arnaud halvick - business statistics

7/31/2019 Arnaud Halvick - Business Statistics

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2010

ISEG PARIS

Arnaud HALVICK

Att. Dorothy McAleer

[BUSINESS STATISTICS]


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[BUSINESS STATISTICS] 2010

Arnaud HALVICK Att. Dorothy McAleer 2

CONTENTWhat are the types of sample selection techniques and the associated strengths and

weaknesses of each type? .................................................................................................. 3

Probability sampling ................................................................................................. 3

Simple random Sampling ...................................................................................... 3

Stratified Sampling ................................................................................................ 5

Systematic Sampling ............................................................................................. 7

Cluster Sampling ................................................................................................... 8

Multi-Stage Sampling .......................................................................................... 10

Non-probability sampling ....................................................................................... 11

Convenience Sampling ........................................................................................ 11

Judgment Sampling ............................................................................................. 12

Referral Sampling ................................................................................................ 12

Quota Sampling ................................................................................................... 13

How do business managers design statistically strong samples that can be used for

multiple purposes? ........................................................................................................... 14

How do business managers adjust sample designs so that the samples remainrepresentative as organizational characteristics change over time? ............................... 16

INDEX 1.............................................................................................................................. 17

INDEX 2.............................................................................................................................. 18

References ........................................................................................................................ 19


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What are the types of sample selection techniques and the

associated strengths and weaknesses of each type?

Probability sampling

With probability sampling techniques, every unit of the population has a chance to

be selected in the sample (which means a chance higher than 0). The selection is

random but the probability of each unit to be selected can be accurately determined

and all units have an equal chance of being selected. This is like picking a name out of a

hat. Nowadays, we mostly use computers for generating random sampling.

Strengths

o All units have the same chance of being selected

o All units have an equal chance of being selected

Weaknesses

o Sometimes you dont want to consider all units

o No weighing = you cant increase or decrease the probability of a unit

for being selected

In order to define the different probability sampling methods, we need to define the

basic terms, which are:

n = number of cases in the sample

N = number of cases in the sampling frame

C = number of combinations of n from N

f= n/N = sampling fraction

There are 4 methods : Simple random, Stratified, Systematic and cluster sampling.

Simple random Sampling

This is the most basic form of sampling. The objective of this method is to select n

units out of N total units in order that C has an equal chance of being selected. To do so,

we use a table of random numbers and a computer with a random number generator or

any other mean to generate a random number.

Real Example:

A service agency would like to survey its clients in order to know if they are satisfied

by the offered service. Lets consider that they had 1000 clients the last year and that

the agency already had the list on a computer so we can begin the sampling directly.

Surveying all the clients would take too much time so we decide to survey only 100

clients which should be representative. Therefore, the sampling fraction (f) would be


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100/1000 = 10%. Now to draw the sample we can use any method with an equal chance

of selecting every unit, whether its printing them and do it mechanically or using a

computer. However, doing it with a computer is quicker and no specific application isneeded because Excel can generate random numbers. In a few minutes, we will get the

sample.

Advantages:

Very simple to set up and to explain.

Very quick.

No need for a good knowledge of statistics.

Drawbacks:

No weighting. It can be very problematic because with this method you can

end surveying mostly young people while most of the clients are old or

mostly men while most of the clients are women.

The sampling might not be representative if the total number of units is

heterogeneous => bad representation of subgroups.

The results depends on your luck.


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Stratified Sampling

With this method, the population is divided into homogeneous subgroups and then

we take a simple random sample (like in Simple random sampling) in each subgroups.The objective is to have a better representation of the population by stratify N:

N = N1 + N2 + N3 + + Nx Then take a random sample of f = n/N in each subgroup.

Example:

Lets consider the service agency we talked about before. Lets consider that we only

need to stratify the sample of 1000 clients depending on the sex and age. By stratifying

the clients we get:

Women Units f (10%)

< 24 100 10

25 34 200 20

35 44 150 15

45 54 100 10

55 64 40 4

> 65 10 1

TOTAL 600 60

Men Units f (10%)

< 24 80 8

25 - 34 90 9

35 - 44 150 15

45 - 54 40 4

55 - 64 20 2

> 65 20 2

TOTAL 400 40

GLOBAL 1000 100

We take f = 10% as in the simple random sampling but we have subgroups.

Therefore we take 10% units in each subgroups and have a better representation of the

population.


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Advantages:

Better representation of the population.

Possibility to introduce key subgroups (like minorities).

Possibility to weight the strata.

More statistical precision if the variability in each subgroup is lower than the

variability of the whole group.

Drawbacks:

Takes more time.

More complicated.

Sometimes you cant use f because you might need to take only a part of the

units (if we had 111 unit in a subgroup we would have to take 11,1 unit).

Loss of time if the main sample is already homogeneous or if the subgroups

are so small that it is not relevant to consider them.


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Systematic Sampling

This approach is very different from the previous ones. In order to make a

systematic random sample you have to:

1. Number the units of the population (1 to N)

2. Define the sample size (n)

3. Define the interval size (k = N/n)

4. Select a random number between 1 to k (it has to be an integer)

5. Take the unit with the rank k in each interval

Example:

Lets consider the service agency again. We have 1000 clients and we want a sample

of 100 units. The interval will be k = N/n = 1000/100 = 10. We choose a random number

and get 6 so we will take the 6th

unit of each interval of 10 unit (6, 16, 26, 36, 46, 996)

Rank Client

1 A

2 B

3 C

4 D

5 E

6 F

7 G

8 H

9 I

10 J

11 K

12 L

13 M

14 N

15 O

16 P17 Q

18 R

19 S

20 T

21 U

1000 ZZ


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The units of the population have to be randomly ordered or ordered according to

what we need to measure. If not the result will be biased.

Advantages:

Very easy.

Very quick.

A bit more accurate than simple random sampling (the selection is less based

on luck).

Possibility to customize by ordering the units (e.g.: by age so you have units

of each subgroup in the sample).

Better than Simple random sampling if there is no other sampling choice.

Drawbacks.

No weighting.

The sampling might not be representative if the units are ordered

heterogeneously.

If there are various subgroups, the sample wont be very representative.

Cluster Sampling

The purpose of cluster sampling is to simplify the work of the interviewers. Indeed, it

is possible that the 100 clients selected from the sample of the agency are located all inthe same town while the 1000 clients are located in every part of the region. Thus, the

sample is not representative.

It can also be the opposite, the 100 client can be located all around the region and

we might have to meet them personally which can be very complicated. We would lose

a lot of time and money.

Cluster sampling solves this issue by:

1. Dividing the population into clusters (usually geographic areas)

2. Randomly sample the clusters (with one of the previous methods of

example)

3. Measure all units of the sampled clusters.

Example:

The agency considers that the satisfaction is not much related to the location of the

customers for the reason that they are mostly operating in Paris. Therefore, they will

meet personally only the clients close to the agency:


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Source: http://www.orthodoxesaparis.org/images/plans/plan_paris.png (image modified by me)

The clients are located all around the city and the region but we will visit only the

ones located in the yellow area, close to the agency.

Advantages:

Solves geographic location issues (save time and money)

Easy and quick to do (if data available)

Drawbacks:

The result might not be as accurate as if we would have taken the whole

geographic area. Maybe some unknown geographic factors affect the results.


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Multi-Stage Sampling

The main issue of the 4 previous methods (Simple Random, Stratified, Systematic

and cluster sampling) is that they are all very basic and very simple. Most of the time wewill need more complex methods to deal with real life sampling strategies. The Multi-

Stage sampling is nothing more than combining these 4 methods in order to get more

complex samples and more accurate results. This way, we can get interesting data even

with basic methods.

Example:

We can first use the cluster methods to interview only close clients and then stratify

the clients into subgroups to have more accurate results. Comparing the subgroups of

the selected areas and of the other areas might reveal differences in the subgroupswhich would lead to another sampling methods to be more accurate.

Advantages:

More accurate.

Better results.

Better use of available data.

Drawbacks:

Takes more time.

More complex.


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Non-probability sampling

The main difference between these methods and the probability sampling methods

is that here the selection is not random. This does not mean that non-probabilitymethods does not give representative samples. It means that we are in a situation in

which we cant rely on probability theories.

In general, researchers will prefer probabilistic methods because they consider them

more representative of the reality and more accurate. Nevertheless, there are some

circumstances in which it is not practically or theoretically possible to do probabilistic

sampling. Consequently, non-probabilistic methods will be used.

Advantages:

Solve problematic situation.

Can be useful if a different approach is needed.

Drawbacks:

Less accurate.

Less representative of the reality.

There are 4 methods: Convenience, Judgment, Referral and Quota sampling.

Convenience Sampling

Also called Accidental or Haphazard sampling, this method consist of take the most

convenient unit as a sample. As an example, when a journalist is interviewing someone

in the street he just ask random people their opinion. The opinion will not be

representative of the public opinion but it is more convenient.

In many psychological researches, the sample are often college students because it

is more convenient to reach them. It is obviously not because they are representative of

the whole population.

In clinical experiences, paid or not, the sample units are often composed of

volunteers. Nevertheless, the researcher can set up selection criteria in order to have

people of different ages and sex.

Advantages:

Very simple.

Very convenient.


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Drawbacks:

Cannot be defined as being representative.

If the results are considered as being representative, the following

experiences could be disastrous.

Judgment Sampling

The purpose of Judgment sampling is to select the persons who are most likely to

give the information required. As an example, if we are looking for information on the

average age of male financial manager, we will directly ask these persons instead of

taking a representative sample of the population.

The selected sample will provide the best information to the researcher and can

provide additional qualitative data which can be useful. Also, this is the best method for

obtaining data specific to the selected population

Advantages:

Useful to analyze a specific population.

Easy to set up.

Can provide specific qualitative data.

Drawback:

Limited information.

If the criteria are not well define this can lead to bad results.

It can be hard to find people corresponding to the criteria.

Referral Sampling

This methods is used when there is a lack for people meeting the selection criteria.

Therefore, we begin by identifying someone who meets the criteria to be selected for

the study and then ask this person to recommend other persons meeting the criteria.

Even if this method does not seem to lead to representative results, it can sometimes be

the best alternative. As an example, if we are looking for a specific type of engineer but

cant find enough of them or if they are scattered in a big area, we can ask one of the

engineer if he knows other ones of the same type. Thus, this method can be very useful

when it is hard or impossible to reach a population (e.g.: people with a specific name,

from a specific region, from a specific culture, homeless people, )


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Quota Sampling

The purpose of Quota sampling is to get a sample accordingly to specific needs. The

people are not selected randomly but according to fixed quota (e.g.: 50% male, 50%female). The quota sampling can be proportional or non proportional.

Proportional quota sampling:

Here the objective is to represent the main characteristic of the population by

sampling a proportional amount of each subgroup. As an example, if there is 45% of

men and 55% of women in the population and that we want a sample size of 1000 we

will take 450 men and 550 women. Therefore, if we reach 550 women but have only 800

persons in total, we will stop sampling women and only focus on men (the quota is

met).

Advantages:

Not very complicated.

Can lead to more accurate results.

You can define a precise area of research.

Drawbacks:

Hard to define the characteristic: does it have to be the gender, age,

education, ?

If the data on which you base your choice is not reliable, the results will be

bad.

Non proportional quota sampling:

Here we do not care if the numbers match the proportions in the population. We

define ourselves the numbers required (e.g.: we will take 30 men and 10 women). This

way you can decided how much units of each groups you want to have, which can be

useful to represent small groups.

Advantages:

Helpful to represent small groups.

Can be useful to sample only a part of the population.

Drawbacks:

Less representative.


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How do business managers design statistically strong samples that

can be used for multiple purposes?

When a manager is designing samples, he always wishes to use it for multiple

purpose. This is simple because it saves a lot of time and efforts. However, it is not as

easy as it seems to get good samples that can be used for many purposes.

First of all, the manager will have to define specific criteria that can be used for

various purposes (e.g.: Age, gender, job, ). Thus, the manager needs to know exactly

what are his needs and what are the needs of the people he is working for. As an

example, I worked in a restaurant and I had to build a survey. Therefore, I asked my

manager what were its needs, then I asked to the waiters if they had ideas, and then the

cook what did he needs, and so on. As a result, I had many different questions and

information needed (e.g.: the cook wanted to know the opinion of clients about the

taste, the presentation, the size, the drinks, ). However, I had too many questions to

put them all into the survey.

This is where the second step starts: selecting. Actually, a manager will usually want

a lot of information about everything. However, for practical purposes it is impossible to

get all the data. If the survey takes too much time, the person who is filling it will get

bored and go faster, resulting in less accurate answers or less answers. In my example,

we selected the most relevant data and made various categories1:

Top of the questionnaire:

o Name and Surname ( we determined the gender from the name to

limit the questions.

o Birthday (to determine age).

o E-mail (to send info).

Service.

Food.

Place.

Consuming habits. Other information.

We note here that most of the data is quantitative. It built this way because people

were asked to fill the survey at the end of their meal. Thus, to get more information it

was better this way considering that people tend to give less answer to qualitative

questions because it takes more time (it has been proven to be true when analyzing the

answers). This an important step because it helps defining which information we need

1Index 1 : the whole survey (in Spanish given that it was in Argentina)


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exactly and also to get information about many different subjects (e.g.: we had more or

less the same number of question about food, service and place).

Another fundamental step in designing samples are the questions themselves.

Designing the question plays very important role in both the quantity and the quality of

the answers. Still in my example, I made very simple questions with very simple answers

(mostly multiple choice questions). This makes the job of the client very easy and fast. It

has been very efficient and we got a very good answering rate2. The choice of the

number of questions depends on the time the person has to answer and its willingness

to answer. Therefore, if you ask for volunteers willing to come for one hour to answer

questions, you have different options. Still in the question design, the question is not

the only element to consider. The answers also have to be clear, to cover all possible or

necessary answers and also to be in correlation with the type of information needed.

Actually, it is vital to have information which can be used. This is why by using multiple

choice we can have a better overview of the situation than if people where only

answering qualitatively.

The next step is to design the survey so it is easy to read and to fill. The best way to

do so is to test it with some people by asking them to fill it and to give their opinion. The

order of the question is important. In my example, the most important questions are at

the top because it increases the answering rate. The qualitative questions are at the

bottom because they take more time to answer and may reduce the answering rate ofthe whole survey. The colors also play a role given that it was in a restaurant where

people come to have a good time. The design has to be attractive.

The last step is to be ensured that the data will be collected correctly, in a good way.

It is important the data is collected the same way all the time so the results will be more

accurate. The best way is to set up a procedure to collect the data (how to ask the

questions, when, ). This will give more reliable data. In my example, we asked to the

waiter to give the questionnaire to the clients with the bill when they had asked for it. It

was the best moment to ask them (before would have been weird, by e-mail would give

less answers).

As we can see, the information needed, the design of the questions, the design of

the survey and the way it is conducted play a very important role is building a strong

sample that can be used for multiple purposes. When analyzing the data, we notice

what is missing or could be improved, which is also very useful for the next samples.

2Index 2 : the answering rates (% who have answered on the left, others on the right). Results based

on the data collected by the survey and analyzed through an access database made by myself.


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How do business managers adjust sample designs so that the

samples remain representative as organizational characteristics

change over time?Indeed, the data research has to be constant as trends vary over the time. Thus, the

manager will need to readjust its sample design. It is a key element in statistical analysis

because it maintain the representativeness of the samples.

In order to cover all different points of change over the time, I will consider a PESTEL

analysis, often used in marketing. Why? Simply because if covers almost every changing

aspect of our world. Therefore, by using a PESTEL analysis a manager will know which

samples have to be changed.

Political: Key events can lead to change to dramatic changes. Therefore, the

manager has to monitor elections, changes in tax policies, labor laws,

environmental laws, key events, big issues that occurred, Governments also

have an impact on the education, health and infrastructure.

Economic: Many changes can occur in the economy: variation of purchasing

power, of employment, of prices in specific areas, variation in economic growth,

inflation rates, interest rates All of this has to be considered.

Social: the social changes also play a role in these changes: cultural changes,

changes in age distribution, variation of the population growth rate, attitudes

toward job, health, safety

Technological: once again, there are many elements to monitor: degree of

automation, variation in R&D investments, technology incentives, speed of

technological changes

Environmental: the possible changes include: weather condition, climate,

These changes affect many aspects of the society: farming, tourism, and then

companies and their growth potential.

Legal: the law is constantly changing, the laws can concern: antitrust,

employment, health, consumers, safety,

A manager has to constantly update the information on these points in order to

have representative samples.


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References

William M.K. Trochim, Research Methods Knowledge Base, Last revised 10/20/2006

http://www.socialresearchmethods.net/kb/sampprob.php

http://www.socialresearchmethods.net/kb/sampnon.php

Accessed on 01/04/2011

arnaud halvick - business statistics

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