Transcript Empirical Notes 1 20/04/2016 File

Research in business studies
Department of Business Administration
SPRING 2016-17
MGMT 434
Empirical Lecture Notes 1
Reference chapters 6, 7,8,9 and 10 - Ghauri and Gronhaug-2010, 4. Ed.
by
Prof. Dr. Sami Fethi
Research Methods in Business Studies
© 2011/12, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2010, 4. Ed.
Research in business studies
Empirical Questions
 Examples and Solutions
2
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Research in business studies
Why collect data ?
 Managers need reliable information to make decisions
about the running of their organizations. This
information is provided by data collection and
processing.




Initially, data are raw materials.
Having processed, transformed into information.
Managers need information before they can make decisions.
Managers should examine all available information before
making decision.
 Managers should have enough information to allow good
decisions.
 The information should be reliable.
 The information is provided by data collection and analysis.
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Time and quantity of data collection
 Data collection is expensive so it is sensible to decide
what the data will be used for before they are collected.
In principle, there is an optimal amount of data which
should be collected. These data should be as accurate
as possible.
 Data collection should be designed.
 Before deciding the use of data, it should be analysed.
 Data collection and processing inevitably costs money.
 Collecting unnecessary data mislead users.
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Type of data
 Data of different types can be collected in different
ways. There are several classifications of data,
including quantitative, qualitative, nominal, ordinal,
cardinal, discrete, continuous, primary and secondary.
 Nominal data-categorical data- i.e. man and women
 Ordinal data-ranking data- i.e. Primary, secondary
graduates
 Cardinal data- order (ranking) and equal distance
 Interval data- continuous data- i.e. 777.78
 Ratio Scale- comparison of absolute magnitude of
data- i.e. 2/4
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Example: type of data
Data type:
nominal
ordinal
cardinal
Uncompiled (original measurement list in order of observations, = "raw data")
red
third
3
green
first
1
red
third
3
blue
second
2
green
first
1
Compiled, with frequencies (ordered list)
2 x green
2 x first
1 x blue
1 x second
2 x red
2 x third
interval
1.6
2.4
1.6
5.1
1.2
2x1
1x2
2x3
1 x 2.4
1 x 5.1
2 x 1.6
1 x 1.2
1
2
3
2.4
5.1
1.6
1.2
Compiled
green
blue
red
Research Methods in Business Studies
first
second
third
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Charesteristic of level of measurement
Scale
Difference
Rank
Distance
Origin point
Method
Test
Nominal
√
−
−
−
Mode
x2
Ordinal
√
√
−
−
Median
Spearman
Interval
√
√
√
−
Arith.Mean
T and F
Ratio
√
√
√
√
Goe. Mean
T and F
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Example: Design of questionnaires
 If reasonable data set are not available, an
organization must use primary data. Most data
collection uses a questionnaires. It is therefore
important to design questionnaires carefully and after
a great deal of thought.
 Let us design a questionnaire. See sample of a
questionnaire
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Research in business studies
Example: Design of questionnaires
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Example: Mean-Arithmetic mean
 It is obtained by adding all the data values and
dividing by the number of items.
 Example: Let us consider the following class-size
data for a sample of five college classes-46, 54,
42, 46, 32. Compute the sample mean.
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Example: Median
Research in business studies
 If there is an odd number of items, the median is the
value of middle item when all items are arranged in
ascending order. If there is an even number of items,
the median is the average value of the two middle
items.
 Example: Let us consider the following class-size
data for a sample of five college classes-46, 54,
42, 46, 32. Compute the median.
 32, 42, 46, 46, 54- n=5 and median is 46.
 Example: considering the following numbers; 32,
42,46,48, 49, 54.
 n=6 and median
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Example: Mode and Range
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 The mode is the data that occurs with greatest
frequency.
 Example: Let us consider the following class-size
data for a sample of five college classes-46, 54,
42, 46, 32, 48, 46, 54. Compute the mode.
 32, 42, 46, 46, 46, 48, 54 and mode is 46.
 Range is the difference between largest value and
smallest value
 Example: 2825, 2210, 2320 and 2450
 R= 2825-2210=615.
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Research in business studies
Example: Percentile
 A percentile provides information about how the data
items are spread over the internal from smallest to
the largest value.This can be calculated as follows:
o Step1: arrange the data in ascending order
o Step2:compute the index i- i=(P/100)*n
o Step3: (a) if i is not an integer, round up to the next
one. (b) if i is an integer, the pth percentile is the
average of the data values i and i+1.
 Example: Let us consider the following numbers2210, 2255, 2350, 2380, 2380, 2390, 2420, 2440,
2450, 2550, 2630, 2850.
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Research in business studies
Example: Percentile
 Example: Let us consider the following numbers2210, 2255, 2350, 2380, 2380, 2390, 2420, 2440,
2450, 2550, 2630, 2850.
 Find the 85th percentile for the data set provided.
 First we need to ararange the data in ascending
order.
 We need to use index formula i=(P/100)*n- n=12
 i=(P/100)*n= (85/100)*12=10.2≈11 and the number is
2630.
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Example: Mean
 A quality control inspector found the following numbers
of
defective
parts
on
16
different
days11,14,18,14,21,17,13,21,25,19,17,13,28,13,17,18.
 (a) Find the mean (b) compute the median (c) calculate the
mode (d) compute 90th percentile. Do not forget to put data
in ascending order.
 (a) mean
 (b) median is av. Of 8. and 9. ((17+17)/2)=17
 (c) mode is 13 and 17 cause they occur 3 times. Data is
bimodal.
 (d) i=(P/100)*n= (90/100)*16=14.4≈15 and the number is
25.
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Research in business studies
Example: Range
 A quality control inspector found the following numbers
of defective parts on 4 different days- 2825, 2210,
2320, 2450.
 (a) Find the range
 (2825-2210)=615
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Research in business studies
Example: Variance
 It is a measure of dispersion that utilizes all the data
values. The variance is based on the difference
between each data value and mean. The is called a
deviation about the mean.
 Example: use the following data and calculate its
sample variance.
number of students in a class (x)
46
54
42
46
32
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Research Methods in Business Studies
S
2
(x


i
 x)
2
n 1
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Research in business studies
Example: Variance
 The variance can be though as a useful measure in
comparing the amount of dispersion in two or more
data sets (i.e. The larger variance has the most
dispersion).
S2= 256/4=64
number of students in a class (x)
mean
Deviation from the mean
sq( Deviation from the mean)
46
44
2
4
54
44
10
100
42
44
-2
4
46
44
2
4
32
44
-12
144
0
256
SUM
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Example: Standard Deviation
 It is defined to be positive square root of variance.
σ= √S2= √256/4=8
Std. Dev is measured in the same units as original data.
For this reason, this is more easily compared to mean
and the other statistics. This is used most widely measure
of spread.
number of students in a class (x)
mean
Deviation from the mean
sq( Deviation from the mean)
46
44
2
4
54
44
10
100
42
44
-2
4
46
44
2
4
32
44
-12
144
19
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SUM
0
256
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Coefficient of Variation
 This measures the Std. Dev relative to mean.
CoVar = (8/44)*100= 18.2%
The figure calculated shows that std. dev of the sample is
18.2% of the sample mean value.
number of students in a class (x)
mean
Deviation from the mean
sq( Deviation from the mean)
46
44
2
4
54
44
10
100
42
44
-2
4
46
44
2
4
32
44
-12
144
20
SUM
Research Methods in Business Studies
0
256
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Research in business studies
Example
 The scores for six games were 182, 168, 184, 190, 170
and 174. Using the relevant data as a sample and
compute the followings.
a) Range b) Variance c) std dev. d) CoVar
Number
mean
dev from mean
sq dev from mean
182
178
4
16
168
178
-10
100
184
178
6
36
190
178
12
144
170
178
-8
64
174
178
-4
16
sum
376
a)
largest-smallest
190-168
12
b)
variance
376/6-1
75.2
c)
std. dev
sqroot ( 75.2)
8.67
d)
CoVar
(8.67/178)*100
4.87
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Research in business studies
Covariance
 so far we have seen examined and discussed
numerical method that are used to summarize the data
for one variable at a time. Now we will analyze
covariance and correlation as descriptive measure of
relationship between two variables.
 The mean is the most widely used measure of location,
however St.dev and Var are the most widely used of
dispersion.
S xy 
 ( xi  x ) ( yi  y )
n 1
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rxy 
 x y  (( x  y ) / n)
 x  (( x ) / n )  y  (( y ) / n )
i i
2
i
i
2
i
i
2
i
2
i
22
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Research in business studies
Example
 The datum shows volume of sales and advertisement
expenditures. Using the relevant data as a sample and
compute the followings.
Midterm-subject
a) covariance b) corelation coefficient
sales (x) ad.expd (y) mean (x) Mean (y) x-xmean y-ymean sq (y-ymean) sq (x-xmean) (x-xmean) (y-ymean)
2
50
3
51
-1
-1
1
1
1
5
57
3
51
2
6
4
36
12
1
41
3
51
-2
-10
4
100
20
3
54
3
51
0
3
0
9
0
4
54
3
51
1
3
1
9
3
1
38
3
51
-2
-13
4
169
26
5
63
3
51
2
12
4
144
24
3
48
3
51
0
-3
0
9
0
4
59
3
51
1
8
1
64
8
2
46
3
51
-1
-5
1
25
5
30
510
30
510
0
0
20
566
99
Research Methods in Business Studies
SUM
23
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Research in business studies
Example-CV and CC
S xy
xy
Sq(x)
Sq(y)
100
4
2500
285
25
3249
41
1
1681
162
9
2916
216
16
2916
38
1
1444
315
25
3969
144
9
2304
236
16
3481
92
4
2116
1629
110
26576
(x  x) ( y  y)


i
i
n 1
rxy 
Midterm-subject
SUM
 x y  (( x  y ) / n)
 x  (( x ) / n )  y  (( y ) / n )
i i
2
i
i
2
i
i
2
i
2
i
 Sxy=99/9=11
 rxy=1629-(30)((510/10))/√(110- (302/10))(√26576-(5102/10))
= 0.93
Research Methods in Business Studies
24
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Research in business studies
Example-CV and CC
 Sxy=99/9=11
 rxy=1629-(30)((510/10))/√(110- (302/10))(√26576-(5102/10))
= 0.93
 The coefficient of variation is useful because the
standard deviation of data must always be understood
in the context of the mean of the data. In contrast, the
actual value of the CV is independent of the unit where
the measurement has been taken, so it is a
dimensionless number. For comparison between data
sets with different units or widely different means, one
should use the coefficient of variation instead of the
standard deviation.
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Example-CV and CC
 Sxy=99/9=11
 rxy=1629-(30)((510/10))/√(110- (302/10))(√26576-(5102/10))
= 0.93
The coefficient of variation is useful because the standard
deviation of data must always be understood in the context of the
mean of the data. In contrast, the actual value of the CV is
independent of the unit where the measurement has been taken,
so it is a dimensionless number. For comparison between data
sets with different units or widely different means, one should use
the coefficient of variation instead of the standard deviation. When
the mean value is close to zero, the coefficient of variation will
approach infinity and is therefore sensitive to small changes in the
mean. Unlike the standard deviation, it cannot be used directly to
construct confidence intervals for the mean.
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Example-CV and CC
 Sxy=99/9=11
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Midterm-subject
 rxy=1629-(30)((510/10))/√(110- (302/10))(√26576-(5102/10))
= 0.93
Covariance and correlation describe how two variables are related.
Variables are positively related if they move in the same direction.
Variables are inversely related if they move in opposite directions.
Both covariance and correlation indicate whether variables are
positively or inversely related. Correlation also tells you the degree
to which the variables tend to move together.
You are probably already familiar with statements about
covariance and correlation that appear in the news almost daily.
For example, you might hear that as economic growth increases,
stock market returns tend to increase as well. These variables are
said to be positively related because they move in the same
direction. You may also hear that as world oil production increases,
gasoline prices fall. These variables are said to be negatively, or 27
inversely, related because they move in opposite directions.
Research Methods in Business Studies
© 2011/12, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2010, 4. Ed.
Example-CV and CC
Research in business studies
 Sxy=99/9=11
 rxy=1629-(30)((510/10))/√(110- (302/10))(√26576-(5102/10))
= 0.93
 Correlation is another way to determine how two variables
are related. In addition to telling you whether variables are
positively or inversely related, correlation also tells you the
degree to which the variables tend to move together.
 covariance measures variables that have different units of
measurement. Using covariance, you could determine
whether units were increasing or decreasing, but it was
impossible to measure the degree to which the variables
moved together because covariance does not use one
standard unit of measurement. To measure the degree to
which variables move together, you must use correlation.
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 Sxy=99/9=11
Example
Research in business studies
 rxy=1629-(30)((510/10))/√(110- (302/10))(√26576-(5102/10))
= 0.93
Correlation standardizes the measure of interdependence between
two variables and, consequently, tells you how closely the two
variables move. The correlation measurement, called a correlation
coefficient, will always take on a value between 1 and – 1:
•If the correlation coefficient is one, the variables have a perfect
positive correlation. This means that if one variable moves a given
amount, the second moves proportionally in the same direction. A
positive correlation coefficient less than one indicates a less than
perfect positive correlation, with the strength of the correlation
growing as the number approaches one.
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 Sxy=99/9=11
Example
Research in business studies
 rxy=1629-(30)((510/10))/√(110- (302/10))(√26576-(5102/10))
= 0.93
•If correlation coefficient is zero, no relationship exists between the
variables. If one variable moves, you can make no predictions
about the movement of the other variable; they are uncorrelated.
•If correlation coefficient is –1, the variables are perfectly
negatively correlated (or inversely correlated) and move in
opposition to each other. If one variable increases, the other
variable decreases proportionally. A negative correlation coefficient
greater than –1 indicates a less than perfect negative correlation,
with the strength of the correlation growing as the number
approaches –1.
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Example
Research in business studies
 Sxy=99/9=11
 rxy=1629-(30)((510/10))/√(110- (302/10))(√26576-(5102/10))
= 0.93
• In our case, a large positive value indicates a strong relationship
between sales volume and advertise expenditures base on the
correlation formula.
The covariance between sales volume and advertise expenditures
is 11. Since the covariance is positive, the variables are positively
related base on the covariance formula.
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Example- CV and CC
 The datum shows GPA grade point average and SAT
mathematics test scores for a six local schools. Using the
relevant data as a sample and compute the followings.
GPA
SAT
2.7
450
3.5
560
3.7
700
3.3
620
3.6
640
3
570
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Example- CV and CC
 The datum shows GPA grade point average and SAT
mathematics test scores for a six local schools. Using the
relevant data as a sample and compute the followings.
a) develop a scatter diagram with GPA on the horizantal axis
b) covariance
c) corelation coefficient
d) briefly explain the case
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Example- CV and CC
 The datum shows GPA grade point average and SAT
mathematics test scores for a six local schools. Using the
relevant data as a sample and compute the followings.
a)
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Example- CV and CC
 The datum shows GPA grade point average and SAT
mathematics test scores for a six local schools. Using the
relevant data as a sample and compute the followings.
b)
(x-xmean)(y(x-xmean)(x(y-ymean)(yGPA (x) SAT (Y) x mean Ymean x-xmean y-ymean
ymean)
xmean)
ymean)
2.7
450
3.3
590
-0.6
-140
84
0.36
19600
3.5
560
3.3
590
0.2
-30
-6
0.04
900
3.7
700
3.3
590
0.4
110
44
0.16
12100
3.3
620
3.3
590
0
30
0
0
900
3.6
640
3.3
590
0.3
50
15
0.09
2500
3
570
3.3
590
-0.3
-20
6
0.09
400
19.8
3540
19.8
3540
0
143
0.74
Midterm-subject
Research Methods in Business Studies
36400
SUM
35
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Research in business studies
Example- CV and CC
 The datum shows GPA grade point average and SAT
mathematics test scores for a six local schools. Using the
relevant data as a sample and compute the followings.
b-c-d)
S xy
Sx 
Sy 
rxy 
(x


i
 x ) ( yi  y )
n 1
2
(
x

x
)
 i
n 1
(y
i
 y)2
n 1
S xy
SxS y
 28.6  A
 0.3847
 85.32
strong
positive
relationship
between
GPA and SAT. When
GPA increases, SAT is
expected to increase.
 0.8713
Midterm-subject
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Indices
 In business, the value of most variables changes over time.
An index can be used to measure these changes by
calculating the ratio of the current value over a base value.
In other words, the easiest way of actually measuring such
changes is to use an index or index number.
index for the tim e  value at time/va lue in base period
index for the tim e  value at time/ba se value
index in period N  (value in period N/base value) *100
Included for Final exam subjects
37
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Research in business studies
Example Indices
 Using the information (crime figures) in the following table
and calculate the each year’s index.
year
value
calculation base year 1
index
1
127
127/127
1.00
2
142
142/127
1.12
3
116
116/127
0.91
4
124
124/127
0.98
 First year is the base year. Second year tells us the crime
rate is 12% higher than the base value. The third year figure
tells the crime rate is 9% lower than the base value.
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Example Indices
 A shop sells an item for $ 20 in january, $ 22 in Feb, $ 25 in
March and $ 26 April. What is the price index in each month
using January as the base month?
Month
Jan
Feb
Mar
Apr
value
20
22
25
26
calculation base month 1
(20/20)*100
(22/20)*100
(25/20)*100
(26/20)*100
index
100.00
110.00
125.00
130.00
 First month is the base month. Second month tells us the
market price rate is 10% higher than the base value. The
third and fourth month figures tell the market price rates are
25% and 30 % higher than the base value respectively.
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Research in business studies
Example Indices
 A shop offers on one model. The advertised price for this
model in four consecutive quarters is given in the following
table. How will you describe the changes in price?
Hint: calculate index, price rise, percentage price rise and
percentage point price rise
Period
Price
1
10450
2
10800
3
11450
4
9999
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Research in business studies
Included for Final exam subjects
Example Indices
Period Price
Index
Price
Rise
% Price rise
% Point
Price rise
1
10450
104.5
0
0
0
2
10800
108
350
3.3
3.5
3
11450
114.5
650
6
6.5
4
9999
100
-1451
-12.7
-14.5
price rise
350
10800-10450
% Price rise
3.3
((10800-10450)/10450)*100
% Point Price rise
3.5
350/100
This calculations show the historical prices in relation to the
latest price so price first increased from 3.3 % up to 6% then
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decreased 12.7%.
Research Methods in Business Studies
© 2011/12, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2010, 4. Ed.
Research in business studies
Example Indices
The table shows the monthly index for sales of an item.
(a) If the sales in month 3 are 240 units, calculate sales in
month 8.
(b) Take the based month as month 1 and rearrange the index.
(c) Find growth rate of sales
(d) Briefly explain the case.
Month
1
Index 121
2
3
4
5
6
7
8
9
10
11
12
112
98
81
63
57
89
109
131
147
132
126
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Research in business studies
Included for Final exam subjects
Example Indices
Month
Index
Index
Re
Sales
Growth
month
3
1
121
100.0
296
98
109
2
112
3
98
4
81
92.6 81.0 66.9
274 240 198
-7.4 -12.5 -17.3
240
x
5
63
6
57
7
89
8
109
9
131
10
147
11
132
12
126
52.1
154
-22.2
47.1
140
-9.5
73.6
218
56.1
90.1
267
22.5
108.3
321
20.2
121.5
360
12.2
109.1
323
-10.2
104.1
309
-4.5
267
((274-296)/296)*100=
Growth
-7.4
The table shows the calculated sales units based on the index
numbers have direct relationship . This means that the higher
price on the good, the more units sold.
New index= (value in period M/new base value)*100
New index= old index*(old base value/new base value)
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Growth= ((current value-previous value)/previous value)*100
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Research in business studies
Purpose of sampling
 Data collection often uses sampling, where data from
a sample are used to estimate data for the population.
This is done when data collection from the entire
population would be too expensive, time-consuming or
impractical.
 If reasonable secondary data are not available, an
organization must use primary data. The data are
collected from a representative sample of items or
people and these are used to infer characteristics
about all items or people.
 For example, a company is about to launch a new
product and wants some data about likely sales.
44
 This topic is excluded from midterm- It is for final...
Research Methods in Business Studies
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Research in business studies
Purpose of sampling
 It could be asked everybody in a country. This way
may be expensive and time-consuming. i.e. Population
census.
 It could take a sample of people in a country. This
method may be inexpensive and time-saving. i.e.
Sampling.
 Type of Sample
Census, random, systematic, quota, stratified, multistage and cluster.
This topic is excluded from midterm- It is for final...
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Research in business studies
Example: Random Sample
 The easiest way of arranging data collection is to take
a random sample. It is worth emphasizing that a
random sample is not disorganized.
 Example: In a factory, 1000 workers had their
lunch. If we want to take sample of 100 worker
whether they are satisfied with lunch or not, how
might this sample be calculated?
 P= n/N where N is population and n is sample
 P=100/1000=0.10 or 10 %
 This sample can be conducted if the group is
homogenous
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This topic is excluded from final exam...
Research Methods in Business Studies
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Research in business studies
Example: Systematic Sample
 The easiest way to organize a non-random sample is to
collect data at regular interval.
 Example: A company receives 1000 invoices in a
financial year. An auditor does not have time to
examine each of these, so takes a random sample of
50. How might this sample be organized?
 K= N/n where N is population and n is sample
 P=1000/50=20 R ϵ [1,K] and R ϵ Z+
 Assume that 8 is randomly selected
 {8, 8+20, 8+2*20....8+(50-1)*20}
 8,28,48,68,88,108,128,148,168,188...,988
This topic is excluded from final exam...
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© 2011/12, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2010, 4. Ed.
Research in business studies
Example: Systematic Sample
 The easiest way to organize a non-random sample is
to collect data at regular interval.
 Example: A production line produces 5000 unit a
day. Quality control checks are needed on 2% of
units. How could a systematic sample identify
these?
 (2*5000)/100=100
 P=5000/100=50
 A systematic sample to get 100 units a day would
check every fiftieth unit, which is 50.
 This topic is excluded from final exam...
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Example: Quota Sample
Research in business studies
 An alternative way of giving some structure to
samples is to make sure that the overall sample has
the same characteristics as the population i.e. We
want to find how people would vote in an election.
 Example: 56300 people are eligible to vote in an
electoral constituency. Census records suggest
the following mix of features. We want to a poll of
1200 people to measure their probable voting
behaviour.
 How many people should be in each category?
This topic is excluded from final exam...
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Research in business studies
Example: Quota Sample
Age
Sex
Social Class
18-25-16%
26-35-27%
36-45-22%
46-55-%18%
56-65-12%
66 and over-%5
Female-53%
Male-47%
A-13%
B-27%
C1-22%
C2-15%
D-23%
This topic is excluded from final exam...
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© 2011/12, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2010, 4. Ed.
Research in business studies
Example: Quota Sample
 for example: 18-25 Age--(1200*16)/100=192 people
(192*53)/100=102 women, (102*13)/100=13 social class A
or (102*27)/100=27 social class B...etc...
 This topic is excluded from final exam...
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Research Methods in Business Studies
© 2011/12, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2010, 4. Ed.
Research in business studies
Example: Quota Sample
18-25
26-35
36-45
46-55
56-65 66 and over
female A
13
22
18
15
10
4
B
27
46
38
31
21
9
C1
22
38
31
25
17
7
C2
15
26
21
17
11
5
D
23
40
32
26
18
7
male A
12
20
16
13
9
4
B
24
41
34
27
18
7
C1
20
34
27
22
15
6
C2
14
23
19
15
10
4
D
21
35
29
23
16
6
This topic is excluded from final exam...
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Research in business studies
Example: Stratified Sample
 We can use an extension to quota sampling when
there are distinct groups or strata in the population.
Then it may be a good idea to have some
representatives from each stratum in the sample
 Example: 2000 people are divided into three groups
such as high, middle and low based on their income
levels. 500-high, 600 middle and 900 low. If we want
to take sample of 100 people whether they are
satisfied with their income levels or not, how might
this sample be organized?
 This topic is excluded from final exam...
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Research Methods in Business Studies
© 2011/12, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2010, 4. Ed.
Research in business studies
Example: Stratified Sample
 N=2000, n=100, h=3 (type of income level), Nh= 500,
Nm=600
NL= 900
N=N1+N2+....+Ns
ti=Ni/N, ni=ti*n
 t1=N1h/N=500/2000=0.25
t2=N2m/N=600/2000=0.30
t3=N3L/N=900/2000=0.45
 n1=t1h*n=0.25*100=25
n2=t2m*n=0.35*100=35
n3=t3L*n=0.45*100=45
This topic is excluded from final exam...
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Research in business studies
The End
Thanks
55
Research Methods in Business Studies
© 2011/12, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2010, 4. Ed.