Setting the scene
(Session 01)
SADC Course in Statistics
Learning Objectives
At the end of this session, you will be able to
• recognise situations where statistical
modelling in relevant
• understand the purpose of modelling
• for a given scenario, be able to identify the
key response variable of interest and
potential factors that may affect the
variation in the key response
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Session Contents
In this session you will be
• provided with examples of situations
where modelling is relevant to answer
questions of importance in policy decisions
• given the opportunity to explore examples
in order to develop some insight into
modelling ideas
• introduced to the associated terminology
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Examples where modelling is relevant
Two examples will be discussed initially…
• Child malnutrition and feeding practices in
Malawi, in Food and Nutrition Bulletin,
Volume 18, No. 2, 1997. United Nations
University Press, Tokyo, Japan
• Gender-sensitive education statistics and
indicators, in UNESCO Training Materials
for workshops on Education Statistics and
Indicators in Ghana (1996), Côte d’Ivoire
(1997).
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Example 1 - Nutrition:
The data come from the Malawi Demographic
and Health Survey, 1992. Primary interest
was in identifying factors affecting malnutrition.
The factors were:
• gender, age, birth size, type of breast
feeding, maternal education & area of
residence amongst 4-11 month olds infants
• age, birth size, preceding and succeeding
birth interval, if still breast feeding, no. of
days with diarrhoea in past 2 weeks and
other household characteristics amongst 1259 month old children
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Example 2 - Education:
A cross-country study to determine factors
which hinder gender equality in education.
One outcome variables was a gender-equity
sensitive indicator (GESI). Some factors
studied were:
• Total fertility rate
• GNP per capita
• % female teachers in primary education
• Male & female enrolment ratios at primary
and secondary education
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Identifying response and
regressor (explanatory) variables
In each of the above examples, there was a
key response of interest. This is called the
dependent variable, usually denoted by y.
Factors identified as possibly influencing the
variability in y are called explanatory, or
regressor variables. They form the x’s in the
model. In statistical modelling, we assume
they are measured without error.
What are the y and x’s in previous examples?
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What is a statistical model?
A model is a simple equation which relates a
key response (y) of interest to one or more
other variables (x1, x2, …) which are believed
to contribute to the variability in the key
response.
For example, y = 38.1 – 1.91x, where y is
perinatal mortality per 1000 live births and x
the number of health centres per 1000 HHs.
This describes the relationship between
mortality and availability of health facilities.
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Purpose of Modelling
• To determine a simple summary of the
way that a key response (y) relates to a
set of x’s
• To understand factors (x’s) affecting y
• To use the model equation to make
predictions about y
• To determine which values of the x’s will
optimise y in some way
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Types of key response
In the simplest type of statistical modelling,
the key response is a quantitative
measurement, assumed to follow a normal
distribution. This module focuses on such
responses.
However, there are other types of key
responses. Often have binary variables, e.g.
whether or not a household is below the
poverty line, whether contraceptives are
used or not, person is HIV positive or not.
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Example 3: a binary response
See Impact of HIV on tuberculosis in
Zambia: a cross-sectional study, in British
Medical Journal, 1990, Vol.301, pp.412-5
This includes studying the relationship of
HIV-1 antibody state (yes/no) to
• years of full-time education
• housing (no. of people sharing bedroom)
• marital state (married, single, other)
• history of treatment for sexually
transmitted diseases (yes/no)
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Example 4: a multinomial response
See Patterns of Tobacco Use in the Early
Epidemic Stages: Malawi and Zambia, 20002002, in American J of Public Health, 2005,
Vol. 95, No. 6, pp. 1009-1015.
This was a study relating tobacco use (none,
light smoker, heavy smoker) to
• age, education, occupation, religion, and
• residence (rural/urban), and
• marital status (married, single, other)
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Types of regressor variables
In above examples, the explanatory
(regressor) variables can be:
• quantitative measurements, e.g years of
education;
• ordered categorical variables, e.g. extent
of smoking (low, medium, high)
• nominal (type of occupation);
• binary (possess a specific asset or not).
Quantitative x’s will be considered in sessions
1-10, and other types in later sessions.
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Practical work follows to
ensure learning objectives
are achieved…
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