SAMPLING. A collection of items from a population which are taken to be representative of the population.

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1 SAMPLING Sample A collection of items from a population which are taken to be representative of the population. Population Is the entire collection of items which we are interested and wish to make estimates for, test hypothesis etc. We have two types of population i.e Target Population - it is the collection of all the units/elements of a population from which a sample is to be collected.(those items we would like to investigate) Study Population - Those items we are able to investigate. How you select a sample is an important matter Selecting an important unrepresentative sample would be a waste of time since any inferences drawn from the sample would be misleading. When a sample is unrepresentative, it is said to be biased. Infinite Population- N is not known but very large Finite Population - N is known In order to select a sample from a population we need some kind of list which is called a frame. Sampling Frame The listing of all the elements of a finite population e.g voter s roll, University register gives the names of all students in the University. The problems arising from an inaccurate frame(over/under coverage) causes bias. 1

2 Under-coverage- occurs when some members of the population are inadequately represented in the sample. Over-coverage- occurs when some members of the population are over represented in the sample. Sampling Unit Refers to what we are sampling. Reasons for Sampling Its more economic (much cheaper) Less time is needed Accessibility Destructive sampling (Data on a certain random variable might entail destroying the product and hence it will be more practical to sample than to take the whole population.) Not necessary to consider the whole population if the sample is good Data collection arises from designed experiments or sample surveys Census entire study population Sample Survey sample from study population Survey Well planned data collection strategy. Sample representation of population. Uses results while information is current. Experiment apply treatments sample usually a predetermined portion of the population. 2

3 1 Sampling Procedures There are two main different types of sampling procedures. These are probabality sampling procedures and non-probability sampling. The probability sampling procedures that will be covered are; simple random sampling systematic random sampling stratified random sampling cluster sampling The non probability sampling procedures that will be covered are; convinience sampling judgemetal sampling quota Sampling Any sampling methods in which the observations are not selected in a random manner are non-probability samples. Their major disadvantage is the unrepresentative nature of the sample being drawn. When sample are selected in a random manner from the population, then they are called probability sampling methods. Types of Random Sampling 1. Simple Random Sampling 2. Systematic Random Sampling 3. Stratified Random Sampling 4. Cluster Sampling, etc. You can sample with/without replacement. If N is large the differences are minimal. 3

4 Simple Random Sampling Each subset of N of size n has the same probability of being selected. To be completely assured of obtaining a random sample from a finite population, you should number the members of the population from 1 to N(the population size) and, using a set of random numbers, select the corresponding sample of n population elements for your sample. However for situations in which the population is extremely large, this strategy may be impractical, and instead you can use a sampling plan that is nearly random. Systematic Random Sampling The sample of n is obtained by sampling every k th record, where k is an integer approximately equal to N n e.g A bank wants a sample of customers to determine their reaction to a proposed new service. The bank knows that on average they see 720 customers a day. if a sample of n = 100 is desired, they could select to interview every = 7th customer by randomly choosing the starting point. This is a situation where a simple random sample is not advisable, since it would be very difficult to randomly select customers during the working day. Stratified Random Sampling Stratified random sampling is applicable when the population is heterogeneous with respect to the random variable understudy, but can be divided into segments called strata which will be homogenous. Def ination A stratified random sample is a sample obtained by dividing the population into non-overlapping groups, called strata and then select a random sample from each stratum. OR Split population into non-overlapping groups such that each group has similar items and maximise difference between groups. Usually used if we want; similarity within groups differences between groups 4

5 Defination of groups will depend on what is being studied. Once you divide into groups, you select a simple random sample from each group. example Suppose one would like to assess the feasibility of income packages offered by a company to its employees. The population might be divided into 3 strata, i.e, senior management, middle management and juniour management. Stratification offers an alternative to simple random sampling and in many instances increases the accuracy of the information available for estimating the population parameters. The most popular type of stratification is called stratification with proportional allocation. This is when a stratified random sample is obtained according to the proportion of the strata in the population. Cluster Sampling When units to be sampled are grouped together, possibly geographically, then cluster sampling can give more information for a given cost than the other sampling techniques. Def ination Seperate population into non-overalapping groups so as to maximise differences within groups i.e cluster should represent the whole population. Select a simple random sample of cluster (often only 1) and then select a simple random sample of items from the selected cluster (sometimes the whole cluster). improves accuracy cheaper, less time Convinience Sampling It is when elements are chosen on the basis of their proximity to the interviewer. It is sampling drawn to suit the convinience of the researcher. example A reseacher might be interested in finding the shopping habits of people and would just use a shopping mall close to his/her home by interviewing shoppers on a certain day. 5

6 Judgemental Sampling It is when one uses expert opinion to come up with a sample. For example only sports person might be selected to comment on the national team selection. Defination It is when sample elements are chosen based on the interviewer s own assessment of what constitutes a representative sample. Quota Sampling It is when various characteristics of the population are noted, for example, the divisions on sex, age and job type and the sample aims to include sim ilar proportions of people with these characteristics. Each interviewer is the given a number, or quota, of people with these characteristics to contact. The final selection of the individual is left up to the interviewer. Def ination Quota sampling is when a population is divided into segments and a specified number of observations is collected from each segment. 6

7 2 Introduction to Demography Def- Demography It is the scientific study of human population primarily with respect to their size, structure and development.(un Dictionary) Demography is hence concerned with current size and characteristics of human population, how they were attained and how they are changing. Why Study Demography? Demography data is used by many professionals (statisticians, actuaries, health policy planners, e.t.c). They use them for social, economic and environmental planning, e.t.c. Demographic Data There are three major factors which affect the size and growth of the population. Fertility, i.e a birth may occur. Mortality, i.e a death may occur. Migration, i.e a migrant may enter or leave the country. There are other factors which determine the structure or composition of the population. They do not affect the size of the population. These are (i)age, (ii)sex, (iii)marital status, (iv)education, e.t.c Terminology 1. Population Composition - this is the statistical distribution of individuals in a population according to characteristics ( same as above, age, sex, marital status, e.t.c) 2. Vital Events - events which change the size or composition of a population, e.g, deaths, births, marriages, migration, e.t.c. 3. Censuses and Surveys - These determine population size and composition. 7

8 4. Vital/Registration System - These records vital events as they occur. e.g, birth certification, death certification, e.t.c. Census This is a process of collecting, compiling, analysing and publishing demographic, socio and economic data about the entire population of a well defined territory at a specified time. It is a huge, complex and expensive operation taken at regular interval, each census requires extensive planning before and can take weeks or years before the analysis appears or published. Census therefore requires educated and skilled manpower. There are 2 types of census namely; De-facto. De-jure. De-facto - individuals are counted whenever they happen to be on census night. De-jure - Individuals are counted by their usual place of residence. Sources of Demographic Data Census/Surveys. Vital registration - birth, death, e.t.c. Basic Measures in Demography 1. Absolute and Relative Numbers Demographic data is also published in terms of absolute numbers, e.g, 3000 people died of cholera in Zimbabwe. Such absolute numbers are useful in themselves but usually we are more interested in making comparison of these numbers relate country s population. To obtain more useful information that can be used for comparison to demographers use relative numbers, e.g, ratios, percentages, proportions and rates. 8

9 2. Population Pyramids The 2 most characteristics describing a population are, (i)age, (ii)sex. Demographers display such data in the form of a pyramid. Population pyramids are seperated back to back histograms for males and females and age distributions. Normally 5 years age groups are used, but, other groupings can be used, 10 years or single year age groups. Developed and Developing country Typical Developing Countries high mortality/high fertility/high dependence ratio Typical Developed Countries low mortality/low fertility/low dependence ratio Three Common Ratios 1. Sex Ratio defined as the number ) of males per 100 females 100 ( Number of males Number of females Sex ratio may be calculated for different age groups and it is called age specific sex ratio. It is not constant over time. 2. Child/Woman Ratio This ( is ) Number of children aged 0 14 years Number of females aged years 100 gives a measure of fertility. The ratio of young children to women of reproductive age gives a rough and ready measure of a country s fertility. 9

10 3. Dependency Ratio defined as ( Number of people aged 0 14 and 65+ years Number of people aged years ) 100 This measures the economic ratio of a country, and assesses the number of people uneconomically active relative to those that are economically active. Crude Rates These are found by dividing the total number of vital events occuring in a year by population size at mid year. 1. Crude Birth Rate (CBR) ( total number of live births in a year population size at mid year ) Crude Death Rate (CDR) ( total number of deaths in a year population size at mid year ) 1000 The difference between CBR and CDR is called the crude rate of natural increase. Age Specific Fertility Rate (f x ) This is ( the number of babies born to women of age group X number of women in age group X in the population ) 1000 Age Specific Mortality Rate (M x ) This ( is ) the number of deaths of people in age group X number of people in age group X in the population

11 Life Tables Mathematical models which are used to project/predict the number of years an individual can be expected to survive, at any given age. Males and females have got seperate life tables. 11