Brief Description

This unit explains the basic techniques involved in opinion polls. It is centred around a practical poll to find out pupils' favourite records, and the wider implications to all polls are stressed throughout. Both random and stratified sampling are introduced.

Design time: About 6 hours

Aims and Objectives

Pupils will learn how to conduct an opinion poll and identify possible pitfalls. On completion of the unit they will know that a sample needs to be representative and will be able to choose a random sample and a stratified sample to help ensure this.

They meet examples of samples which are unrepresentative through being too small, self-selected or clearly biased in nature. They carry out one com- plete survey and plan another. They will be more aware of the practical problems that arise in data collection and the relationship between sample and population. They practise filling in tables, using random number tables, drawing bar charts and writing a report on a statistical experiment.

Prerequisites

Pupils should be able to use random number tables, draw bar charts, make tally charts, multiply whole numbers by a fraction and round to the nearest whole number.

Equipment and Planning

Each pupil will need a sheet of random number tables. For the school poll, class lists for the first five years and the total numbers of pupils in each year are required. A list of the current 'Top 30' long-playing albums is also needed. These are published in New Musical Express, Melody Maker and Sounds. Graph paper is required in Sections C and D. A calculator will be useful for C6. Sections B2, B3 and C7 are optional. It is possible to end the unit with Section C and return to Section D at a later date.

Detailed Notes

Section A

This section introduces the opinion poll and the idea of a sample. It sets the scene for the rest of the unit. As such, it would be valuable to use this section for discussion on the purpose of polls, what sort of information may be required and how it may be used.

Surveys are conducted on many diverse topics. A list of those reported to the Survey Control Unit is published in Statistical News. Most of those in A1 are selected from these lists. Two major companies involved in opinion polls are National Opinion Polls and Gallup Polls, whose most publicized polls are those concerning prediction of election results.

A1
Pupils are invited to match up the organizations who commissioned the polls with the topics and the relevant population. The poll on the reliability of cars was run by the Consumers' Association, who questioned drivers (2). The Department of Industry carried out the poll on the Recycling of Waste Materials by interviewing adults (3). The Ministry of Agriculture, Fisheries and Food asked farmers about growing lettuce under glass (4). Doctors asked mothers about the decline in breast feeding (5).

A2
The poll on the reliability of cars is used to introduce the purpose of and the background work to a poll, including the need to take a sample. The purpose of the poll which the pupils will carry out in C8 is also introduced. It is important to get the purpose of the poll clearly defined, since this will determine who should be asked and the nature of the questions. The questions raised can act as a basis for discussion to help pupils appreciate how each stage of the unit will lead up to the poll. No definite answers are expected: these will emerge as work through the unit progresses. Some points relating to these questions are made in D2.

Section B

This section deals with whom and what to ask to obtain the information you need. After discussion, it may be suitable for homework.

B1
All questions here relate to the proposed school record library. Asking pupils which albums they would like to borrow has the advantage that it links directly with the purpose of the library. The disadvantage is that pupils may not know what is available. Asking a local shop about sales has the advantage of showing which is popular. A disadvantage is that sales are made to people of all ages, not just school pupils. Asking pupils which albums they like best has the advantage of finding out pupils' preferences. A disadvantage is that some will write down more titles than others and their views will be over-represented. Asking pupils which they would buy has the advantage of finding the pupils' favourite records. A disadvantage is that the records they might buy are not necessarily those that they might want to borrow.

A list of the 'Top 30' restricts choice and simplifies the analysis of results. Any that do not appear in the 'Top 30' will almost certainly not be the main favourites at the moment.

*B2
This section is optional and allows for further work on collecting the required information by referring to the weekly 'Top 30' singles charts.

Asking a sample of record shops about their sales is the method least open to abuse. It is the method that is used, with the check that if a record goes up more than 10 places, the returns for that record are scrutinized to see if one particular shop or area is involved.

The number of requests is a self-selected sample, and ignores people who do not write in. It can also be easily 'fixed' by phoney requests. The panel of disc jockeys may not be representative and could be affected by self- interests. Sampling record buyers would be too time-consuming to repeat each week. The number of times a record is played on the radio may well reflect the views of an individual producer or disc jockey.

*B3
B3 is optional and raises the problem of how to choose which shops to put in the sample. In choosing a local sample, one could choose at random from the larger shops' these should be more representative than the smaller ones. A wid e geographical spread o f shops is needed to ensure full representation of national views.

The 'Top 30' singles gain much publicity from the TV and radio programmes featuring them. Other 'Top 30s'are not featured to that extent on programmes.

B4
Here we identify the populations for a survey. It is important to determine whom to ask and start with the correct total population (sampling frame), although this may be difficult or even impossible. It may be different for different purposes. The population could be as follows:

School dinners: (i) all pupils in the school, (ii) all pupils who take dinner, (iii) all pupils and staff, etc.

Airports: (i) all travellers using the airport on a given day, (ii) all people in the airport on a given day, etc.

Parks: (i) all people in the town, (ii) all people who use a park in the town, etc. (To ask people in the park at a particular time would yield a biased sample.)

Section C

This section contains the actual record album poll in C8. The early parts of the section deal with the distinctions between good and bad samples. A random sample and a stratified sample are taken and compared to see how well they represent the population. A report of the poll is written.

Some of the work in C3 and C4 may be omitted or replaced by discussion. For the pupil poll, the simplest way may be to take samples from pupils in the first five years, depending on your school. The total population should be under 1000, otherwise four-figure random numbers are needed. To avoid this, you could use only the first three or four year groups. The class lists of these years and the total number in each year will be required.

C1

1. It is extremely time-consuming and difficult to question all the pupils in the school and to analyse their replies. A sample is easier to do.
2. A sample should be chosen fairly and be representative of the population. It is possible that a fair method may give an unrepresentative sample (e.g. a random sample of pupils could contain only girls from one year, although this is very unlikely in a large sample.)
3. The fairest methods are to choose every tenth pupil and to ask one in ten pupils from each year group. Slight variations on these are expanded later. The former is a systematic sample, and a fuller condition of

fairness requires that a random process be used to select the person from the first ten. Asking 50 pupils in the playground may give too many younger pupils, boys playing football or girls skipping. Asking 50 pupils from one year group ignores all other year groups. The school magazine gives a self-selected sample and ignores all those who do not respond. Asking four pupils from each class is only fair if all classes are the same size. Using volunteers from assembly gives another self- selected sample and will get those with strong opinions. Asking only five pupils as they enter school gives too small a sample. Inviting pupils to attend a meeting gives. another self-selected sample.

C2
There are many examples of bad sampling. It is important to bear them in mind. Polling by telephone only includes people with a telephone, and this principle led to a wrong prediction in the 1936 US presidential poll. The Scottish newspaper example is a self-selected sample, while the next sample is too small. The post office sample is likely to be heavily weighted towards mothers. The first 10 people off a bus gives too small a sample, whilst the last example is likely to omit those with knowledge about fashionable teenage clothes. The parents may well be at work while the teenagers are at school or work.

C3
This section provides pictorial clues to badly chosen samples. Each of the groups at the bus stops can be related to particular activities at certain times, e.g. pupils travelling to school, football or rugby supporters going to a match and housewives shopping.

C4
Pupils may need more help in the use of random number tables and where to find them. They are introduced in the Level One units Being Fair to Ernie and If at first... It is usual to ignore repeats, although one could use the same pupil's view twice. In this case both methods are fair: the distinction is between sampling without and with replacement. Either can be valid, but it is important to decide which you mean to do (and why) before you begin.

3. The second method would lend itself more easily to a large population.

C5
A simple random sample is drawn. This may be done as a class activity with each pupil (or pair of pupils) taking one class list with numbers allocated accordingly across all the lists. The sample size of 50 may be varied, depending on what is a convenient sample size for the stratified sample (in C6) in your particular school. As the two samples are to be compared, it is simpler i f the sample sizes are equal. It may be helpful to obtain an extra three or four 'reserves' for this sample, as reserves may be needed for the stratified sample in C6. Reserves will be used in carrying out the poll with the stratified sample if any of the sample are absent.

3. If the stratified sample of C6 is to be used in the actual poll, it is only necessary here to write down the names of pupils from one form or year.

The class will need to know the numbers of pupils in each year to complete column 5 of Table 3. They may be able to decide whether each year is fairly represented (i.e. in proportion to the numbers in each year of the population) simply by inspection. It is unlikely that each year will be fairly represented, hence the suggestion of the stratified sample in C6.

C6
A stratified sample is drawn up according to the numbers of pupils in each year. It is possible to stratify according to sex as well as age if there are grounds for belief that choice of record album will vary from boys to girls. This is more complicated but could be considered by the most able classes.

1. Selecting l0 from each year would be unfair if there were different numbers of pupils in each year.

The method of finding the number of pupils to be asked in each stratum (year group) is shown by a worked example using different numbers. A simpler example may help less able pupils see the principle. For example:

A sample of 50 is ⁵⁰/₅₀₀ i.e. ¹/₁₀ of the school, so we need ¹/₁₀ of each year. It may be necessary to adjust the figures slightly if rounding leads to a sample size other than 50. Reserves for each year should be chosen before carrying out the poll. It may be interesting to see if some years needed significantly more reserves than others.

*C7
Bar charts are drawn to enable the comparison of the numbers in each year in each of the two samples (from C5 and C6) to be made with the numbers of pupils in each year of the population. An alternative way would be to use percentages and draw up a table. The comparison should show that the stratified sample is the more representative, and so this gives the list of pupils to be used in the poll in C8.

C8
It is important that the actual poll is carried out and the results analysed. The actual questioning of the sample can be carried out by the pupils at registration or other convenient time, and their results brought to the next lesson to be collated. An alternative is to enlist the help of form teachers. The collation can be carried out as a class activity with each pupil recording the number of votes for each album as they are read out. A discussion of the poll is beneficial as a prelude to writing the report. This should be one piece ofcontinuous prose, not a list of answers to the listed points which are given purely as a guide to the structure and content of the report.

Section D

D1
Here some artificial results are presented of l000 pupils to enable a comparison between random and stratified sampling. This section could be done in groups and the results pooled, with some doing the random sample, some the stratified sample and others obtaining the overall results. The stratified sample may be obtained by taking every twelfth (or fourteenth), having chosen the first out of the first twelve (or fourteen) at random, rather than use random numbers.

Bar charts are used to help make the comparison between the random and stratified samples, although percentages and/or pie charts could be employed. Stratification does make a difference as the first year prefer B, the second year prefer A, while the third year prefer C. The overall result is 348/311/341.

D2
This section applies general principles in specific polls. This should help pupils remember the wider implications of polling and would make suitable homework material. You may like to add alternative suggestions to the list of possible polls. These may be either topical or of particular interest in your school, e.g. uniform, youth clubs and year councils.

Page R1

Table 3 - Opinion polls

Total no. of pupils = _____
Table 4 - Numbers of pupils in each year

Table 5 - Number of votes for each group (from a random sample)

Table 6 - Number of votes for each group (from a stratified sample)

Test Questions

Here are three opinion polls that might be carried out:

1. Find the views of pupils on school dinners.
2. Find out whether Scotland wants a separate government.
3. Find out whether a new type of washing powder will sell.

1. For each poll decide who might be interested. Choose from this list:
   Manufacturers
   Pilots
   School caretakers
   Housewives
   Parliament
   School cooks
   
   Poll a
   Poll b
   Poll c
2. For the same polls decide whom you might ask. Choose from this list
   Scottish people
   Housewives
   Farmers
   Pupils
   Teachers
   Tourists in Scotland
   
   Poll a
   Poll b
   Poll c
3. Expiain why the following samples chosen for the three polls are not representative.
   Poll a: Ask the first 25 pupils in the dinner queue.
   Poll b: Ask people who wrote to their MP about the subject.
   Poll c: Ask only three housewives at a supermarket.
4. A youth club has a free ticket for a concert each week. Which of these three methods is the fairest way of deciding which members should have it?. Explain why the other two are not fair.
   1. Give it to the first member to arrive.
   2. Put the names of the members in a hat and draw one.
   3. Let the youth leader decide.
5. 600 people attend a concert. Their seats are numbered from 1 to 600. How would you choose a random sample of 25?
6. A school has 50 teachers. It also has 600 pupils of whom:
   300 are aged 11 to 13; 200 are aged l4 to 16; 100 are aged l7 to 19.
   You want to find out the views of the pupils and teachers (together) on classical music.
   1. Give one reason why you might use a stratified sample.
   2. In a stratified sample of size 65, how many teachers would you interview?
7. You are to do a survey on which magazines should be in the school library. You decide to ask a sample of pupils.
   1. What do you want to find out?
   2. Who might use the information you collect?
   3. Whom will you ask?
   4. How will you choose your sample?
   5. What problems may occur in interviewing? How would you overcome them?
   6. How will you present your results?

Answers

Connections with Other Published Units from the Project

Other Units at the Same Level (Level 3)

Car Careers
Multiplying People
Net Catch
Phoney Figures
Cutting it Fine

Units at Other Levels in the Same or Allied Areas of the Curriculum

Level 1

Being Fair to Ernie
Leisure for Pleasure
Wheels and Meals

Level 2

Authors Anonymous
Opinion Matters

Level 4

Sampling the Census
Smoking and Health
Retail Price Index

This unit is particularly relevant to: Humanities, General Knowledge, Mathematics, Commerce.

Interconnections between Concepts and Techniques Used In these Units

These are detailed in the following table. The code number in the left-hand column refers to the items spelled out in more detail in Chapter 5 of Teaching Statistics 11-16.

An item mentioned under Statistical Prerequisites needs to be covered before this unit is taught. Units which introduce this idea or technique are listed alongside.

An item mentioned under Idea or Technique Used is not specifically introduced or necessarily pointed out as such in the unit. There may be one or more specific examples of a more general concept. No previous experience is necessary with these items before teaching the unit, but more practice can be obtained before or afterwards by using the other units listed in the two columns alongside.

An item mentioned under Idea or Technique Introduced occurs specifically in the unit and, if a technique, there will be specific detailed instruction for carrying it out. Further practice and reinforcement can be carried out by using the other units listed alongside.

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