Lecture 5
Data analysis
Charts and Graphs
Data can be shown by charts and graphs in addition to the text and tables. Although the text and
tables are useful for explaining and interpretation, charts and graphic illustration may add to the
value of information because they provide information to the reader in a glance. Due to
availability of computer software, it is now very easy and quick to make these charts and graphs.
There are many kinds of charts that can be used in data analysis, but we will mention only three
types which are more common: Pie chart, Line chart (graph), Bar chart.
Pie Chart
Pie chart is probably the most familiar chart used in representing quantitative data. A pie chart is
simply a circle divided into sections, with each of the sections representing a portion of the total.
As the sections are presented as part of the whole, pie chart is particularly more useful in
showing relative size. Pie chart is prepared for categorical data.
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Example
Share of market of different brands of mobile phone sets.
A pie chart can have many sections or slices, but it is recommended that no more than six sections
should be generated in a pie.
Example
In order to determine the significant source of business,WR hotel examined the check- in cards
of 1000 customers randomly. They found the following break-up of data.
Individual travelers
230
Tour groups
125
Business travelers
378
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Government officials
143
Others
124
Total
1000
Solution
Line Chart or Graph
Pie chart is one scale chart. It is best used for static comparison that is the phenomenon at one
time. The bar chart is having two dimensions one of which usually is the time. It shows dynamic
relation of the changes with time such as time series fluctuations. In the chart X-axis represents
time and Y-axis, the values of the variables. More than one variable can be plotted on the same
graph but each variable is represented by different lines in different colors or form (dashes or dots)
with explanations in the legend at the bottom of the graph.
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Example
Year
S
T
Y
2000
4.3
3.2
5.2
2001
4.8
4.2
6
2002
6
5
6.2
2003
5.8
3.1
6.8
2004
7.2
3.7
7.5
2005
4.6
4.1
6
2006
6
5.1
7
2007
7.5
5.4
8.5
25
20
15
Y
T
10
S
5
0
2000
2001 2002
2003
2004
2005
2006
2007
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In a bar chart, each category is depicted by a bar, vertical or horizontal. The length or height of
the bar shows the frequency or percentage of observations falling into a category. The lengths or
heights of different bars allow the user to compare the magnitudes of different categories easily.
Example
The expansion of a bank in terms of opening of new branches from 2001 to 2007 was as follows
Years
Values
2001
15
2002
28
2003
14
2004
21
2005
19
2006
23
2007
25
30
25
20
15
Series1
10
5
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0
2001
2002
2003
2004
2005
2006
2007
Variation in Bar Chart
Bar chart has variation. Pictures can be used instead of bars e.g people for population, pictures
of cars of automobile production, and piles of 1000 rupees note for sales. Another variation of
bar chart used frequently is grouped bar chart where more than one category can be captured and
can be compared side by side in different colours. Let us again take the data of split air
conditioners as given in the line graph.
Example
A survey of retail sales of split air conditioners of 3 brands S,T,Y from 2000 to 2007, revealed
the following values in million of rupees.
Sales of split air conditioners in million of rupees
Year
S
T
Y
2000
4.3
3.2
5.2
2001
4.8
4.2
6
2002
6
5
6.2
2003
5.8
3.1
6.8
2004
7.2
3.7
7.5
2005
4.6
4.1
6
2006
6
5.1
7
2007
7.5
5.4
8.5
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Data analysis
Hypothesis Testing
Hypothesis is educated guess, a tentative statement about the relationship between two or
more variables.
It is to be empirically tested and be stated before the marketing project begins.
Hypotheses must be formally stated. These are focal points for researchers in
marketing. Hypotheses may be in operational (general) terms or null and alternative
forms.
Null and Alternative Form of Hypothesis
Testing of hypothesis usually begins with stating the hypothesis in a null and alternative form.
For example, we might want to see whether mean age of a class of consumer is 30 years. In this
case The null hypothesis (Ho) will be
Ho:µ=30
We can write the null and alternative hypothesis
as: Ho:µ=30
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H1:µ≠30
One tailed and two tailed test
Previous example of alternative hypothesis is two tailed as we will reject the null hypothesis if
the mean age was lesser or greater than 30.
Another alternative hypothesis in this situation could be that the mean age is greater than 30.
In this case we would write null and alternate form of hypothesis as:
Ho:
µ=30
H1:
µ>30
Here the hypothesis is one tailed as we have a specific direction in mind for the
alternative hypothesis. We can also phrase the null hypothesis to cover a range of values.
For example,
Ho: µ≤30
Which implies an alternative hypothesis
H1: µ>30
Here again one tailed test would apply.
The researcher should be careful to phrase the alternative hypothesis in a way as to accept the
alternative hypothesis that is of real interest if null hypothesis is rejected. One-Tailed or TwoTailed Test
Defective parts are more than 2 % - One-tailed
Sales returns are less than 4% p.m.-One-tailed
Within one per cent of the mean –
Between 5% and 6%
two-tailed
_ two-tailed
We use one and two- tailed concept when we look critical values in the probability
tables. We should have this concept clearly we that we can look into the appropriate
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table.
Steps in Hypothesis Testing
Following steps are usually followed in hypothesis testing:
·
Formulate a null and alternative hypothesis
·
Specify the significance level
·
Select the appropriate statistical technique according to the nature and type of
data collected
·
Perform the statistical test applying the technique above
·
Look for the value of test statistics (critical value) in the relevant standard normal table
on the confidence level as specified in step # 2 above.
·
Compare the value of statistics as calculated in step #4 with critical value and accept
or reject the hypothesis.
·
At the end researcher draws conclusion.
Different Statistical Tests
Which statistical technique or test to select for our analysis or hypothesis testing depends on our
objectives of research project. Objectives may be translated into research questions and/or
research hypotheses.
There are many statistical tests and techniques which are used in data analysis in
marketing research. Some of them are described in the next lectures in detail.
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