Dr J Frost (jfrost@tiffin.kingston.sch.uk) www.drfrostmaths.com S3: Chapter 2 – Sampling Dr J Frost (jfrost@tiffin.kingston.sch.uk) www.drfrostmaths.com Last modified: 30th August 2015

Sampling As you’ve seen both in S2 and at GCSE, a sample is some subset of a population for which we have made observations, intended to represent the population. We want to chose things for our sample as random as possible to avoid bias. Population Sample The chapter looks at the variety of types of survey (many of which you’ve covered before). In the exam you are typically tested on: How you conduct the sampling method. Advantages and disadvantages. Advantages Disadvantages Census Should give completely accurate result. Time consuming and expensive. Can not be used when testing involves destruction. Large volume of data to process. Sample Survey Cheaper. Quicker. Less data to process. Data may not be accurate. Data may not be large enough to represent small sub-groups. ? ? ? ?

Types of Sampling I recommend laying out your notes like this for the rest of the chapter… Type How to carry out Advantages Disadvantages Random Sampling Lottery Sampling Systematic Sampling Stratified Sampling Quota Sampling

Random Sampling Type How to carry out Advantages Disadvantages Random Sampling What is it : Each thing has an equal chance of being selected. Random Number Sampling: Each element of sampling frame assigned a number. (See below) Numbers truly random and free from bias. Easy to use. Each number has a known equal chance of being selected. ? ? Not suitable when population size is large. ? ? “Suppose you wanted to take a sample of 50 from a population of size 400. Write down the first five random numbers starting at the seventh column from the left of the table (page 139) and working down.” Population = 400, Numbers: 372, 039, 172, 117, 053 ?

Random Sampling “Suppose you wanted to take a sample of 50 from a population of size 65. Write down the first seven random numbers starting at the second column from the left of the table (page 139) and working down.” Numbers: 48, 06, 39, 32, 49, 53, 52 ? “Suppose you wanted to take a sample of 50 from a population of size 3500. Write down the first seven random numbers starting at the third column from the left of the table (page 139) and working down.” Numbers: 0730, 0593, 1476, 1001, 1248, 1343, 2706 ?

Lottery Sampling ? ? ? Lottery Sampling Type How to carry out Advantages Disadvantages Lottery Sampling What is it : Each element of population identified by some characteristic put on a ticket. Tickets drawn randomly from container (without replacement). The tickets are drawn at random. It is easy to use. Each ticket has a known chance of selection. ? ? It is not suitable where the population size is large. A sampling frame is needed. ?

Systematic Sampling ? ? ? Systematic Sampling Type How to carry out Advantages Disadvantages Systematic Sampling What is it : Required elements are chosen at regular intervals in ordered list. i.e. Take every kth elements where: 𝑘= 𝑝𝑜𝑝 𝑠𝑖𝑧𝑒 𝑁 𝑠𝑎𝑚𝑝 𝑠𝑖𝑧𝑒 𝑛 Simple to use. Suitable for large samples. ? ? Only random if the ordered list is truly random. Can introduce bias. ?

Stratified Sampling ? ? ? Stratified Sampling Type How to carry out Advantages Disadvantages Stratified Sampling ? What is it : Population divided into groups (strata) and a simple random sample carried out in each group. Same proportion 𝑠𝑎𝑚𝑝 𝑠𝑖𝑧𝑒 𝑛 𝑝𝑜𝑝 𝑠𝑖𝑧𝑒 𝑁 sampled from each strata. Used when sample is large and population naturally divides into groups. It can give more accurate estimates than simple random sampling where there are clear strata present. Reflects the population structure. ? Within the strata, the problems are the same as for any simple random sample. If the strata are not clearly defined they may overlap. ?

Quota Sampling ? ? ? Quota Sampling Type How to carry out Advantages Disadvantages Quota Sampling ? What is it : The population is divided into groups in terms of gender, social class, etc. A quota of people in each group is set to try and reflect the group’s proportion in the whole population. Interviewer selects the actual sampling units. Enables fieldwork to be done quickly because a representatitive sample can be achieved with a small sample size. Costs kept to a minimum. Administering the test is easy. ? Not possible to estimate the sampling errors (Process is not a random one). Interviewers have to choose the respondents and may not be able to judge the characteristics easily. Non-responses are not recorded. Can introduce interviewer bias in who is included. ?

Exam Questions ?

Exam Questions ?

Exam Questions ?

Exam Questions ?

Exam Questions ?

Exam Questions ?