The Class started with the introduction of PERMAP which was alien initially but as the session progressed we understood the significance of this software.
PERMAP
is an interactive program for making perceptual maps. The program,
PERMAP, uses conventional metric multidimensional scaling techniques. That is,
it uses pairwise numerical values (correlations, proximities, dissimilarities,
etc.) to construct a map showing the relationship between objects. A unique
feature of PERMAP is that it embeds the mapping techniques in an interactive,
graphical system that minimizes several difficulties associated with
multidimensional scaling practices. It is particularly effective at exposing artefacts
due to local minima, incomplete convergence, and the effects of outliers. It
can associate various attributes with the resultant groupings and provide
line-linking options to help the researcher identify the nature of perceived
relationships. Problems involving multiple matrices can be treated using three
different aggregation methods. The optional use of weighting factors is
available.
Its fundamental
purpose is to uncover any "hidden structure" that might be residing
in a complex data set. PERMAP takes
object-to-object proximity values (similarities,
dissimilarities, correlations, distances, interactions, psychological
distances, dependencies, confusability, preferences, joint or conditional
probabilities, etc.), or up to 30
object attribute values, and uses multidimensional scaling (MDS) to make a map
that shows the relationships between the objects. Succinctly, it makes
classical metric and nonmetric MDS analyses in one, two, three or eight
dimensions, for one-mode two-way or two-mode two-way data, with up to 1000
objects and with missing values allowed. In addition, it can make several new
types of MDS analyses involving error bounds or boundary conditions and it can
show the effect of degrading the similarity information.
Then we were introduced the term Z Scores
Z-Scores:
Sometimes we want to do
more than summarize a bunch of scores. Sometimes we want to talk about particular
scores within the bunch. We may want to tell other people about whether or not
a score is above or below average. We may want to tell other people how far
away a particular score is from average. We might also want to compare scores
from different bunches of data. We will want to know which score is better.
Z-scores can help with all of this.
Z-Scores tell us whether a particular score is equal to the mean, below
the mean or above the mean of a bunch of scores. They can also tell us how far
a particular score is away from the mean. Is a particular score close to the
mean or far away?
Interpreting Z Scores
If a Z-Score….
- Has a value of 0,
it is equal to the group mean.
- Is positive, it is
above the group mean.
- Is negative, it is
below the group mean.
- Is equal to +1, it
is 1 Standard Deviation above the mean.
- Is equal to +2, it
is 2 Standard Deviations above the mean.
- Is equal to -1, it
is 1 Standard Deviation below the mean.
- Is equal to -2, it
is 2 Standard Deviations below the mean.
Z-Scores
can help us understand how typical a particular score is within bunch of scores.If data are normally distributed,
approximately 95% of the data should have Z-score between -2 and +2. Z-scores
that do not fall within this range may be less typical of the data in a bunch
of scores.
Z-Scores
can help us compare individual scores from different bunches of data. We can use
Z-scores to standardize scores from different groups of data. Then we can
compare raw scores from different bunches of data.
Normal Distribution and Skew Distribution were the concepts we learnt next...
Normal
Distribution:
A probability distribution that plots all of
its values in a symmetrical fashion and most of the results are situated around
the probability's mean. Values are equally likely to plot either above or below
the mean. Grouping takes place at values that are close to the mean and then
tails off symmetrically away from the mean.
The normal distribution is the most common type
of distribution, and is often found in stock market analysis. Given enough
observations within a sample size, it is reasonable to make the assumption that
returns follow a normally distributed pattern, but this assumption can be
disproved.
Data can be "distributed"
(spread out) in different ways.
Or it can be all jumbled up
But there are many cases where the data tends to be around a
central value with no bias left or right, and it gets close to a "Normal
Distribution"
And the yellow histogram shows some data that follows it closely, but not perfectly
(which is usual).
It is often called a "Bell Curve"
because it looks like a bell.
The Normal Distribution has:
mean = median = mode
50% of values less than the mean and
50% greater than the mean
Data can be
"skewed", meaning it tends to have a long tail on
one side or the other.
Negative Skew No Skew Positive Skew
It
is called the Negative Skew because the long "tail" is on the
negative side of the peak. It is referred as "skewed to the left"
(the long tail is on the left hand side)
Positive Skew
Positive skew is when the long tail is on the positive side
of the peak, and it is referred as "skewed to the right”. The mean is on
the right of the peak value.
A Normal Distribution is not skewed. The Normal Distribution has No
Skew.
It is perfectly symmetrical.
And the
Mean is exactly at the peak.
Calculating Skewness
"Skewness" (the amount of skew) can be calculated, for
example you could use the SKEW() function in Excel or Open Office Calc.
Before the 7th Session ended we learnt concepts about Mean, Variance and Standard Deviation.
Mean:
The mean is just the average of
the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are.
Variance:
The Variance is defined as the average of the squared differences of the
mean
To calculate the variance follow
these steps:
- Work out the Mean (the
simple average of the numbers)
- Then for each number:
subtract the Mean and square the result (the squared difference).
- Then work
out the average of those squared differences.
Standard Deviation:
The Standard
Deviation is a measure of how spread out numbers are. Its symbol is σ (the Greek
letter sigma). The formula is easy: it is the square root of
the Variance.
In the 8th Session we learnt about Bubble Graphs and developing Bubble Graphs using Excel.
Bubble Graphs:
Bubble charts
or bubble graphs are extremely useful graphs for comparing the relationships
between data objects in 3 numeric-data dimensions: the X-axis data, the Y-axis
data, and data represented by the bubble size. Essentially, bubble charts are
like XY scatter graphs except that each point on the scatter graph has an
additional data value associated with it that is represented by the size of a
circle or “bubble” centered on the XY point.
Bubble Chart: This
chart shows the relationship between “Profit” (Y-Axis), “Cost” (X-Axis), and
“Probability of Success (%)” (Bubble Size).
Bubble
Charts in Business:
Bubble
charts are often used in business to visualize the relationships between
projects or investment alternatives in dimensions such as cost, value, and
risk. By visualizing project portfolios using bubble charts, you can find
clusters of relatively attractive projects in one area of the graph, such as
areas of high value, low cost, and/or low risk, and compare them with
relatively less attractive projects in a different area of the graph, such as
an area of low value, high cost, and/or high risk.
Differentiating Bubbles in Bubble Charts
Bubbles are usually
differentiated by colour, pattern, number labels, or a combination of these. Colours
are usually adequate for small numbers of bubbles, but subtle differences in colours
become difficult to distinguish in larger number of projects. Therefore,
numbers corresponding to a chart legend becomes a more useful method of
distinguishing bubbles.
The session was very interesting and ended with watching a video from TED where the presenter Hans Rolling explained when India and China would catch up with US and UK economy using Bubble Graphs..
Written by
Pakala Kalyani
Group Members:
1. Nishidh Vilas Lad
2. P.Priyatham Kireeti
3. Kartheeki
4. Priyadarshi Tandon
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