processing and analysis

1. Chapter-7
Processing and Analysis of Data

2. Processing of Data
Processing: The Processing of data is an
arrangement and management of data so
that it is ready for analysis to fulfill the
objectives of the research.

3. Processing Operations
There are four processing operations:
(i) Editing: It is a process of examining the
collected raw data to detect errors and
omissions and to correct these when
possible.
(ii) Coding: It refers to the process of
assigning numerical figures or other
symbols to answer the responses of
interviewee.

4. Processing Operations (cont.)
(iii) Classification: Most of the research studies result in a
large volume of raw data. It must be reduced into
homogeneous groups to get meaningful relationship.
This fact necessitates of arranging data in groups of
classes on the basis of common characteristics.
There are various classifications, such as:
(a) One-way classification
(b) Two-way classification
(c) Three-way classification
and so on..

5. Processing Operations (cont.)
(iv) Tabulation: When a mass of data has been
assembled, it becomes necessary for the researcher to
arrange the same in some kind of concise and logical
order. This procedure is referred to as tabulation. Thus,
tabulation is the process of summarizing raw data and
displaying the same in compact form for further analysis.
A table is complete one when the following information are
available:
(a) Title of the table
(b) Sub-heading of the table
(c) Entry in the table
(d) Source of information

6. Statistical Analysis
• Central Tendency & its Measures:
– Mean( AM, GM & HR)
– Median
– - Mode
• Dispersion and its Measures :
– Range,
– Mean deviation,
– Standard Deviation,
– Quartile deviation,
– Coefficient of Variation.
• Skew ness and Kurtosis
• Measures of Relationship
– Correlation
– Simple Regression Analysis
– Multiple Correlation and
– Multiple Regression
– Partial Correlation
– Association in Case of Attributes

7. Statistical Analysis -cont
• Probability :
• Probability distribution
– Binomial distribution
– Poisson distribution
– Normal distribution
• Sampling Distribution
– Z statistic
– T statistic
– X2 statistic
– F statistic

8. Statistical Analysis -cont
• Test of Hypothesis
– Hypothesis
– Test
– Test of hypothesis
– Degrees of freedom
– Type I & Type II Error
– Level of Significance
– Acceptance Region
– Critical Region
– One & Two sided Test

9. Test of Hypothesis
• Hypothesis: The assumption or assertion about the
Population Characteristic (Parameter) is called a
hypothesis.
• Test: Test is a body (set ) of rules which is used to
decide whether the hypothesis is true or false.
• Rules:
• i) Develop a test statistic ( Z, t, F etc )
• Ii) Calculate the Value of Test Statistics using
sample data.
• Iii) Find out tabulated value of the test statistic for
certain level of significance and for required
degrees of freedom
• Iv) If the calculated value of test statistic is
greater than or equal to the tabulated value of
the test statistic we may reject the Ho
otherwise the Ho. is accepted.

10. Level of Significance
• Type-I error: Reject Ho: when it is true.
• Type-II error: Accept Ho: when it is false.
• Level of significance : The probability of
type- I error ie The probability of
rejecting a Ho. when it is true
• Power of the Test: The probability of
rejecting a Ho. when it is false.
• Degrees of freedom (df): It is the no. of
independent variables involve in a
relation ( test statistic).

11. Types of Hypothesis
• Parametric hypothesis
The parametric hypothesis refers to the assumption
about parameters. As for example
H :m =m
0 0 • Non-parametric hypothesis
Again the Non parametric hypothesis refers the
assumptions about the distribution.
For example Ho. The distribution of marks follows
normal distribution
0

12. s 2222
• Null VS Alternative Hypothesis
s 2
• Null Hypothesis:
• The hypothesis which is to be tested in the
research is called null hypothesis.
• As for example Ho; μ = 0
• Alternative Hypothesis:
It is other than null hypothesis
• As for example Ho; μ ≠ 0

13. Mean Test
i) Single Mean test for known variance
Let x1, x2, x3, - - - - xn be a random sample from
a normal population with mean μ and variance σ2,
test the Ho: μ = μ0.; when variance is known.
0
m -
0s
We can test the above Ho Using Z statistic
Where
n
Z x
0
=

14. Mean Test Cont
ii) Single Mean test for unknown variance
Let x1, x2, x3, - - - - xn be a random sample
From a normal population with mean μ and
variance σ2, test the Ho: μ = μ0. ;when
variance is unknown.
We can test the above Ho Using t statistic
Where
x Z 0 m -
s
n
=
þ ý ü
î í ì
x x
å - å
-
=
n
n
s
2
2 ( )
1
1

15. Mean Test Cont.
iii) Double Mean test for known
& equal/unequal variance
Let x1, x2, x3, - - - - xn be a random sample
from a normal population with mean μx and
variance σx
2 and Let y1, y2, y3, - - - - yn be
another random sample from a normal
population with mean μy and variance σy
2,
test the Ho: μx = μy.

16. We can test the above Ho Using Z statistic
Where ( - m ) - ( -
m
)
x y
s s
2
2
x y
2
n n
1
Z
x y
+
=

17. Double Mean Test
iii) Double Mean test for unknown variance
Let x1, x2, x3, - - - - xn be a random sample
from a normal population with mean μx and
variance σx
2 and Let y1, y2, y3, - - - - yn be
another random sample from a normal
population with mean μy and variance σy
2,
test the Ho: μx = μy.

18. We can test the above Ho Using t- statistic
Where ( x - ) - ( y
-
)
t x y
. 1 1
n n
1 2
s
+
=
m m
ù
ú úû
é
ê êë
þ ý ü
î í ì
y y
+ å - å
þ ý ü
î í ì
x x
å - å
+ -
=
2
2
2
1
2
2
1 2
( ) ( )
2
1
n
n
n n
s

19. Single Variance Test
• Let x, x, x, - - - -xbe a random sample
123n from a normal distribution with mean μ
variance σ2 .
• To test the Ho: σ2= σ2 We can use the test
0
c2 ( )
statistics , where
c = å x - x
2
0
2
2
s

20. Double variance test
Let x1, x2, x3, - - - - xn be a random sample
from a normal population with mean μx and
variance σx
2 and Let y1, y2, y3, - - - - yn be
another random sample from a normal
population with mean μy and variance σy
2,
2 = σy
test the Ho: σx
2

21. • We can test the above Ho; using F
statistics, where
2
1
s
2
2
F =s
þ ý ü
î í ì
y y
å - å
-
=
þ ý ü
î í ì
x x
å - å
-
=
2
2
2
2
2
2
1
2
2
1
2
1
( )
1
( ) . 1
1
1
n
n
and s
n
n
s

22. Test of Association
• Contingency Table: A two way classified
data is called a contingency table if at
least one of the variable is qualitative.
• The relation between two qualitative
variables( Attributes) is called association.
The association of attribute of a contingency
table can be tested using χ2 statistics

23. • Where χ2 = Σ(O2/E) - N
• O: Observed frequency
• E : Expected frequency
• N : Total no. of observation.
• df of χ2 : (r-1)(c-1)

24. Test of Association
for 2x2 Contingency Table
Sex
Res
M F Total
U a b a+b
R c d C+d
Total a+c b+d N= a+b+c+d

25. Test of Association
• We can test the association of the above
2x2 contingency table using χ2 statistic
• Where
χ2 = N (ad - bc)2 / [(a+c) (b+d) (a+b) (c+d)]
df of χ2 is (r-1)c-1) = 1