Random sampling Population data: Lesson 2

Sampling: selecting from across the world There are currently 196 countries in the world. In order to fully analyse the worldwide picture, we would need to use the data on every country, i.e. the population of the data. However, in order to save time and money (usually where using all the data is unfeasible and unrealistic) we select a number of items. In this case, we would select a sample of countries. It’s important to be unbiased when selecting, in order to gain a fair sample. 2

Sampling: selecting from across the world How can we select a fair sample? Random sampling: Data is picked at random, usually using some random generator. Systematic sampling: Data is chosen at regular intervals (every 5th entry, for example). Cluster sampling: Data is grouped in ‘clusters’ and random clusters are selected. Stratified sampling: Data is selected in proportion to ‘cluster’ sizes. (Quota sampling: Keep selecting data until you have enough for the given category) 3

Sampling: selecting from across the world You have been provided with a list of 210 countries, principalities and sovereign states that have been put into clusters by continent. Africa The Americas Asia Europe Oceania In order to describe the population change of each continent, we will select a sample to analyse statistically. 4

Sampling: selecting from across the world Random sample: Africa There are 57 countries listed in Africa. How can we randomly select 10?  Assign each country the numbers 1 to 57.  Using a calculator, generate a number between 1 and 57 inclusive. RanInt#(1,57) =  Repeat the process until you have 10 unique numbers (press = to get a new random number)  Highlight the 10 countries these numbers refer to in the list. 5

Random sampling 6

Sampling: selecting from across the world Systematic sample: the Americas There are 40 countries listed in the Americas. How can we systematically select 10?  Select countries by highlighting one every so many down the list.  40 ÷ 10 = 4  Choose a starting point within the first four countries on the list and highlight.  Highlight every 4th country down the list. 7

Systematic sampling 8

Sampling: selecting from across the world Cluster sample: Europe There are 45 countries listed in Europe. How can we cluster the countries in order to select a group of 10?  The continent is already split into North, West, East, South.  Select one of these clusters that has the appropriate number of countries in it. 9

Cluster sampling 10

Systematic sampling There are 51 countries listed in Asia, divided into five regions. How can we proportionally select 10 countries across the regions of Asia?  Find the number of countries needed from each region.  No. countries in region ÷ total no. countries × number in sample  E.g. for Western Asia: 18/51 × 10 = 3.53 (4)  Select four countries (randomly or systematically) 11

Sampling: selecting from across the world Your choice: Oceania There are 17 countries listed in Oceania. Select one the sampling methods you have used so far to highlight a list of 10 Oceania countries. (Some will be more appropriate than others.) 12

Sampling: selecting from across the world For each of the sampling methods you have just done, state one advantage and one disadvantage of the method. Sampling method AdvantageDisadvantage Random All items of data equally likely to be chosen, hence it will be fair Can be time-consuming and impractical on a large scale SystematicUnlikely to get a bias sample The process may not be random, as start position and order of data may affect selection Cluster A quick and efficient way of selecting a sample Open to a biased sample if the clusters aren’t similar Stratified It’s the best way to fairly reflect the population Can be time-consuming and impractical on a large scale 13

Sampling: selecting from across the world You can improve the reliability of the sample in all cases by … … increasing the size of the sample 14

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