SADC Course in Statistics Setting the scene (Session 01)

To put your footer here go to View > Header and Footer 2 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

To put your footer here go to View > Header and Footer 3 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

To put your footer here go to View > Header and Footer 4 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, 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 dIvoire (1997).

To put your footer here go to View > Header and Footer 5 Example 1 - Nutrition: The data come from the Malawi Demographic and Health Survey, 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 month old children

To put your footer here go to View > Header and Footer 6 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

To put your footer here go to View > Header and Footer 7 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 xs in the model. In statistical modelling, we assume they are measured without error. What are the y and xs in previous examples?

To put your footer here go to View > Header and Footer 8 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 (x 1, x 2, …) 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.

To put your footer here go to View > Header and Footer 9 Purpose of Modelling To determine a simple summary of the way that a key response (y) relates to a set of xs To understand factors (xs) affecting y To use the model equation to make predictions about y To determine which values of the xs will optimise y in some way

To put your footer here go to View > Header and Footer 10 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.

To put your footer here go to View > Header and Footer 11 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 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)

To put your footer here go to View > Header and Footer 12 Example 4: a multinomial response See Patterns of Tobacco Use in the Early Epidemic Stages: Malawi and Zambia, , in American J of Public Health, 2005, Vol. 95, No. 6, pp 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)

To put your footer here go to View > Header and Footer 13 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 xs will be considered in sessions 1-10, and other types in later sessions.

To put your footer here go to View > Header and Footer 14 Practical work follows to ensure learning objectives are achieved…