SADC Course in Statistics

Setting the scene

(Session 01)

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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 Demographicand Health Survey, 1992. Primary interestwas 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 12-59 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 primaryand 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, 2000-2002, 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 sessions1-10, and other types in later sessions.

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Practical work follows to ensure learning objectives

are achieved…