Transcript Types of Probability Samples

Research in business studies
Department of Business Administration
SPRING 2009-10
sampling in empirical research and analysis of data
by
Assoc. Prof. Sami Fethi
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Sampling in empirical research










Why take sample
Sampling procedures
Probability sample
Determining sample size
Sampling in qualitative research
Editing and coding
The role of statistics
Analysing one variable
Cross-tabulation
Test of hypotheses
2
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Why take sample?
Research in business studies
 Sample
 When research problem and design as well as data collection
instrument are developed, next step is to collect the information.
 e.g. First one is to collect information from each member of the
population. The second one is to collect information from a
portion of the population by taking a sample of element from the
larger group and infer or understand something about the larger
group.
 Sampling is extremely important in quantitative studies.
 e.g. A well known example is an election poll on the basis of a
small fraction of all voters and also infer (figure out) something of
the voting intentions of all potential voters.
 There are at least two reasons for taking a sample instead of
including all units or elements. (1) the costs of including all units
may be prohibitive ( too expensive). (2) the time needed may be
too long.
 Bottom line is that the cases selected should be representative of
the whole gruop.
3
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Why take sample?
Research in business studies
 Sample
 In some Cases, samples may be more accurate than censues.
 e.g. The US Bureau of Census uses sample survey to check the
accuracy of the various censues.
 Population in these sentences refers not only to people but also
to firms, products etc...
 e.g. Deciding on the relevant population is not always easy.
 The key question is to know who or what one wants information
about.
 The following figure outlines and explains a useful procedure
when drawing a sample.
 A sample frame is ( in principle) a listing of units from which the
actual sample will be drawn.
 e.g. A telephone book as a sample frame of household. This is
difficult to find a sample frame that perfectly corresponds to the
target population of interest.
4
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Procedure for Drawing a Sample
Figure 1 Procedure for drawing a sample
5
Source: Based on Churchill (1995: 557).
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Sampling
 Two broad categories;
o (1) probability (2) non-probability samples.
 In probability samples, each unit has known, non-zero chance of
being included in the sample which allows for statistical inferences.
 e.g. By drawing a probability sample of voters and asking them
about their voting intentions, inferences about voting intention for
the population of voters may be drawn.
 In non- probability samples, it is not possible to make valid
inferences about the population. This means that such sample are
not representative. İn other words, what has been found in the
sample, for example, distribution of voting intentions, is valid within
certain limits.
 non- probability samples can be divided into three categories
 (1) convinience sample- an accidental sample- happen to know
personally via interview. (2) judgement sample- is used to get a
sample that is representative of the population. (3) quota sample- if
certain subgroups of units such as small firms are represented in
the sample in approximately the same proportions as they are
represented in the population (Churchill, 1995: 579-585).
Research Methods in Business Studies
6
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Sampling
 probability vs. non-probability samples
 non-probability samples are easy to draw, but they may
give misleading results if in spite of our judgement, they
happen to be unrepresentative of the population.
 The major drawback of nonprobability samples is that
such samples give no basis for evaulating the size of
the sampling variation and the error of estimation
 e.g. If possible, we should therefore use a probability
sample. This is specially important if we want to
estimate unknown parameters or draw valid inferences
regarding the population on the basis of the sample..
 It is usually assumed that non-probability samples are
not useful in scientific research, meaning that such
samples are not valid for statistical testing hypotheses
or drawing inferences regarding a larger population.
This smples mey be useful to gain insights into a 7
phenomenon in qualitative research.
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Probability Sampling
 Sampling error
 Probability samples allow for assesment of the
amount of sampling error.
e.g. If we want to know whether students at our
university are satisfied with the courses and
teaching methods, we might decide to interview
our students to ask for the opinion and the level
of satisfaction. However, if we have 10000
students, in the university, we cannot interview
all of them. Considering time and money spent,
we can interview 500 students to draw a reliable
conclusion-one out of every 20 students- This
will allow us to avoid any sampling error.
8
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Types of Probability Samples





Types
Simple random sampling
Systematic sampling
Stratified sampling
Cluster sampling
9
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Types of Probability Samples


o
o
o


o
o
Simple random sampling
A key characteristic of such samples is that all units in the
population have chance (probability) of being included. To apply a
random sample, the following question must be considered.
What is the basic unit to be examined?
How should the population (target population) be defined?
What variables or parameters are of interest?
e.g. value→ unit →variable → population. The population can be
described in terms of variables or parameters. Variables can be
defined as a set of values. A value can be delineated as a piece of
information based on a unit.
e.g. Typical parameters to be estimated in a sampling survey are
population total, population means, population proportions,
population variances and population ratios. More than one variable
is involved, population correlation coefficients and population
regression coefficients.
How should the sample be drawn?
How many units should be included? i.e. Sample size..
Research Methods in Business Studies
10
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Types of Probability Samples



o
o
o


Advantage and Disadvantage of Simple random sampling
Advantage? Due to its method, simple random sampling is easy to
understand and apply.
Disadvantage?
A complete framework is needed.
The cost of obtainning the sample can be high if the units are widely
scattered.
The standard errors of estimators can be high. i.e. reduce standard
errors of estimation for the same sample size.
e.g. If the units have quite different values for a variable of interest,
simple random sampling can be improved by making the probability
of inclusion in the sample proportional to the value of the variable.
This is called sampling with probabilities proportional to size.
e.g. Total consumption of toilet paper in the population of plants can
be included in the sample in proportion to the number of workers in
the plant. This should be work well since consumption of toilet paper
is highly correlated with number of workers.
11
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Types of Probability Samples
 Systematic sampling
 A systematic sample involves selecting every nth unit after a
random start.
 e.g. A firm wants to estimate the average order size, so it
selects a number between 1 and 10 at random, say 7, and
selects every tenth unit 7, 17, 27 and so on.
 Prerequisite for applying systematic sampling is that the units in
the population can be ordered in some way:
o Records that are ordered in a file
o names that are ordered alphabetically in a telephone directory
o houses that are ordered along a road
o Customers who walk one by one through an enterance, and so
on.
 Advantages: The method is simple and its framework is not
always needed.
 Disadvantages (or drawbacks): is the danger of hidden
periodicities such as a deficiency in producing product occurs at
specific interval.
12
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Types of Probability Samples
 Stratified sampling
 A stratified sample is a probability sample where
o The parent population is divided into a mutually exclusive and
exhaustive subset.
o A simple random sample of units is chosen independently from
each subset.
 An important reason for stratified sampling is that variability, and
thus standard error of estimates may be reduced.
 A stratum (singular of strata) is simply a part or subdivision of the
population.
 A stratified random sample is obtained by taking a simple random
from each stratum. The idea stratified sampling is to ensure that
every stratum gets a better representation. This is especially
important if the means are very different in the different strata.
 e.g. A firm has three different division as such A=1000 employees,
B=750 and C=500, so for the sake of employees’ satisfaction, a study
should be conducted on the basis of a sample of 10 percent of the
employees which includes 100 employees from A, 50 from B and 7513
from C that is a total sample of 225.
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Types of Probability Samples
 Advantage and disadvantage of Stratified sampling
Advantage: A stratified random sampling can give higher
precision with the same sample size or alternatively the
same precision with a smaller sample. A stratified random
sampling can also give separate results for each stratum.
A stratified random sampling also simplifies data
collection.
 Disadvantage: A complete framework is needed.
Additional information such as knowledge of standard
deviations and costs may be needed for each stratum.
 The bottom lie is that ıf the population can be divided
into strata that are homogeneous within but
heterogeneous between, precision can be increased or
costs lowered.
14
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Types of Probability Samples
 Cluster Sampling.
 In such sampling, the population is divided into mutually
exhaustive subsets.
 A random sample of subsets is selected. If the
researcher examines all units in the selected clusters,
the procedure is called one-stage cluster sampling. If a
sample of units is selected probabilistically from the
selected subsets, the procedure is known as two-stage
cluster sampling.
 Stratified sampling is selected from each subgroup.
 Cluster Sampling chooses a sample of subgroup due to
a small scale model. Within this sampling, subgroup
should be formed to be as heterogeneous as possible.
 e.g. When you want to study students’ working habits,
school classes may be considered as cluster cause
students vary in interest, talents and preparations.
15
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Types of Probability Samples
Research in business studies
 Advantage and disadvantage of Cluster
sampling
 Advantage: we do not need to a complete
framework of the secondary sampling units.
Such as area sampling which is the
geographical concentration of the units to be
interviewed.
 Disadvantage: If there is large variation
between clusters in the variables to be
examined the method may yield poor
precision.
16
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Determining sample size
 What is the sample size needed?
 It depends on the desired precision from the estimate. Precision is the
size of estimating internal when the problem is one of estimating a
population parameter.
 e.g. A researcher investigateing average income and wants the sample
estimate to be within +/- € 100 of the true population mean. This is more
precise than a requirement to be +/- € 200 of the true value.
 Concept of standard error: is central to sampling theory and to
determining the size of a sample. The formula for standar error SE is
SE= SD/ sq root of n
SD is stadard deviation
n= sample size
 Concept of population variance known
 e.g. Assume that A researcher wants to estimate to be within +/- € 25 of
the true population mean. Further, the researcher wishes to be 95 %
confident that interval (25x+/- 25) will contain the true population mean.
This implies constructing an interval +/-z SD around the observer mean in
which z is approximately 2.
17
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Determining sample size
 Confident interval?
 H= z SE= z (SD)/sq root of n where H is half of the internal,
i.e. 25 and based on the previous studies, SD is around 100.
n=z2 (SD2)/ (H2)=22 (1002 /252)= 64
If the estimate must be twice as precise that is a desired
interval (x+/- 12.5) so n =256.
Concept of proportions, Π: population proportion is
another parameter of interest for example; percentage of
voters, percentage with specific interest and so on. The
distribution of sample proportion Π is centred about the
population proportion.
The formula for standard error of proportion SDP is given by
SDP= sq root of Π (1- Π)/n
H= z SDP= z . sq root of Π (1- Π)/n
n=z2 / (H2)=Z2 . Π (1- Π)/n
18
n=22 / (H2)=Z2 . Π (1- Π)/n
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Determining sample size
 Assume that voting for the party within +/- 2
%, 95% confident interval, voting for the party
is believed as 40%
H= z SDP= z . sq root of Π (1- Π)/n
n=z2 / (H2)=Z2 / (H2). (Π (1- Π))
n=22 . / (0.022). (0.40 (1- 0.40)
n= 2400
See table 1 and 2 for more details about
sample size as well as desired precision.
19
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Sample size is influenced
by the desired precision
Table 1 Sample size is influenced by the desired precision
Research Methods in Business Studies
20
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Typical sample sizes for studies of
human and institutional populations
Table 2 Typical sample sizes for studies of human and institutional populations
21
Source: Sudman, S. (1976: 87). Copyright © 1976, with permission from Elsevier.
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Table 3 Basic
terminology in
sampling
Copyright © Source: Bryman
and Bell (2003: 93).
22
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Editing and Coding
 Editing and Coding?
 Editing: The basic purpose of editing is to secure a quality
standard for the data. Editing involves inspection and if
necessary correction of questionnaire or observation forms.
 Coding: Coding can be seen as some sort of classification.
The first step in coding is specifying the categories or
classes into which the responses are to be placed. There is
no definite or right number categories.
 Code book: Developing such a book is an important step
in the coding process. The code book contains the general
instructions how each items of data is coded in the following
table.
 Especially, when applying open-ended questions, multiple
answers are often reported.
 Reliability in coding: If there are 20 questions in a
questionnaries, it should be asked to at least 200 persons. 23
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Classification and Categorisation
Table 4 Code book format
Research Methods in Business Studies
24
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
The Role of Statistics
 The role of statistics
 The field of statistics involves method for describing and
analysing data and for making inferences (decisions) about
phenomena represented by the data. Methods in the first
category are referred to as descriptive statistics, methods in
the second category are called inferential statistics.
 Descriptive statistics: enable the researcher to summarize
and organize data in an effective and meaningful way.
 Inferential statistics: It is used to make inferences by
interpreting patterns.
 e.g. If we hypothesize that workers are less politically
conservative than civil servants on the data given, we
employ inferential statistics to determine whether differences
between the groups support our expectations.
25
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Analysing One Variable
 Univariate frequency distribution:
 If a single variable is investigated, the method
used is called Univariate frequency distribution. This
shows the frequency of observations in each
category of the variable
 e.g. In the following table, 140 firms are surveyed
and most firms are found in region D. If we find
percentage of firm in region A, we need to the
calculate by using this form (15/140) x100= 10.7.
 In table 3, the reported data are at the ordinal
level which implies that observations can be ranked.
The data shows that observations are skewed
towards agreement.
26
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Frequency Distribution of Customers’
Location
Table 5 Frequency distribution of customers’ location
Research Methods in Business Studies
27
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Frequency Distribution of Degree of
Agreement
Table 6 Frequency distribution of degree of agreement
Research Methods in Business Studies
28
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Using graphs and histograms
 Graphs:
 An alternative way of presentating the data is by using
graphs.
o the pie chart
o the bar chart
o the histogram
 e.g. Both the pie chart and the bar chart can be used at
the nominal and ordinal levels. The histogram is used to
display meausure at interval or ratio levels.
 in the following figure, the pie chart shows differences in
frequencies or percentages among categories of nominal or
ordinal scaled variables by displaying the categories as
segments of a circle.
29
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
PIE CHART
Figure 2 Degree of agreement
Research Methods in Business Studies
30
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Using graphs and histograms
 Histograms :
 The histograms are used to display
frequency distributions of interval or ratio
levels data. A histogram looks like a bar
chart with no spaces between the
rectangles. Unlike the bar chart, a
histogram cannot display information for
more than one variable.
 e.g. In the following figure, an example of
histogram can be seen.
31
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Histograms
Figure 3 Change in performance
Research Methods in Business Studies
32
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Descriptive Measures
Research in business studies
 Measure of central tendency:
 e.g. Mode, median, and mean.
 Mode: Appears most frequently in the distribution.
 Median: The median is the middle of a distribution.
 Mean : the sum of all observations divided by their number.
 Measure of dispersion:
o measurement of dispersion or variation about the central value is valid
for both metric (interval and ratio scaled) and non-metric ( nominal and
ordinal scaled) (Weisberg 1992).
 e.g. Average deviation, variance, standard deviation and coefficient of
variation
 Average deviation: is to calculate the deviation from the arithmetic
mean.
 Variance: Squaring the deviations in the average deviation formula, it
gives the variance.
 Standard deviation: taking square root of variance, it gives standart
deviation.
 Coefficient of variation: ratio of standard deviation to arithmetic mean.
33
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Types of Frequency Distribution
Research in business studies
 Types :
 e.g. Normal, skewed (left or right distribution compared
to normal), kurtosis (more picked or flatter compared to
normal), t-distribution and chi-distribution.
 The properties of normal curve:
o It is symmetrical and bell-shaped.
o The mode, median and mean are at the centre of the
distribution.
o The curve is based on an infinite number of observations.
o A single mathematical formula describes how frequencies
are related to the values of the variable.
 e.g. in the following figure, the normal curve can be seen
which is very important in the field of statistics.
34
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Types of Frequency Distribution
Figure 4 Portions under the normal curve
Research Methods in Business Studies
35
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Descriptive Measures of Employment
What does Table 7 tell you?
Table 7 Descriptive measures of employment
Research Methods in Business Studies
36
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Cross Tabulation
 Cross Tabulation :
 e.g. If We want to study the possible relationship
between the level of education of customers
(independent) and the interest in a certain product
(dependent) or second independent such as
gender or sex can be added to explain all
differences, cross-tabulation method is conducted.
 e.g. Conclusions based on a cross-tabulation
may appear untenable or indefensible when
additional variables are introduced (see figures 8
and 9).
37
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Cross Tabulation
Table 8 Product interest by level of education
Research Methods in Business Studies
38
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Cross Tabulation
Table 9 Product interest by level of education and sex
Research Methods in Business Studies
39
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Test of Hypotheses
 Test of Hypotheses :
 e.g. If We want to test a hypothesis which
shows the possible relationship or covariation
between the level of education of customers
(independent) and the interest in a certain product
(dependent) this method can take place in both
quantitative and qualitative research.
e.g. alternative hypothesis based on the
relationship or covariation whether exists between
the level of education of customers and the
interest in a certain product against null
hypothesis.
40
Research Methods in Business Studies
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.
Research in business studies
Test of Hypotheses
Table 10.7 Types of errors in hypothesis testing
Research Methods in Business Studies
41
© 2009/10, Sami Fethi, EMU, All Right Reserved, Pearson Education, 2005, 3. Ed.