attribute data, we have the number text date binary orlarge binary large object which is also known as BLOB data. when we are talking aboutnumbers, we would be dealing with either I mean real numbers, integer numbers. So, we canhave integer values or we can have float values. So, when we are coding the data specially forthe raster type of data, are we have to be very careful about what kind of data set we arecreating because say suppose if you have a float operation and your data type you are definingit as integer, it would discard all the float values.
So, we have to be very careful about the I mean the kind of data that we are handling. So,specifically in case of raster. So, similarly we can have float data. So, the data resolution alsowould come into picture when we are dealing with raster data set. It could be a 2 bit data, itcould be a 4 bit or 8 bit data, 12 bit data depending on the I mean the size of the I meandifference of the highest values and the lowest values.
Now, attribute data is measured by different scales. So, we have different types of attributedata. The first one that we come across is the nominal data which describe the different kindsor categories of data. So, examples of this kind of data could be your land use data or data aresuch a soil data, so where in you give the categories of land use or the categories of soil. Thenext data that we deal with is the ordinal data. So, it I mean differentiates the data by aranking relationship.
So, we can say suppose we have a data set, so we can quantify the intensity like in thisparticular case we are talking about soil erosion. So, whether the erosion is severe ormoderate, we can also talk about proximity matrix like it is very near or far or I mean we canhave different types of measures and rank the relationships. Now, the interval data are theintervals between different values have known intervals, like suppose we can categorise thetemperature data into different groups and we can have group where in we can have a colddata temperature which are normal or comfortable and temperatures which are warmer.
So, we can categorise the data and these are known as interval data. The last one which weoften used for data modelling in GIS is the ratio data and this is the most powerful tool which
we have. So, we can use both integer type of your numerical data or float type data when wework with ratio data sets. So, your I mean it is the ratio basically. So, I mean for an examplewe can talk about the population density in different words which is an example of ratio data.
Now, there are four types of database design whenever we take GIS tasks, we can createdifferent types of database depending on the size of the database. So, if the database is smallwe can create a flat file nomenclature where in we have a single file and the data is arranged ina two dimensional array of data elements. The next one is the hierarchical data in which thedata can be organised in a tree like structure and it implies that there is a single parent for eachrecord.
The next data type is the network data type. So, it is a modification, further modification ofthe hierarchical data set and it embodies many to many relationships in a tree like structure in a
hierarchical structure. So, this data structure or this type of database design it allows formultiple parents. So, if you have leaf nodes you can have multiple parents to those leaf nodes.
The last type for the database design is the relational database which is the most powerful dataI mean database design when you have very big data sets. So, we generally used or relationaldatabase management system to model the entire data to do the designing of the entire datasets. So, I mean it is based on predicate logic and it is based on set theory. So, we have namecolumns of relation which are called attributes and domain and this domain is the sets of valuesof the attributes.
So, we can have database management systems which work in the back end when it handlesyour GIS data sets the attribute data. So, it builds and handles the GIS database. So, theseDBMS tools they provide I mean solutions for data input for search and retrieval for data
handling and for generating output from your queries, your GIS can interact from I mean datafrom multifarious sources.
So, I mean we can connect to remote data bases and this GIS has the capability to access suchdata bases I mean multiple data bases. So to I mean connect this multiple databases, we wouldneed to have a unique field which is known as keys. So, we have a relational database where inwe have collection of tables and they would be connected to each other by a feature id whichis known as keys and the relations are built into it.
There are different types of keys. First is we talk about the primary keys I mean these are theattributes whose values are unique and it can be identified as a record in a table. We also havea foreign key which is one or more attribute that refer to the primary key in another table,another reference table in which some other data sets are available.
We had also talked about the BLOB which is the binary large object which stores of hugeblock of data I mean for example it could be the coordinates of the I mean the points or thelines I mean for I mean generally we store the feature geometries as block files. So, it could bealso images or it could be multimedia data and these I mean files generally store thiscoordinates as binary numbers.
Now, the types of relationships that we have in the database management system could be ofthe four types. The first one is the one-to-one relationship. So, each record in the table isrelated to one and only record, one and only record in another table. So, if we have two tablesit is a one-to-one relationships I mean you do not see multiple connections in this type ofrelationships.
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The next one that is the one-to-many relationship. In this one record of the table is related tomany records in another table. So, you can see for each of these particular records they arerelated to multiple records in other table.
Now, there could be many-to-one relationship. In this many record in the table I mean yourattribute table may be related to one record in another table. So, in this case you have yourattributable table, GIS table and you may have another database where in you see there aremultiple connections from your input database to your to another database another data table.
The next one is many-to-many relationships in which many records in a table would be relatedto many records in another table. So, this is how these two tables are. They would have theiridentifiers or the keys that we have talked about. So, I mean they would be related to eachother in a many-to-many relationship.
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Now, talking about database management system we can join the attribute data I mean we cando a non-spatial join of the attribute table. So if we have multiple attribute table, in this caseyou can see that we have the population tables for different states of India in which we havepopulation, we have the male and the female population, we have the difference between themale and the female and the sex ratio in the first table which has a primary key and in the nexttable, we have the total population which is urban and the total population which is rural wehave the area as well as the density and it has a foreign key.
So, in this in the earlier slide we had talked about the primary key and the foreign key. So, youcan see how they are located and they would be related or in any query or search operation orprocessing further processing these two keys would be related for in a non-spatial join. So, wecan see how we can do a non-spatial join.
So, for merging the attribute data there are few options which are available in GIS softwares.So, most of these packages have got these operations. So, first one is the join operation wherein the two tables using the keys, the common keys is are join and the columns are appendedfrom one table to the another table. So, for the in the input table the I mean it would becomean extended table, where in the all the fields would be appended.
The next one, next way to merge the attribute data is the relate operator, where in ittemporally connects two tables by using the common keys or the fields that we have seen arecommon tool, both the tables. Now, the 3rd one is the spatial join which uses a spatialrelationship to join the two data sets of the spatial features as well as their attribute data. So,we can see an example of spatial data, a spatial join.
So, in our earlier slide we had seen the data pertaining to the population statistics for differentstates of India. So, you can see here a spatial join operation has been done in the blue pi chart,pi you can see that it is the population and the orange one gives you the fraction of the urbanpopulation in the different states. So, you can identify the states where in which has thehighest amount of urban population those two tables where join together using a spatial joinand we can see the output here.
So, recapitulation of what we have covered today, we have talked about UnivariateDescriptive Statistics, where in we had talked about the central tendencies of mean, medianand mode for a univariate data which has only one attribute column. We had then talked aboutmultivariate data analysis, we had talked about inferential statistics, we had talked about thedifferent types of attribute data and then we have finally talked about data management.
We had talked about how we can do the data entry and what are the different types of data. Inthat we had talked about the database design, we had talked about the relational database, thedata operations. So, thank you for your patient hearing till we meet again in the next lecture.
Thanks so much.
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