Session 7th and 8 th ......

Premap :

 Permap is an interactive computer program. It solves problems in up to eight dimensional space and allows boundary conditions to be imposed on the solution, or up to 30 object attribute values which can be used to calculate one of the forgoing types of proximities, and uses multidimensional scaling (MDS) to make a map that shows the relationships between the objects.

The MDS algorithm uses object-to-object proximity information to construct the map.

proximity :  A proximity is some measure of likeness or nearness, or difference or distance, between objects. It can be either a similarity (called a resemblance in some disciplines) or a dissimilarity. If the proximity value gets larger when objects become more alike or closer in some sense, then the proximity is a similarity. If the opposite is the case, the proximity is a dissimilarity.

      Difference between a perceptual map and any ordinary map :

Usually, a perceptual map is taken to be a map  that involves object-to-object relationships which       are not amenable to simple and physical measurement.

Z-Score :

A z-score (aka, a standard score) indicates how many standard deviations an element is from the mean. A z-score can be calculated from the following formula.

z = (X - μ) / σ

where z is the z-score, X is the value of the element, μ is the population mean, and σ is the standard deviation.

Standard deviation(σ) :  shows how much variation or dispersion exists from the average mean, or expected value. A low standard deviation indicates that the data points tend to be very close to the mean; high standard deviation indicates that the data points are spread out over a large range of values.

Example:  

Scores: 4,5,5,4,4,2,2,6

Where M is the mean

x	(x-M)2
4	0
5	1
5	1
4	0
4	0
2	4
2	4
6	4
M = 4	S(x-M)2 = 14
SD = 1.32

Why Z- score is required : while analyzing the trend of certain data and if the value of certain object is very large then usually the result tend to shift towards the larger value so in order to avoid this normalization of large values is to be done . and to do so we use Z-score technique.

Properties of z-score

1>    Z-Score always has a mean value of 0 and  standard deviation equals to 1.

2>    It will not change the original distributionof data.

 How to interpret z-scores.

•        z-score less than 0 represents an element less than the mean.
•       z-score greater than 0 represents an element greater than the mean.
•      z-score equal to 0 represents an element equal to the mean.
•     z-score equal to 1 represents an element that is 1 standard deviation greater than the mean; a z-score equal to 2, 2 standard deviations greater than the mean; etc.
•     z-score equal to -1 represents an element that is 1 standard deviation less than the mean; a z-score equal to -2, 2 standard deviations less than the mean; etc.
•     If the number of elements in the set is large, about 68% of the elements have a z-score between -1 and 1; about 95% have a z-score between -2 and 2; and about 99% have a z-score between -3 and 3.

2^nd session we studied about making and analyzing bubble graphs in PASW statistics viewer:

PASW Statistic is a comprehensive system for analyzing data. PASW Statistics can take data from almost any type of file and use them to generate tabulated reports, charts, and plots ofdistributions and trends, descriptive statistics, and complex statistical analyses.

Bubble graph :

•     Three values per data point     Three values are required for each bubble. These values can be in rows or columns on the worksheet, but they must be in the following order: x value, y value, and then size value.
•     Negative values     Bubble sizes can represent negative values, although negative bubbles do not display in the chart by default. You can choose to display them by formatting that data series. When they are displayed, bubbles with negative values are colored white (which cannot be modified) and the size is based on their absolute value. Even though the size of negative bubbles is based on a positive value, their data labels will show the true negative value.
•     Multiple data series     Plotting multiple data series in a Bubble chart (multiple bubble series) is similar to plotting multiple data series in a Scatter chart (multiple scatter series). While Scatter charts use a single set of x values and multiple sets of y values, Bubble charts use a single set of x values and multiple sets of both y values and size values.

 Example :

 the worksheet in the following picture contains values for three types of data: number of products, dollar value of sales, and percentage size of market share.

In a Bubble chart, the size of the bubbles is determined by the values in the third data series. For example, the following Bubble chart displays bubble sizes that correspond to the values in the third column of the sample data (Market share %).

with this we end our 7and 8th session.

Submitted by : Neha Gupta

Group Member :

Raghav Bhatter

Prachi kasera

Parthajit

Neha Gupta 

Nitesh Beriwal