Statistics: Introduction
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What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
Statistics: Introduction
Ekaterina A. Aleksandrova
Associate Professor
Department of Economics
Centre for Health Economics, Management, and Policy
National Research University
Higher School of Economics in Saint Petersburg
ea.aleksandrova@hse.ru
January, 2020
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
1
What Is Statistics?
2
Types of Data
3
Vaiables and Scales of Measurement
4
Applying Statistics in Business
Applying Statistics in Business
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
1
What Is Statistics?
2
Types of Data
3
Vaiables and Scales of Measurement
4
Applying Statistics in Business
Applying Statistics in Business
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
We generally divide the study of statistics into two branches:
descriptive statistics and inferential statistics
Descriptive statistics refers to the summary of important aspects
of a data set
This includes collecting data, organizing the data, and then
presenting the data in the form of charts and tables
In addition, we often calculate numerical measures that summarize,
for instance, the data’s typical value and the data’s variability
The unemployment rate, the president’s approval rating, the
Dow Jones Industrial Average, batting averages, the crime rate,
and the divorce rate are but a few of the many ‘statistics’ that
can be found in a reputable newspaper on a frequent, if not
daily, basis
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
Despite the familiarity of descriptive statistics, these methods
represent only a minor portion of the body of statistical applications
The phenomenal growth in statistics is mainly in the field
called inferential statistics
Generally, inferential statistics refers to drawing conclusions
about a large set of data — called a population — based on a
smaller set of sample data
A population is defined as all members of a specified group
(not necessarily people), whereas a sample is a subset of that
particular population
The individual values contained in a population or a sample
are often referred to as observations
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
In most statistical applications, we must rely on sample data
in order to make inferences about various characteristics of the
population
For example, a 2016 Gallup survey found that only 50% of
Millennials plan to be with their current job for more than a
year
Researchers use this sample result, called a sample statistic, in
an attempt to estimate the corresponding unknown population
parameter
In this case, the parameter of interest is the percentage of all
Millennials who plan to be with their current job for more than
a year
It is generally not feasible to obtain population data and calculate
the relevant parameter directly, due to prohibitive costs
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
Population vs Sample
A population consists of all items of interest in a statistical
problem
A sample is a subset of the population
We analyze sample data and calculate a sample statistic to
make inferences about the unknown population parameter
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
The Need for Sampling
A major portion of inferential statistics is concerned with the
problem of estimating population parameters or testing hypotheses
about such parameters
If we have access to data that encompass the entire population,
then we would know the values of the parameters
Generally, however, we are unable to use population data for
two main reasons:
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
The Need for Sampling
Obtaining information on the entire population is expensive
Consider how the monthly unemployment rate in the United
States is calculated by the Bureau of Labor Statistics (BLS). Is
it reasonable to assume that the BLS counts every unemployed
person each month? The answer is a resounding NO! In order
to do this, every home in the country would have to be contacted.
Given that there are approximately 160 million individuals in
the labor force, not only would this process cost too much, it
would take an inordinate amount of time. Instead, the BLS
conducts a monthly sample survey of about 60,000 households
to measure the extent of unemployment in the United States)
It is impossible to examine every member of the population
Suppose we are interested in the average length of life of a
Duracell AAA battery. If we tested the duration of each Duracell
AAA battery, then in the end, all batteries would be dead and
the answer to the original question would be useless
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
Populations and Samples
population: the 31 flavors of ice cream at a 31-flavor ice cream
store
sample: the five flavors that you have tested in order to determine
whether this store sells good ice cream
population: all voters in the US
sample: the 3,000 people who are interviewd as part of an
opinion poll
population: all people in Russia
sample: the people from 5,000 households interviewed in RLMS
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
1
What Is Statistics?
2
Types of Data
3
Vaiables and Scales of Measurement
4
Applying Statistics in Business
Applying Statistics in Business
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
Cross Sectional Data
Sample data are generally collected in one of two ways. Crosssectional data refer to data collected by recording a characteristic
of many subjects at the same point in time, or without regard
to differences in time
Subjects might include individuals, households, firms, industries,
regions, and countries
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
Time Series
Time series data refer to data collected over several time periods
focusing on certain groups of people, specific events, or objects
Time series can include hourly, daily, weekly, monthly, quarterly,
or annual observations
Examples of time series data include the hourly body temperature
of a patient in a hospital’s intensive care unit, the daily price of
General Electric stock in the first quarter of 2019, the weekly
exchange rate between the U.S. dollar and the euro over the
past six months, the monthly sales of cars at a dealership in
2016, and the annual growth rate of India in the last decade
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
Cross-Sectional Data and Time Series Data
Cross-sectional data contain values of a characteristic of many
subjects at the same point or approximately the same point in
time
Time series data contain values of a characteristic of a subject
over time
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
1
What Is Statistics?
2
Types of Data
3
Vaiables and Scales of Measurement
4
Applying Statistics in Business
Applying Statistics in Business
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
When we conduct a statistical investigation, we invariably focus
on people, objects, or events with particular characteristics
When a characteristic of interest differs in kind or degree among
various observations, then the characteristic can be termed a
variable
We further categorize a variable as either qualitative or quantitative
For a qualitative variable, we use labels or names to identify
the distinguishing characteristic of each observation
For instance, the 2010 Census asked each respondent to indicate
gender on the form
Each respondent chose either male or female
Gender is a qualitative variable
Other examples of qualitative variables include race, profession,
type of business, the manufacturer of a car, and so on
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
A variable that assumes meaningful numerical values is called
a quantitative variable
Quantitative variables, in turn, are either discrete or continuous
A discrete variable assumes a countable number of values
Consider the number of children in a family or the number of
points scored in a basketball game
We may observe values such as 3 children in a family or 90
points being scored in a basketball game, but we will not
observe 1.3 children or 92.5 scored points
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
The values that a discrete variable assumes need not be whole
numbers
For example, the price of a stock for a particular firm is a
discrete variable
The stock price may take on a value of 20.37or20.38, but it
cannot take on a value between these two points
Finally, a discrete variable may assume an infinite number of
values, but these values are countable; that is, they can be
presented as a sequence x1 , x2 , x3 , and so on
The number of cars that cross the Golden Gate Bridge on a
Saturday is a discrete variable
Theoretically, this variable assumes the values 0, 1, 2, . . .
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
A continuous variable is characterized by uncountable values
within an interval
Weight, height, time, and investment return are all examples
of continuous variables
For example, an unlimited number of values occur between
the weights of 100 and 101 pounds, such as 100.3, 100.625,
100.8342, and so on
In practice, however, continuous variables may be measured in
discrete values
We may report a newborn’s weight (a continuous variable) in
discrete terms as 6 pounds 10 ounces and another newborn’s
weight in similar discrete terms as 6 pounds 11 ounces
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
Qualitative Variables vs. Quantitative Variables
A variable is a general characteristic being observed on a set
of people, objects, or events, where each observation varies in
kind or degree
Labels or names are used to categorise the distinguishing characteristi
of a qualitative variable; eventually, these attributes may be
coded into numbers for purposes of data processing
A quantitative variable assumes meaningful numerical values,
and can be further categorized as either discrete or continuous
A discrete variable assumes a countable number of values,
whereas a continuous variable is characterized by uncountable
values within an interval
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
The Nominal Scale
The nominal scale represents the least sophisticated level of
measurement
If we are presented with nominal data, all we can do is categorize
or group the data
The values in the data set differ merely by name or label
Consider the following example
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
The Nominal Scale
Each company listed in Table is a member of the Dow Jones
Industrial Average (DJIA)
The DJIA is a stock market index that shows how 30 large,
publicly owned companies based in the United States have
traded during a standard trading session in the stock market
Table also shows where stocks of these companies are traded:
on either the National Association of Securities Dealers Automated
Quotations (Nasdaq) or the New York Stock Exchange (NYSE)
These data are classified as nominal scale since we are simply
able to group or categorize them
Specifically, only four stocks are traded on Nasdaq, whereas
the remaining 26 are traded on the NYSE
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
The Nominal Scale
Often we substitute numbers for the particular qualitative characteris
or trait that we are grouping
One reason why we do this is for ease of exposition; always
referring to the National Association of Securities Dealers Automated
Quotations, or even Nasdaq, becomes awkward and unwieldy
In addition, as we will see later in the text, statistical analysis
is greatly facilitated by using numbers instead of names
For example, we might use the number 0 to show that a company’s
stock is traded on Nasdaq and the number 1 to show that a
company’s stock is traded on the NYSE, or in tabular form:
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
The Ordinal Scale
Compared to the nominal scale, the ordinal scale reflects a
stronger level of measurement
With ordinal data we are able to both categorize and rank the
data with respect to some characteristic or trait
The weakness with ordinal data is that we cannot interpret
the difference between the ranked values because the actual
numbers used are arbitrary
For example, suppose you are asked to classify the service at
a particular hotel as excellent, good, fair, or poor
A standard way to record the ratings is
Category
Excellent
Good
Fair
Poor
Rating
4
3
2
1
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
The Ordinal Scale
Here the value attached to excellent (4) is higher than the value
attached to good (3), indicating that the response of excellent is
preferred to good
Category
Excellent
Good
Fair
Poor
Rating
4
3
2
1
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
The Ordinal Scale
However, another representation of the ratings might be
Category
Excellent
Good
Fair
Poor
Rating
100
80
70
40
Excellent still receives a higher value than good, but now the
difference between the two categories is 20 (100-80), as compared
to a difference of 1 (4-3) when we use the first classification. In
other words, differences between categories are meaningless with
ordinal data. (We also should note that we could reverse the
ordering so that, for instance, excellent equals 40 and poor equals
100; this renumbering would not change the nature of the data)
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
The Ordinal Scale
Nominal and ordinal scales are used for qualitative variables
Values corresponding to a qualitative variable are typically
expressed in words but are coded into numbers for purposes of
data processing
When summarizing the results of a qualitative variable, we
typically count the number or calculate the percentage of persons
or objects that fall into each possible category
With a qualitative variable, we are unable to perform meaningful
arithmetic operations such as adding and subtracting
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
The Interval Scale
With data that are measured on an interval scale, not only can
we categorize and rank the data, we are also assured that the
differences between scale values are meaningful
Thus, the arithmetic operations of addition and subtraction
are meaningful
The Fahrenheit scale for temperatures is an example of an
interval scale
Not only is 60 degrees Fahrenheit hotter than 50 degrees Fahrenheit,
the same difference of 10 degrees also exists between 90 and
80 degrees Fahrenheit
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
The Interval Scale
The main drawback of data on an interval scale is that the
value of zero is arbitrarily chosen; the zero point of an interval
scale does not reflect a complete absence of what is being
measured
No specific meaning is attached to zero degrees Fahrenheit
other than to say it is 10 degrees colder than 10 degrees Fahrenheit
With an arbitrary zero point, meaningful ratios cannot be
constructed. For instance, it is senseless to say that 80 degrees
is twice as hot as 40 degrees; in other words, the ratio 80/40
has no meaning
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
The Ratio Scale
The ratio scale represents the strongest level of measurement.
Ratio data have all the characteristics of interval data as well
as a true zero point, which allows us to interpret the ratios of
values
A ratio scale is used to measure many types of data in business
analysis
Variables such as sales, profits, and inventory levels are expressed
as ratio data
A meaningful zero allows us to state, for example, that profits
for firm A are double those of firm B
Measurements such as weight, time, and distance are also measured
on a ratio scale since zero is meaningful
Unlike qualitative data, arithmetic operations are valid on intervaland ratio-scaledvalues
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
Definitions
Continuous
Data that can take on any value in an interval.
Synonyms: interval, float, numeric
Discrete
Data that can take on only integer values, such as counts.
Synonyms: integer, count
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
Definitions
Categorical
Data that can take on only a specific set of values representing
a set of possible categories.
Synonyms: enums, enumerated, factors, nominal, polychotomous
Binary
A special case of categorical data with just two categories of
values (0/1, true/false).
Synonyms: dichotomous, logical, indicator, boolean
Ordinal
Categorical data that has an explicit ordering.
Synonyms: ordered factor
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
1
What Is Statistics?
2
Types of Data
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Vaiables and Scales of Measurement
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Applying Statistics in Business
Applying Statistics in Business
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
A firm preparing to introduce a new product needs to estimate
the preferences of the consumers in the relevant market. It
can often do this by conducting a marketing survey based on
interviews with some randomly selected HHs. The results of
the survey can then be used to estimate the preferences of the
entire population
Statistical techniques are needed to disentangle the separate
effects of several different factors. For example, the demand
for ice cream in a community can be expected to depend on
the price of ice cream, the level of average income, the number
of children in the community, and the average temperature. If
you have observations of all the different factors involved, you
can use correlstion or regression analysis to determine which
factors have the most important effects
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
An auditor has a job of checking the books of a company to
make sure that they accurately reflect the financial condition
of the company. The auditor will need to check through piles
of original documents such as sales slips, purchase orders, and
requisitions. It would require massive amounts of work to check
every single original document; instead, the auditor can check
a randomly selected sample of documents and make inferences
about the entire population of documents based on that sample
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
Before a new drug is marketed, it is necessary to perform
extensive experiments to make sure the drug is safe and effective.
Some people need to be given the drug to test it, but you
won’t know if the drug makes a difference unless you have
another group so you can compare/ Yhe best way to test a
drug is ti take two groups that are as much alike as possible,
give the drug to one of the groups but not to the other, and
then see whether the results for the two groups are different.
The group that is given the drug is called the experimental
group (or treatment group), and the other group is called the
control group. Statistical analysis is necessary to determine
whether any observed differences really were caused by the
drug or could have been caused by other factors
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
If you are receiving a large shipment of goods from a supplier,
you will want to make sure that the goods meet the quality
standards agreed upon. It would be very expensive to perform
a quality control check on every single item, but once again
statistical techniques come to the rescue by allowing you to
make inferences about the quality of the entire lot by checking
a randomly selected sample of items chosen from the lot
Financial investments involve risk. Statistical analysis allows
you to estimate the risk and expected return from an investment
portfolio, and how changing the composition of a portfolio can
affect the risk and return
What Is Statistics?
Types of Data
Vaiables and Scales of Measurement
Applying Statistics in Business
Insurance actuaries need to study statistics to estimate the
probabilities of various events and to analyze the risk for the
insurance company
Advertising rates for television and radio stations are based on
ratings, which are determined by statistical samples
When analyzing natural phenomena, such as weather or wildlife
populations, you usually have to work with a sample because
it is impractical to observe the entire population
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Statistics: Research
Ekaterina A. Aleksandrova
Associate Professor
Department of Economics
Centre for Health Economics, Management, and Policy
National Research University
Higher School of Economics in Saint Petersburg
ea.aleksandrova@hse.ru
May, 2020
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Useful cuotes
‘If something exists it can be measured’
E.L. Thornike
‘The purpose of computing is insight, not numbers’
R. Hamming
‘Nothing has such power to broaden the mind as the ability to
investigate systematically and truly all that comes under thy
observation in life’
Marcus Aurelius
‘In many spheres of human endeavor, from science to business to
education to economic policy, good decisions depend on good
measurement’
Ben Bernanke
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What does empirical research mean?
We test various models, theories, hypotheses
We use real data
Our resuls are useful for policymakers, firms, general public,
etc.
Our methods are based on the synthesis of theory, measurements,
and statistical instruments
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Empirical Research
Make sure that the the question you pose is actually answered
in the body of the work
Typically, your research question should answer the question
“WHY?”
Always start from the MECHANISMS
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Example I
RQ: Are better educated people healthier?
We start from the question ‘Why?’
Mechanism 1: more education => more money => more investment
to health => better health
Mechanism 2: more education => more stress => more smoking
/ drinking => bad health
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Example II
RQ: Is it true that high concentration of firms in one sector in
one sity leads to innovations in this sector?
WE start from the question ‘Why?’
Mechanism 1: more firms => higher competition => more
investment to R&D => more innovations
Mechanism 2: more firms => higher competition => lower
prices => no money for investments => no innovations
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Empirical Research
How to find a mechanism?
Search the related theory
Read some articles (type keywords in scholar.google.com and
you will be surprised how many texts have been published yet)
Just google
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Database
Download your database
Read the information about database carefully!!!
Read not only the codebook but also the questionnaire!!!
Be sure that you know who collected this database and for
what the reasons
How was this database collected? (expert opinion, self-reported
measures, ...)
What is the item of observations in your database? (country,
firm, people, ...)
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Measurement Problems
In most cases, we work with abstract (ideal) items which are
not strictly measurable
Examples: human capital, health
What is to be done?
We use proxies (variables that approximate the initial item in
an appropriate way), indexes, sets of indicators or variables
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Proxy Variables of Initial Characteristics
We work with initial characteristics:
Human capital
Firm performance
Poverty
Innovations
Health
Entrepreneurial activity
How to measure them?
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Proxy Variables of Initial Characteristics
Plenty of definitions and each depends on the item:
Human capital
Labour Economics
Individual level data — years of education;
Country level data — the share of citizens with higher education
(tertiary education)
Firm performance
Corporate Finance or Performance Management
Sales, Revenue, ROS, ... It might be also the growth of such
Salest
indicators if we are interested in firm performance change Sales
t−1
Poverty
Demography or Sociology or Economics
Definitions vary across countries. If you work with country
level data, use the definition of WB.
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Proxy Variables of Initial Characteristics
Plenty of definitions and each depends on the item:
Innovations
Economics of Innovation
Firm-level data — R&D investment, number of patents, etc.
Health
Health Economics, Public Health, Demography, Epidemiology
Individual level — self-assessed health, EQ–5D, SF–36, number
of chronic deseases, doctor visits, etc.; country level — mortality,
morbidity, life expectancy, etc.
Entrepreneurial activity
Entrepreneurship
Individual level — self-employment status, etc.; country level
— the share/number of SMEs, new firms, self-employed people,
etc.
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Discussion of Proxy Variables
You are recommended to choose (at least) two proxies if it is
possible
Try to explain the difference of them:
Not the same interpretation; different scales; which one is better
or not for your initial variable; advantages and disadvantages
Why two or more proxies?
It gives you:
Robustness check;
Comparable results;
More details about analysed mechanisms;
Sensitivity analyses of your results;
Perhaps, more information for discussion?
Flexible conclusion
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Six Stages of Data Processing
Data collection
Data preparation
Data input
Processing
Data output or Interpretation
Data storage
See more details here:
talend.com/resources/what-is-data-processing/
Conclusion
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Data ‘Cleaning’
Encode into missings the following observations:
“Refuse to answer”, “I do not know” ’, etc.
These answers are usually encoded as 999, 9999999, -9, etc.
Drop missings! BUT ensure the reduction in you sample (if
the reduction is too big, you might make a biase conclusion =
selection problem)
Work in Stata and write all the command in do-file — it helps
to come back and redo/correct your data processing
Attach the final do-file to your final report (in Appendix)
Make comments in your do-file, it helps to read and understand
your logic
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Data Limitations
You can limit data if it is necessary (according to the goal of
your research or to the theoretical background)
Examples:
Return to human capital. We restrict a sample excluding respondents
who are not in labour force
Special cases: excluding the outliers (sberbank)
Risks
Sample selection can lead to a nonrepresentative subsample
Aggregation errors (“manufacture-centrism”)
Selection bias
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Data Description
Database title
Source of data
Type of data
Time period used
Unit (item) of observations
Number of observations
Advantages and disadvantages of the database used
Data limitations: omitted variables (no information about income),
response rate (number of nonmissings), underrepresentative
subgroups, attrition problem
Describe all the manipulations performed (aggregation, merging
databases, deflation, creating new variables)
Descriptive statistics including descriptive statistics for the
subsamples (male vs female, employed vs unemployed, etc.)
Never use abbreviations for variables in tables!!!
Round to the appropriate numbers (0.0000)
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Measurement Process
Data reconnaissance includes:
Descriptive statistics (min, max, mean, sd, median, etc.)
Densities (kdensity, histogram, box-plot, etс.)
Scatterplots for two variables
Cross-tables
Pair correlations
Tests
+ Everything which allows you to make a conclusion!
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Scales of measuremen
Scales of measurement in research and statistics are the different
ways in which variables are defined and grouped into different
categories
Sometimes called the level of measurement, it describes the
nature of the values assigned to the variables in a data set
Measurement is the process of recording observations collected
as part of a research
Scaling is the assignment of objects to numbers or semantics
These two words merged together refers to the relationship
among the assigned objects and the recorded observations
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What is a Measurement Scale?
A measurement scale is used to qualify or quantify data variables
in statistics
It determines the kind of techniques to be used for statistical
analysis
There are different kinds of measurement scales, and the type
of data being collected determines the kind of measurement
scale to be used for statistical measurement
These measurement scales are four in number, namely:
nominal scale,
ordinal scale,
interval scale,
ratio scale
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NOTE!
The measurement scales are used to measure qualitative and
quantitative data
With nominal and ordinal scale being used to measure qualitative
data
While interval and ratio scales are used to measure quantitative
data
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Characteristics of a Measurement Scale: IDENTITY
Identity refers to the assignment of numbers to the values of
each variable in a data set
Consider a questionnaire that asks for a respondent’s gender
with the options Male and Female for instance
The values 1 and 2 can be assigned to Male and Female respectively
(in sociology)
In statistics we use 0 and 1 (Why?)
Arithmetic operations can not be performed on these values
because they are just for identification purposes
This is a characteristic of a nominal scale
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Characteristics of a Measurement Scale: MAGNITUDE
The magnitude is the size of a measurement scale, where numbers
(the identity) have an inherent order from least to highest
They are usually represented on the scale in ascending or
descending order
The position in a race, for example, is arranged from the 1st,
2nd, 3rd to the least.
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Characteristics of a Measurement Scale: EQUAL INTERVALS
Equal Intervals means that the scale has a standardized order
I.e., the difference between each level on the scale is the same
This is not the case for the ordinal scale
Each position does not have an equal interval difference
In a race, the 1st position may complete the race in 20 secs,
2nd position in 20.8 seconds while the 3rd in 1 min.
A variable that has an identity, magnitude, and the equal
interval is measured on an INTERVAL SCALE
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Characteristics of a Measurement Scale: ABSOLUTE ZERO
Absolue zero is a feature that is unique to a ratio scale
It means that there is an existence of zero on the scale, and is
defined by the absence of the variable being measured (e.g. no
qualification, no money, does not identify as any gender, etc.)
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Levels of Data Measurement
By knowing the different levels of data measurement, researchers
are able to choose the best method for statistical analysis!!!
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Nominal Scale
The nominal scale is a scale of measurement that is used for
identification purposes
It is the coldest and weakest level of data measurement among
the four
Sometimes known as categorical scale, it assigns numbers to
attributes for easy identity
These numbers are however not qualitative in nature and only
act as labels
The only statistical analysis that can be performed on a nominal
scale is the percentage or frequency count.
It can be analyzed graphically using a bar chart and pie chart
We might be interested in dynamics
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Nominal Scale: Example
Which political party are you affiliated with?
Independent, Republican, Democrat
Labeling Independent as “1”, Republican as “2” and Democrat
as “3” does not in any way mean any of the attributes are
better than the other
They are just used as an identity for easy data analysis
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Nominal Scale: Example
Gender: Male, Female, Other.
Hair Color: Brown, Black, Blonde, Red, Other.
Type of living accommodation: House, Apartment, Trailer,
Other.
Genotype: Bb, bb, BB, bB.
Religious preference: Buddhist, Mormon, Muslim, Jewish, Christian,
Other.
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Nominal Scale: Statistics
The most appropriate analyses is
pie-chart
share comparison
distribution analysis (specifically in time)
NOT ALLOWED: mean values, sd, summation, etc.
Absolute Zero exists
Conclusion
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Ordinal Scale
Ordinal Scale involves the ranking or ordering of the attributes
depending on the variable being scaled
The items in this scale are classified according to the degree of
occurrence of the variable in question
Ordinal scale can be used in market research, advertising, and
customer satisfaction surveys
It uses qualifiers like very, highly, more, less, etc. to depict a
degree
We can perform statistical analysis like median and mode using
the ordinal scale, but not mean
However, there are other statistical alternatives to mean that
can be measured using the ordinal scale.
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Ordinal Scale: Example
A software company may need to ask its users: How would you
rate our app?
Excellent, Very Good, Good, Bad, Poor
The attributes in this example are listed in descending order
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Ordinal Scale: Example
High school class ranking: 1st, 9th, 87th. . .
Socioeconomic status: poor, middle class, rich.
The Likert Scale: strongly disagree, disagree, neutral, agree,
strongly agree.
Level of Agreement: yes, maybe, no.
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Ordinal Scale: Statistics
The most appropriate analyses is
histogramms
shares
distribution
NOT ALLOWED: mean values, sd, summation, etc.
Absolute Zero does not exist
Conclusion
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Interval Scale
The interval scale of data measurement is a scale in which the
levels are ordered and each numerically equal distances on the
scale have equal interval difference
If it is an extension of the ordinal scale, with the main difference
being the existence of equal intervals
With an interval scale, you not only know that a given attribute
A is bigger than another attribute B, but also the extent at
which A is larger than B
Also, unlike ordinal and nominal scale, arithmetic operations
can be performed on an interval scale
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Interval Scale: Example
It is used in various sectors like in education, medicine, engineering,
etc.
Some of these uses include calculating a student’s CGPA, measuring
a patient’s temperature, etc.
A common example is measuring temperature on the Celsius
scale. It can be used in calculating mean, median, mode, range,
and standard deviation
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Ratio Scale
Ratio Scale is the peak level of data measurement
It is an extension of the interval scale, therefore satisfying the
four characteristics of measurement scale: identity, magnitude,
equal interval, and the absolute zero property
This level of data measurement allows the researcher to compare
both the differences and the relative magnitude of numbers
The ratio scale of data measurement is compatible with all
statistical analysis methods like the measures of central tendency
(mean, median, mode, etc.) and measures of dispersion (range,
standard deviation, etc.).
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Ratio Scale: Example
Some examples of ratio scales include length, weight, time, etc.
With respect to market research, the common ratio scale examples
are price, number of customers, competitors, etc.
It is extensively used in marketing, advertising, and business
sales
For example: A survey that collects the weights of the respondents
Which of the following category do you fall in? Weigh
more than 100 kgs
81 – 100 kgs
61 – 80 kgs
40 – 60 kgs
Less than 40 kgs
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Ratio Scale: Example
Age
Weight
Height
Sales Figures
Income earned in a week
Years of education
Number of children
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Ratio Scale: Cardinal Numbers
A cardinal number, sometimes called a “counting number,” is
used for counting, like when you count 1,2,3, ...
You use these numbers to answer the question “how many?”
Many times, sets of cardinal numbers create statistics
When this happens, the cardinal numbers disappear
For example, according to the 2010 U.S. Census, the average
number of people per household in the U.S. is 2.58
This number was arrived at by taking the cardinal number of
people in each household and then finding the mean
Once you have taken that set of cardinals and found its mean
(2.58), the statistic is no longer cardinal
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Qualities of a Good Questionnaire
The length of questionnaire should be proper one
The language used should be easy and simple
The term used are explained properly
The questions should be arranged in a proper way
The questions should be in logical manner
Complex questions should be broken into filter questions
The questions should be described precisely and correctly
The questionnaire should be constructed for a specific period
of time
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Qualities of a Good Questionnaire
The questions should be moving around the theme of the investigator
The answers should be short and simple
These answers should be accurate
The answers should be direct one
The answers should be relevant to the problem
The answers should be understandable to everyone of respondents
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Qualities of a Good Questionnaire
It should seek only that data which can not be obtained from
other sources
It should be as short as possible but should be comprehensive
It should be attractive
It should be represented in good Psychological order proceeding
from general to more specific responses
Double negatives in questions should be avoided
Putting two questions in one question also should be avoided.
Every question should seek to obtain only one specific information
It should avoid annoying or embarrassing questions
It should be designed to collect information which can be used
subsequently as data for analysis
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Measurement
Questionnaire surveys are measurement instruments
While scientific measurement instruments measure physical
properties like weight, questionnaire surveys often measure
respondents’ self-reported attitudes, opinions or behaviours
As constructs are intangible and complex human behaviours
or characteristics, they are not well measured by any single
question
They are better measured by asking a series of related questions
covering different aspects of the construct of interest
The responses to these individual but related questions can
then be combined to form a score or scale measure along a
continuum.
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How to measure quality?
As with scientific measurement instruments, two important
qualities of surveys are consistency and accuracy
These are assessed by considering the survey’s reliability and
validity
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Validity
Validity is the extent to which an instrument, a survey, measures
what it is supposed to measure: validity is an assessment of its
accuracy.
How do we assess validity?
Face validity and content validity are two forms of validity that
are usually assessed qualitatively
A survey has face validity if, in the view of the respondents,
the questions measure what they are intended to measure
A survey has content validity if, in the view of experts (for
example, health professionals for patient surveys), the survey
contains questions which cover all aspects of the construct
being measured
Face and content validity are subjective opinions of non-experts
and experts
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Validity
Face validity is often seen as the weakest form of validity, and
it is usually desirable to establish that your survey has other
forms of validity in addition to face and content validity
Criterion validity is the extent to which the measures derived
from the survey relate to other external criteria
These external criteria can either be concurrent or predictive
Concurrent validity criteria are measured at the same time as
the survey, either with questions embedded within the survey,
or measures obtained from other sources
It could be how well the measures derived from the survey
correlate with another established, validated survey which measures
the same construct, or how well a survey measuring affluence
correlates with salary or household income
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Validity
Often the purpose of a survey is to make an assessment about
a situation in the future, say the suitability of a candidate for
a job or the likelihood of a student progressing to a higher level
of education
Predictive validity criteria are gathered at some point in time
after the survey and, for example, workplace performance measures
or end of year exam scores are correlated with or regressed on
the measures derived from the survey
If the external criteria is categorical (for example, how well a
survey measuring political opinion distinguishes between Conservative
and Labour voters), while still criterion validity, how well a
survey distinguishes between different groups of respondents
is referred to as known-group validity
This could be assessed by comparing the average scores of
the different groups of respondents using t-tests or analysis
of variance (ANOVA = our next lecture!!!)
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Validity
Construct validity is the extent to which the survey measures
the theoretical construct it is intended to measure, and as such
encompasses many, if not all, validity concepts rather than
being viewed as a separate definition
Confirmatory factor analysis (CFA) is a technique used to
assess construct validity
With CFA we state how we believe the questionnaire items are
correlated by specifying a theoretical model
Our theoretical model may be based on an earlier exploratory
factor analysis (EFA), on previous research or from our own a
priori theory
We calculate the statistical likelihood that the data from the
questionnaire items fit with this model, thus confirming our
theory
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Reliability
Reliability is the extent to which an instrument would give the
same results if the measurement were to be taken again under
the same conditions: its consistency
How do we assess reliability?
One estimate of reliability is test-retest reliability
This involves administering the survey with a group of respondents
and repeating the survey with the same group at a later point
in time
We then compare the responses at the two timepoints
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Reliability
For categorical variables we can cross-tabulate and determine
the percentage of agreement between the test and retest results,
or calculate Cohen’s kappa
For continuous variables, or where individual questions are
combined to construct a score on a scale, we can compare the
values at the two timepoints with a correlation
One immediately obvious drawback of test-retest reliability is
memory effects
The test and the retest are not happening under the same
conditions
If people respond to the survey questions the second time in
the same way they remember responding the first time, this
will give an artificially good impression of reliability
Increasing the time between test and retest (to reduce the
memory effects) introduces the prospect of genuine changes
over time
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Reliability
If the survey is to be used to make judgements or observations
of another subject, for example clinicians assessing patients
with pain or mental health issues, or teachers rating different
aspects of children’s writing, we can compare different raters’
responses for the same subject; inter-rater reliability
Here we would use the same statistics as for test-retest reliability
As with test-retest reliability the two measurements are again
not taken under the same conditions, the raters are “different;
one may be systematically “harsher” than the other
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Reliability
Parallel-form reliability involves developing two equivalent, parallel
forms of the survey; form A and form B say, both measuring
the same underlying construct, but with different questions in
each
Respondents are asked to complete both surveys; some taking
form A followed by form B, others taking form B first then
form A
As the questions differ in each survey, the questions within
each are combined to form separate scales
Based on the assumption that the parallel forms are indeed
interchangeable, the correlation of the scale scores across the
two forms is an estimate of their reliability
The disadvantage of this is that it is expensive; potentially
double the cost of developing one survey
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Reliability
An alternative is split-half reliability
Here we divide the survey arbitrarily into two halves (odd
and even question numbers, for example), and calculate the
correlation of the scores on the scales from the two halves
Reliability is also a function of the number of questions in the
scale, and we have effectively halved the number of questions
So we adjust the calculated correlation to estimate the reliability
of a scale that is twice the length, using the Spearman Brown
formula
Split-half reliability is an estimate of reliability known as internal
consistency; it measures the extent to which the questions in
the survey all measure the same underlying construct
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Reliability
Cronbach’s alpha is another measure of internal consistency
reliability
For surveys or assessments with an even number of questions
Cronbach’s alpha is the equivalent of the average reliability
across all possible combinations of split-halves
Most analysis software will also routinely calculate, for each
question or questionnaire item in the scale, the value of Cronbach’s
alpha if that questionnaire item was deleted
These values can be examined to judge whether the reliability
of the scale can be improved by removing any of the questionnaire
items
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Final Practical Task
I believe the Confucian adage:
You tell me, I forget
You show me, I remember
You involve me, I understand
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Research Questions
Are big companies more productive than small companies?
Are state-owned companies more productive than private companies?
Do developed and developing countries differ in the level of
entrepreneurial activity?
Are there any gender differences in the level of entrepreneurial
activity in Russia?
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Research Questions
Are employed people healthier than unemployed or self-employed
ones?
Is it true that export-oriented countries have a better environment
for starting a business than import-oriented countries do?
Is it true that countries with better financial systems are better
at international trade?
Is it true that countries with better labour markets are better
at entrepreneurial activity?
Is it true that the better educated the population of the country
is, the more innovative the country is?
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Research Questions
Is it true that the better the country’s financial institutions
are, the more innovative this country is?
Is it true that among transition economies elderly people have
lower trust to financial institutions than youth population?
Is it true that better educated people believe that science
makes our life better?
Is it true that among transition economies there are generation
differences in belief that someone can be rich only at the expenses
of others?
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Questionnaire
Client: The management of Saint Petersburg School of Economics
and Management HSE-University (SEM)
The goal of your survey is to give the client a suggestion (or
suggestions) as to how to improve the process of managing the
university during this period of lockdown (transition from mainly
working face-to-face to working remotely); your main
considerations should be the interests of the two biggest groups of
stakeholders — the teachers and the students.
Problem: The SEM management would like to choose the best
way to adapt the current managerial process in a way that would
be most agreeable to both of these two main stakeholder groups
(the teachers and the students).
Client’s Note: The goal is not to satisfy the students only! The
teachers are a scarce resource; as such, they should have their
interests taken into account.
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Client: Teachers of Saint Petersburg School of Economics and
Management HSE-University (SEM)
The goal of your survey is to give the client a suggestion (or
suggestions) as to how to improve the process of teaching and
communicating with the students during the current period of
lockdown (transition from mainly working face-to-face to working
remotely).
Problem: The teachers would like to be advised on the ways in
which they can make their courses more convenient to take, the
classes more productive and enjoyable, and the communication
more efficient. Also consider the technical aspect of distance
learning (platforms, homework, connectivity, and so on).
Note: Advising on a better way to teach is not equal to “satisfy
students above all else”!
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Client: International Centre for Health Economics, Management,
and Policy HSE-University (CHEMP)
The goal of your survey is to make a survey about mental health
problems in the current period of lockdown.
Problem: We are going through a period of lockdown, which is a
stressful time for everybody. Being stuck at home, the economy’s
being in depression, working remotely, and worrying about
COVID-19 are just a few of the problems that are troubling the
population in these trying times. These problems may lead to
some mental health disorders. It would be interesting to
understand the scale of this problem.
Target group: Students of Saint Petersburg School of Economic
and Management
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Client: International Centre for Health Economics, Management,
and Policy HSE-University (CHEMP)
The goal of your survey is to make a survey about mental health
problems in the current period of lockdown.
Problem: We are going through a period of lockdown, which is a
stressful time for everybody. Being stuck at home, the economy’s
being in depression, working remotely, and worrying about
COVID-19 are just a few of the problems that are troubling the
population in these trying times. These problems may lead to
some mental health disorders. It would be interesting to
understand the scale of this problem.
Target group: Teachers of Saint Petersburg School of Economic
and Management
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Client: International Centre for Health Economics, Management,
and Policy HSE-University (CHEMP)
The goal of your project is to make a survey about people’s
perceptions of COVID-19 pandemic.
Target group: general population
Note: You may narrow the target group down (to just one age
group, gender, or any other social stratum)
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Problem: As billions of people over the world are currently in
lockdown, each of them must have his own view of the
COVID-19-related situation in the world. You need to assess how
well the people are informed of the different aspects of the
coronavirus: whether they know what causes it, how it spreads,
and how to avoid contracting it; whether they believe it to be
man-made or naturally-occurring; whether they are of the opinion
that the virus is real or whether it is a Judeo-Masonic-Reptiloid
conspiracy; whether the people are taking any proactive steps to
make sure that they not become infected with COVID-19;
whether the people believe the WHO statistics on the virus;
whether the people follow the guidelines aimed at reducing the
spread of the virus; whether the people brave the virus-ridden
streets (risk-taking).
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Main elements of the survey
(1) Reformulate the goal of your survey in the form of a list of
specific aims that you should reach as you do your project;
(2) Determine the target group (or target groups) that should be
surveyed; identify who your target group, population, and sample
are.
(3) Develop a questionnaire (perhaps you should start from an
in-depth interview of two-three representative members of the
population you seek to analyse);
(4) Choose the platform for your online questionnaire (the easiest
way is Google Forms);
(5) Make a pilot study (be sure that everybody understands your
questions);
(6) Analyse the results of the pilot study to be sure that you have
a variation in the answers as well as that your questionnaire really
helps to reach the aims formulated in (1);
(7) Alter the questionnaire if you need to;
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Main elements of the survey
(8) Organise the survey;
(9) Process the collected data, encoding it and compiling it into
one database;
(10) Make calculations (descriptive statistics, tests, etc.) to help
you to (a) check the quality of your data/questionnaire/survey;
(b) confirm whether you have attained the aims formulated in (1);
(11) Develop a report on your survey (graphs, descriptive
statistics, tests, etc.);
(12) Make a suggestion (or suggestions) to the client;
(13) Discuss the main limitations of your survey.
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Main elements of the survey
(14) If you use a standard questionnaire developed by others, you
might need to translate it into Russian. If you do so, please
translate the resulting Russian-language version back into English
to see whether the meaning of the questions has remained the
same; this operation must be done by different people to check
whether the questions have the same meaning in both languages.
(15) If the client is the International Centre for Health Economics,
Management, and Policy (CHEMP), you should remember that
the main goal of CHEMP is research that makes it possible for
the centre to make suggestions to policy-makers.
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Main elements of the survey
(16) If you use open-ended questions in your survey, be aware that
doing so may make it difficult for you to conveniently aggregate
the answers into a limited number of opinions; this may prevent
you from getting the information that you set out to discover.
(17) Before you make a questionnaire, have a think about how
you are going to encode the information that you will obtain —
ordered variables/answers, non-ordered answers, binary answers,
Likert scale. . . ).
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EVALUATION FORMULA FOR THE SURVEY
1. (0.1) The quality of the report.
2. (0.1) The quality of the presentation.
3. (0.2) Using a sufficient amount of descriptive statistics,
graphics, tests, and other methods relevant to attaining the aims
of the survey.
4. (0.1) How well the questionnaire fits the goal of the survey.
5. (0.1) Reliability, validity, sensitivity of the questionnaire.
6. (0.1) How well the target group, the population, and the
sample are chosen.
7. (0.1) There being survey limitations.
8. (0.2) How well-argumented the suggestions are; how well the
suggestions are based on and stem from the results of the survey.
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Main elements of the research
(1) Get to know the database that you have been recommended
(read about who collected the data, how the data were collected,
and why the data were collected).
(2) Download the database and study the variables that you have
at your disposal (carefully read not only the variable labels but
also the descriptions of these labels on the website or in the
reports).
(3) Discuss the mechanisms behind the relationship between the
characteristics mentioned in the question. Reformulate the
research question in the form of a list of research hypotheses that
you should reach as you do your project.
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Main elements of the research
(4) You are recommended to describe the "ideal,
"perfect"variables for your research. Choose variables that could
replace your non-existing "ideal"benchmark variable.
(5) Choose proxy variables that are best suited for reflecting the
characteristics that you are studying (for example, how to
measure productivity or innovativeness; how to determine
whether the country is developed or developing).
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Main elements of the research
(6) Reformulate your research question and hypothesis testing in
terms of your proxy variables.
(7) Make calculations (descriptive statistics, tests, etc.) to test
your research hypotheses and to answer your research question.
(8) Develop a report on your survey (graphs, descriptive statistics,
tests, etc.).
(9) Make a conclusion about what the bottom-line answer to your
research question is.
(10) Discuss the main limitations of your research.
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Main elements of the research
NOTE. Be aware of the type of data that you are using. The
choice of criteria that you will use to answer your research
question depends on the type of data.
NOTE. Sometimes, there can be several proxy variables for the
characteristic that you need. It may be a good idea to use not just
one of them but some of them or all of them. You should include
a discussion of how each of the proxy variables is superior or
inferior to the others.
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EVALUATION FORMULA FOR THE RESEARCH
1. (0.1) The quality of the report.
2. (0.1) The quality of the presentation.
3. (0.1) How good your discussion of the mechanisms behind the
relationship between the characteristics mentioned in the question
is.
4. (0.1) How well you discuss your choice of proxy variables.
5. (0.1) How well you discuss the database and its applicability to
the goals of your research.
6. (0.2) Using a sufficient amount of descriptive statistics,
graphics, tests, and other methods relevant to attaining the aims
of the survey.
7. (0.1) How well you discuss the limitations of your research.
8. (0.2) How well your conclusions and the final discussion of your
research are based on your statistical results.