Numbers: B2+
Numbers: B2+
Dawn Willoughby
Louis Rogers
Statistics and data for the non-specialist*The Collins Academic Skills Series - winner of the ELTon 2014 Innovation in Learner Resources Award.*At university you may be expected to analyse complex data and present your findings, whatever your area of study. Collins Academic Skills Series: Numbers gives you the skills you need to make sense of data and numbers and the confidence to use them effectively in your work.Learn how to• interpret statistics and data• conduct surveys• evaluate and question results• present numerical information clearlyCollins Academic Skills Series: Numbers will help you to make the most of your time at university.• Clear information and practical exercises• Information on academic expectations – understand the requirements of studying at university• Helpful tips and summaries• Answer key and glossaryNumbers is part of a new six-book series to help international students achieve academic success at college or university. It is designed to support students who are studying, or preparing to study, at an English-speaking institution.Suitable for students whose level of English is Upper Intermediate / CEF level B2 / IELTS 5.5 and higher.Other titles in the Collins Academic Skills Series:Group Work • Lectures • Presenting • Writing • Research
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You can trust Collins COBUILD
The 4.5-billion-word Collins Corpus is the world’s largest database of the English language. It is updated every month and has been at the heart of Collins COBUILD publishing for over 20 years. All definitions provided in the glossary boxes in this book have been taken from the Collins COBUILD Advanced Dictionary.
Source ISBN: 9780007507153
Ebook Edition © April 2014 ISBN 9780008101848
Version: 2014-07-01
Contents
Title Page (#u67c88dfa-2ecc-5f02-a33d-e251dc67759c)
Copyright (#ue45b060d-c031-53ed-9c77-3749c49db958)
Introduction (#ub83f7cde-9273-519a-a9fe-4147506d7578)
Chapter 1 Getting started (#u3799d65a-9258-5ee7-b7c0-e9a46035ec4b)
look at numbers in everyday life
understand the purpose and use of statistics
learn key terms for working with numbers
learn the basics about spreadsheets
practice referring to and labelling graphics in writing
Chapter 2 Starting primary research (#ufaeb31f1-ac0c-5871-9a0b-9619d8aa91d1)
practise formulating research questions
understand the principles of sampling
learn how to formulate a hypothesis
Chapter 3 Research methods (#udb663fdc-bdaa-57c3-a6ec-001ec0d1efae)
understand some common research methods
understand when to use interviews, questionnaires and focus groups
understand the advantages and disadvantages of common research methods
Chapter 4 Questionnaires (#litres_trial_promo)
understand how to write a questionnaire
practise forming polite question forms
understand different sampling techniques
understand the pros and cons of distribution methods
Chapter 5 Interviews (#litres_trial_promo)
understand how to ask good interview questions
learn how to structure different questions
learn about the interviewer effect
learn how to use reported speech
Chapter 6 Percentages and fractions (#litres_trial_promo)
learn how to work with percentages
learn how to understand fractions
compare fractions and percentages
use verbs and nouns and dependent prepositions
Chapter 7 Averages (#litres_trial_promo)
learn why we use averages
learn about different types of averages
learn when to use frequency tables to find averages
learn how to choose the right average to use
Chapter 8 Presenting your data (#litres_trial_promo)
understand the use of different visual information
use the present simple, past simple and present perfect to describe graphics
use the active and passive voice to describe graphics
Chapter 9 Describing change (#litres_trial_promo)
represent change visually
use verbs of change
use adverbs describing change
use adjective and noun combinations to describe change
Chapter 10 Making comparisons (#litres_trial_promo)
use graphics to compare information
use comparative structures
use superlative structures and cautious language
Chapter 11 Making connections (#litres_trial_promo)
understand correlation
understand the effect of sample size
express links and connections
describe facts and data
Chapter 12 Working with collected data (#litres_trial_promo)
learn how to present survey results
avoid producing misleading results from diagrams
describe cause and effect
express generalizations and specifics
use language of argumentation
use evaluative language
learn how to write conclusions
Further reading (#litres_trial_promo)
The grammar of fractions (#litres_trial_promo)
Glossary
(#litres_trial_promo)
Answer key (#litres_trial_promo)
About the Author (#litres_trial_promo)
About the Publisher (#litres_trial_promo)
Introduction (#ulink_ac99a9cf-ae8e-5583-bfd5-cac0479ebcba)
Collins Academic Skills Series: Numbers will give you the skills you need for doing research, collecting data, presenting it, using numbers and appropriate language to describe it, and working with the collected data.
Designed to be used on a self-study basis to support English for Academic Purposes or study skills courses, it is intended for students on pre-sessional or foundation courses as well as for first-year undergraduate students.
The book has twelve chapters covering the key stages of the research process from start to finish. You will learn how to:
choose the right research methods
use basic maths skills
present your data
analyse your data
At the back of the book there is:
a list of useful books in Further reading
helpful information in The grammar of fractions
a Glossary of key terms
a comprehensive Answer key
Chapter structure
Each chapter includes:
Aims – These set out the skills covered in the chapter.
A self-evaluation quiz – By doing this you are able identify what you already know on the subject of the chapter and what you need to learn.
Information on academic guidelines on how to develop academic skills – These sections will help you understand university practices and expectations so you know what is required.
Practical exercises – These help you to develop the skills to succeed at university. You can check your answers at the back of the book.
Tips – Key points are highlighted for easy reference and provide useful revision summaries for the busy student.
Glossary – Difficult words are glossed in boxes next to where the word appears in the chapter. There is also a comprehensive Glossary at the back of the book.
Remember sections – This is a summary of key points for revision and easy reference.
Glossary boxes
Where we feel that a word or phrase is difficult to understand, we have glossed this word/phrase. All definitions provided in the glossary boxes have been taken from the COBUILD Advanced Dictionary. At the end of the book there is a full alphabetical list of the most difficult words from the book for your reference.
Using Numbers
You can either work through the chapters from Chapter 1 (#u3799d65a-9258-5ee7-b7c0-e9a46035ec4b) to Chapter 12 (#litres_trial_promo) or you can choose the chapters and topics that are most useful to you. The Contents page will help in your selection.
Study tips
Each chapter will take between one and three hours. Take regular breaks and do not try to study for too long. Thirty to sixty minutes is a sensible study period.
Regular study is better than occasional intensive study.
Read the chapter through first to get an overview without doing any exercises. This will help you see what you want to focus on.
Try the exercises before checking the Answer key.
After doing the exercises in the book, try them again using your own research topic and reading materials. If possible, ask a more experienced colleague or friend to give you feedback on your work.
All university departments are different. Use the information in the book as a guide to investigating your own university department.
Write questions you can ask to find out how your department expects you to do research and collect and present data.
There is no one correct way of doing research and working with collected data. Use your experience of doing the exercises to learn what works best for you. Adapt the suggestions in this book to suit your learning style and context.
Learning to do research and work with data is an on-going process, which means you need to practise the same skills many times. Revise regularly.
Other titles
Also available in the Collins Academic Skills Series: Writing, Lectures, Research, Presenting, and Group Work.
1
Getting Started (#ulink_5a5bc926-baf0-54b8-9d68-8b36d8b2d97e)
Aims
look at numbers in everyday life
understand the purpose and use of statistics
learn key terms for working with numbers
learn the basics about spreadsheets
practise referring to and labelling graphics in writing
Quiz
Self-evaluation
Read the statements below. Circle the answers that are true for you.
Numbers and mathematics are very important in our everyday lives because we use them frequently when we manage our finances, go shopping, make travel plans, convert currency, follow instructions for a recipe or take measurements when we are building and creating things. If we carry out an academic study or investigation, then we need to use a branch of mathematics known as statistics which involves collecting and organizing data, making sense of our information and presenting findings.
Glossary
data You can refer to information as data, especially when it is in the form of facts or statistics that you can analyse. In American English, data is usually a plural noun. In technical or formal British English, data is sometimes a plural noun, but at other times, it is an uncountable noun.
This chapter begins by reminding us of the calculations and vocabulary that are used when we are working with money and taking measurements. It then provides an introduction to statistics, explaining where data is used in different subject areas and describing different categories of data. With a more technical focus, the chapter then describes how to use a computer program known as a spreadsheet which can help with storing and presenting data. Finally, an explanation is given of the use of graphics in academic writing, highlighting ways to refer to graphics in your text so that you can comment on your data and findings effectively.
Numbers in everyday life
In this section, we will explore some of the ways in which numbers are used in everyday situations. We will investigate taking measurements and working with money.
Money
It is important to know how to work with money so that you can:
Recognize the value of amounts of money
Estimate your expenditure
Often money calculations will involve the use of percentages and fractions. You will learn about these in Chapter 6 (#litres_trial_promo).
Glossary
estimate If you estimate a quantity or value, you make an approximate judgement or calculation of it.
expenditure Expenditure is the spending of money on something, or the money that is spent on something.
value In mathematics, the value of a symbol or letter is the amount represented by it.
The value of a digit in a number depends on its position in the number. In the following amounts of money, the digit 4 has a different meaning:
A place value diagram may help to remind you how to recognize the value of amounts of money. The highest number in the group is the maximum and the lowest is the minimum.
Estimating can be a useful skill when you are calculating your monthly expenditure because you can work out approximately how much your total bill will be without adding up all of the individual values. Estimating involves rounding prices up or down to the nearest ten pounds, dollars or euros so that you can work out the total more easily.
This list shows the actual expenditure with the estimated value for each cost:
So, when we add up the actual prices the aggregate total price for our shopping is £835.85 and the estimated cost is £840.
Glossary
round up/down If you round an amount up or down, you change it to the nearest whole number or the nearest multiple of 10, 100, 1,000, and so on.
aggregate An aggregate amount or score is made up of several smaller amounts or scores added together.
Measurements
Taking measurements is about finding a number that shows the amount or size of something. We are most often interested in measuring temperature, length, speed, time, capacity and mass. To make an accurate measurement, you would need to choose an appropriate measuring device and use the correct type of units on a scale. Here are some examples:
Glossary
capacity The capacity of a container is its volume, or the amount of liquid it can hold, measured in units such as litres or gallons.
mass In physics, the mass of an object is the amount of physical matter that it has.
Exercise 1
Match the correct unit of measurement with each item to be measured.
There are a number of key terms that are useful to learn when working with numbers and data. Test your knowledge of these by completing the following exercises.
Exercise 2
Use the words in the box to complete these sentences. You might need to change the form of the word.
accurate calculation fraction measurement
aggregate / total capacity mass percentage
approximately estimated maximum / minimum round up / down
1 The ________of 9, 10, 24, 6, 8, 5 is 62. It is also known as the ________.
2 The ________of the lecture theatre is 200 people.
3 Economic forecasters have ________that the economy will grow by 0.5% next year.
4 There are ________300,000 international students studying in the UK.
5 The spreadsheet automatically ________or ________to the nearest whole number.
6 The ________loan available is £5,000 and the ________loan available is £500.
7 The ________of a bowling ball is 7.25 kilograms.
8 ________measurements are essential in many scientific experiments.
Exercise 3
Use another word in the box in Exercise 2 to describe each item below.
1 1/3 ________
2 245 × 6 ________
3 98% ________
4 100 ml ________
Exercise 4
Put the word in brackets into the correct form in each of these sentences.
1 The closest ________was 2 years 4 months. (estimate)
2 There are a number of different ways to ________an average. (calculate)
3 There are ________1.3 billion people in China. (approximate)
4 The ________of another variable completely changed the outcome of the experiment. (add)
5 The values were ________and then used to find the average. (total)
6 The answers were cross-checked to ________predict the outcome. (accurate)
What is statistics?
Every day in our lives, we hear and read about many different types of information in the form of data. Data can tell us interesting and important details about the world around us but it can be challenging to understand the facts and figures.
Statistics is a mathematical science that helps us to make sense of data that has been counted, measured, asked about or observed. It involves four main activities:
Glossary
method A method is a particular way of doing something.
technique A technique is a particular method of doing an activity, usually a method that involves practical skills.
Collecting data – first of all, we decide what type of data we are interested in, which method we shall use to collect the data, and where we would like to collect it from.
Organizing data – we use a range of different techniques to summarize the data we have collected so that we can see interesting features or patterns in the information.
Interpreting data – we use the results of calculations to help us make comparisons about different sets of data, to answer questions and make decisions about the world around us.
Glossary
feature A feature of something is an interesting or important part or characteristic of it.
Presenting data – when we have found out interesting facts about our data, then we will need to display and present the information to other people so that they can understand our conclusions.
Exercise 5
Choose a newspaper or news-related website and look for reports that use statistics to help explain the main points of the article. Think about these questions:
How was the data collected?
What type of organization is using the statistics?
What interesting features or patterns were found in the data?
How is the data presented?
Statistics is important in many different subject areas. The following diagram lists some examples of the type of data that might be collected and used:
Some terminology
In statistics, we use two key words: variable and observation. It is important to understand the difference in their meanings. A variable is a characteristic or an attribute that can have different values; an observation is the value of a variable that has actually been counted, measured or observed. Some variables are shown below, with a list of possible observations next to each one.
Glossary
variable A variable is a factor that can change in quality, quantity, or size, which you have to take into account in a situation.
characteristic The characteristics of a person or thing are the qualities or features that belong to them and make them recognizable.
attribute An attribute is a quality or feature that someone or something has.
The observations for a variable can be described as quantitative or qualitative, depending on what the information is about. Quantitative data is something which can be measured or counted using a number. Qualitative data represents a characteristic that uses words to describe it but does not use any numbers.
Examples of quantitative variables are:
time taken to complete a test
the number of books in a library
the highest temperature in a month
Examples of qualitative variables are:
the nationality of people in a cinema
the favourite sport of children in a school
the colours of balloons at a party
Exercise 6
Match the words on the left to their definitions on the right.
Exercise 7
State whether each of the following variables is quantitative or qualitative:
1 number of pages in a book
2 names of students in a class
3 hair colour
4 weight of apples in a bag
5 height of trees in a park
Exercise 8
Answer these questions.
1 Explain the difference between a quantitative and a qualitative variable.
2 Give an example of each type of variable.
3 Explain why:
‘type of tree’ is a qualitative variable
‘number of pupils in a class’ is a quantitative variable
Exercise 9
Without looking back at the section ‘What is statistics?’, put these statistical stages into the correct order.
1 organize data
2 present data
3 collect data
4 interpret data
Exercise 10
Use the words in the box to complete these questions about the stages above.
data features patterns sets of data
display method present technique
1 What type of ________are we interested in?
2 Which data collection ________shall we use?
3 What ________shall I use to summarize my data?
4 What interesting ________or ________can I see?
5 What questions do my ________answer?
6 What is the clearest way to ________and ________my data?
Exercise 11
Match the questions in Exercise 10 to the stages in Exercise 9.
Using spreadsheets
You can store, organize and present your data in a computer program called a spreadsheet.
Glossary
grid A grid is something which is in a pattern of straight lines that cross over each other, forming squares. On maps the grid is used to help you find a particular thing or place.
row A row of things or people is a number of them arranged in a straight line.
intersection An intersection is a place where lines or roads meet or cross.
cell A cell is one of the small squares in a chart or spreadsheet into which you can add a single piece of data.
A spreadsheet appears as a table or grid containing a set of rows and columns. Rows are displayed horizontally on the grid and each one is labelled with a number (1, 2, 3 …); the label for each column is a letter (A, B, C …) and columns are displayed vertically across the grid.
The empty spreadsheet grid shown below has eight rows and five columns, but a spreadsheet in a computer program will have many, many more rows and columns.
The intersection of a row and a column is called a cell. Each cell has its own name, which consists of the letter of the column followed by the number of the row. The highlighted cell in the spreadsheet grid shown above is called C5 – it is where column C and row 5 meet.
Tip
Use the glossaries to help you with some of the key words in this book. Consider making similar lists for your modules to help you learn key words.
Exercise 12
Look at the section of a spreadsheet below, and answer the questions.
1 What is contained in the following cells?
a A6
b B3
2 What is the reference for the cells that contain the following?
a The number ‘53%’
b The word ‘Statistics’
The data values in each spreadsheet cell can be displayed in different ways depending on how the information is described. You can use:
text
numbers
currency
dates and times
The spreadsheet opposite records the food purchased by a shopper at a supermarket. Row 1 in this grid is used to show the names of the columns so that it is easy to understand what information is being stored.
A spreadsheet is very useful for performing simple calculations. It uses formulae to perform operations such as addition, subtraction and multiplication.
The following spreadsheet shows the different nationalities of students enrolled on an English course. It includes a formula which uses the individual numbers of each nationality to calculate the total number of students enrolled on the course. The formula is usually hidden from view and only the result is displayed.
Glossary
formula A formula is a group of letters, numbers or other symbols which represents a scientific or mathematical rule.
The formula SUM(B2:B8) is used to calculate the total of number of students enrolled on the course. It adds up the numbers in cells B2 to B8. If a number in one of these cells is changed, then the result of the formula is automatically updated by the spreadsheet.
So, if another French student enrols on the course, then the cell B5 becomes 4 and the total in cell B10 is changed automatically to 44 to include the new student.
Once you have organized your data in a spreadsheet, it is then possible to use the computer program to create graphs and charts to display the information in a visual way. The bar chart below has been created using the data in the previous example.
For more information on graphics, see Chapter 8 (#litres_trial_promo).
Tip
When using spreadsheets, you can click on the Help button in the computer program to search for advice on how to use formulae for calculations.
Using graphics
A number of different visuals are used in academic writing to present data or information. In academic texts they are often referred to as figures, but sometimes a wider range of terms such as chart and table are used as well. A pie chart is used to show the proportion of something in different segments. A key is used to label a pie chart when there are many sections. A bar chart is used to compare different amounts of something. A line graph is used to show trends or patterns. The axes are labelled to show what data is being presented. The x axis is horizontal and the y axis is vertical. A table is a grid with columns and rows of numbers. Diagrams are often used to describe functions. For example, they may show the organization of a company or the stages in the process involved in manufacturing or in decision-making.
Glossary
proportion A proportion of a group or an amount is a part of it.
trend A trend is a change or development towards something new or different.
Exercise 13
Look at the pictures below and label them with words from the box.
Exercise 14
Put the words in brackets into the correct position and form in each sentence.
1 The x axis goes ________and the y axis goes ________. (horizontal / vertical)
2 A ________goes vertically and a ________goes horizontally. (row / column)
3 A ________is used to ________a ________. With a ________the ________needs to be labelled. (label / key / pie chart / line graph / axis)
4 How many ________are there in the ________above? (segment / pie chart)
5 Graphics in academic writing are often referred to as ________but sometimes as ________or tables. (chart / figure)
6 Pie charts are generally used to show the ________of something and line graphs to show ________. (trend / proportion)
Referring to graphics in writing
Although graphics generally speak for themselves, it is common to make a brief reference to them in writing to introduce what they show. This can be done with a range of basic phrases, for example:
As can be seen in Figure 12.1, …
From Table 2.1, it can be concluded that …
Language: relative clauses
Relative clauses can be a useful structure for summarizing or referring to key information in a graphic. For example:
The graph shows the number of students from India who were given visas in 2010 was 58,000.
The table shows that the number of students who come from the USA is getting bigger.
In academic writing, relative clauses are often used for defining; in the case of data, they are used to describe or define exactly who or what you are referring to. Note that the relative pronoun (who, whose, which, that) will change depending on what you are defining. For people, use who, that or whose (possessive):
The graph shows people who are motivated by goals often have short-term satisfaction.
The graph shows that people that set realistic goals often enhance their performance.
The chart demonstrates that companies whose managers are not aware of employee motivation are less likely to be successful.
For most things or ideas, use that or which:
The table shows companies that use money as a means to motivate employees.
The table shows teams which use a sports psychologist to motivate teams.
For more information on describing graphics, see Chapters 8 (#litres_trial_promo) and 9 (#litres_trial_promo).
Exercise 15
Complete the table with words from the box.
As is shown graph 2.3 in It can be seen from
Exercise 16
Match 1–5 with a–e to form sentences including a relative clause.
Tip
Try to record all new vocabulary in a similar way and regularly test yourself on the new words.
Remember
You might have to use spreadsheets to analyse your data.
The main purpose and use of statistics.
Relative clauses are useful for referring to and labelling graphics in writing.
The different stages from collection to presentation of data.
2
Starting Primary Research (#ulink_47c38016-2279-5e6d-81f1-dc9dee32f096)
Aims
practise formulating research questions
understand the principles of sampling
learn how to formulate a hypothesis
Quiz
Self-evaluation
Read the statements below. Circle the answers that are true for you.
Early planning and good organization are key to a successful research project. What you decide to research can vary greatly depending on the field you are in, but there are two main starting points: formulating research questions, or formulating a hypothesis to test. Whether you choose one, the other or both, there are some important points to consider:
Does this area interest you enough? After all, this project will become a large part of your life for quite some time.
Has this area been researched before? If so, what new things are you hoping to add with this study?
How does this build on previous research in the area?
Are the research aims focused and limited enough? You will have a limited amount of time and words to complete the project, so it needs to be realistic.
Do you have access to a reasonable cross-section of the population you wish to study?
This chapter will help you to consider some of these key issues. It gives you practical steps to formulate research questions, and helps you understand the basic principles of sampling and to understand the cause and effect nature of hypotheses.
Formulating research questions
Doing a research project is both exciting and challenging at the same time. Research projects at the end of a Bachelor’s or Master’s (BA, BSc, MA, MSc) degree are commonly called a dissertation or a thesis. You usually have a lot of freedom to choose the area you want to research, although sometimes you may be given a choice of questions about a broad area of research to look into. You can start to think about the area you want to research very early on, but try not to narrow it down too soon before you are ready to begin.
It is a good idea to choose a topic or area that interests you, perhaps from a module you enjoyed or a topic that has stimulated your interest in a new area. Sometimes it can be a challenge to think of an area, so talk about it with tutors, friends or other students and perhaps look at some previous projects in your area of study.
Exercise 1
Follow these steps to help find an area that interests you.
1 Brainstorm the different subjects from your degree.
2 Think about particularly interesting modules.
3 Think of an interesting area from that module.
4 Which of these topics particularly interests you?
Once you have a range of topics that interest you, the next step is to narrow it down. This is something that should be done quite quickly as you often have limited time. Thinking about your motivation is important because you will be spending a lot of time on the project. It is also important to try to think about how practical the project is.
Being specific
One of the biggest challenges is choosing a research question that is specific enough. The idea of writing 15,000 or 20,000 words in your own language can make people feel quite worried, and doing it in another language for your Bachelor’s or Master’s degree can seem even more challenging. Many of the English exams to gain entry to a university only require students to write 250 words in English. So when, in perhaps just nine months of completing that test, you have to write 20,000 words, very few people worry about being specific. Many think – can I write that much? When people choose a topic that is too broad it can be difficult to answer in 15,000 to 20,000 words as there are too many things to cover. It can create problems conducting the literature review as you will have too many things to read. It could also mean that you do not have the time or resources to conduct your own research and write it up. Try to build on topics. Think about the following: has this area already been well researched? Is there a clear research methodology I could use? Can I bring a slightly new perspective to the topic? How specific you need to be will vary between courses, but it is essential you think about these questions in order to make your project realistic.
Glossary
specific If someone is specific, they give a description that is precise and exact.
Exercise 2
Which of these research questions sounds specific enough?
1 Does regular exercise reduce stress levels in men aged 18–25?
2 Will a high-fibre and low-fat diet be sufficient to reduce cholesterol levels in middle-aged women?
3 Does exercise improve mental health?
4 Does motivation affect levels of effort?
Tip
Try to be as focused as you can from the start. Look at as many previous students’ dissertations as possible to help guide you. Ask your supervisor for help and guidance when you feel you need it.
Exercise 3
Think about your possible research question and ask yourself these questions.
1 Can you answer your question in just a few months?
2 Is your question specific enough? Brainstorm all the different things you might include and then imagine how many words it might take to cover each.
3 Have you read previous students’ projects? How long was each section?
4 Once you have collected your data how will you analyse it? How long do you think this might take? If you are doing something that requires you to write down what was said, for example an interview, practise this by recording a friend and writing down what they say. Time yourself and then imagine how long this might take once you have interviewed the number of people you want to interview.
5 Can you get access easily to people you want to interview, use in a focus group or give your questionnaire to?
Exercise 4
Decide if the following statements are true or false.
Sampling
Population: when you carry out an investigation to find out information about a group of things or people, this group is known as the population.
Some examples of different populations are:
all the people who live in New York
all the books in a library
all the trees in a forest
all the nurses in a hospital
Glossary
population If you refer to a particular type of population in a country or area, you are referring to all the people or animals of that type there.
Census: you would need to carry out a census if you want to find out information about every member of a population. It is easier to carry out a census if you have a small number of people or things in your population, but if the population is very large then it is usually time-consuming, often expensive and sometimes impractical.
For example, if a biscuit manufacturer that bakes thousands of biscuits every day decided to find out how easily their biscuits break, a census would involve breaking every biscuit that they make. This would be impractical because the population is too big and it would be very time-consuming to test each biscuit individually.
Sampling: instead of carrying out a census of the whole population, you could decide to ask questions or observe just a small group of the things or people within that population. This is called sampling. Using a sample can be a lot less expensive, quicker and much easier than carrying out a census. When you have collected information from a sample, it is then possible to draw conclusions and make estimates about the entire population.
For example, the biscuit manufacturer in the previous example could use a sample to find out how easily their biscuits break by choosing 100 biscuits of different varieties for testing.
Glossary
census A census is an official survey of the population of a country that is carried out in order to find out how many people live there and to obtain details of such things as people’s ages and jobs.
sample A sample of people or things is a number of them chosen out of a larger group and then used in tests or surveys, or used to provide information about the whole group.
Exercise 5
For the investigations listed in the table below, describe the population and decide if it would be practical or impractical to carry out a census to find out information on the whole population.
Avoiding bias
Using sample data, you can only draw conclusions and make estimates about the entire population if you choose a sample of things or people that represents the whole population fairly. If your sample is not representative of the population, then it is known as a biased sample.
The table below describes some samples taken for different investigations, and explains why these samples are not representative of the population. Can you work out why the sample is biased for the last two investigations?
Glossary
biased If someone is biased, they prefer one group of people to another, and behave unfairly as a result. You can also say that a process or system is biased.
Tip
Ask someone else to look at your planned sample before you start your research and ask them if they can see any bias. It can be difficult to look at it objectively yourself, so help and guidance will be useful here.
Exercise 6
Match the words or phrases on the left to a definition on the right.
Exercise 7
Complete these sentences with words from Exercise 6. You may need to change the form of some words.
1 The sample was not large enough to be ________of the whole population.
2 Poor ________meant that it was difficult to draw conclusions.
3 The study was ________over a three-month period.
4 The study aimed to ________the effects of advertising on children.
5 The sample was ________towards middle aged men.
6 The ________net spend per month was £500.
7 A national ________is carried out in the UK every few years.
8 The ________under investigation was international students in the UK.
9 We can ________the ________that advertising has a significant impact on children’s spending patterns.
Formulating a hypothesis
A hypothesis is something that you plan to test in your research and is related to forming your research question. The hypothesis usually states that something will or will not happen. It is something that you would write before starting your research; you plan to see if it is true or not after doing your research.
Glossary
construct In the area of research, a construct is an idea, belief, or subject which is based on evidence which may not be true, and which you want to test and measure.
objectively If you look at something objectively, you base your opinions on facts rather than on your personal feelings.
Examples of hypotheses:
Language is the main challenge in adapting to another culture.
Low income is the main reason for job dissatisfaction.
Blueberries have a positive impact on the mind.
Each of these hypotheses is formed from two or more constructs and often makes a claim for cause and effect. For example:
A construct is something that can be tested or questioned objectively. For example, in the first hypothesis above we could ask:
How can culture be defined?
How can adaptation be measured?
What factors affect adaptation?
How are language and culture related?
Does language impact on adaptation?
Exercise 8
What is the purpose of a hypothesis and what should it clearly state?
Exercise 9
Look at the other two hypotheses from the previous page. What questions could you ask yourself about these hypotheses?
Low income is the main reason for job dissatisfaction.
1How is job satisfaction defined?
2 ________
3 ________
4 ________
5 ________
6 ________
Blueberries have a positive impact on the mind.
1What foods have a positive impact on the mind?
2 ________
3 ________
4 ________
A piece of research may contain more than one hypothesis that will be tested. Another common thing other than cause and effect that is tested is a comparison between two groups or classes.
Example:
Single sex schools produce better academic results than other schools. They are also more of an advantage for girls than boys.
Here the hypothesis is looking at the cause and effect relationship between single sex schools and academic success but it is also making a comparison between boys and girls.
Exercise 10
Which of the following hypotheses make a comparison?
1 People who regularly use computers suffer from more health issues than those who do not use them.
2 Men make more impulse purchases than women.
3 It is more difficult to learn a second language after the age of 20 than before it.
4 Independent study increases academic success.
5 Three minutes’ intensive exercise is enough to maintain fitness levels.
Exercise 11
Look at these possible causes and their effects. Can you join them together to write a hypothesis for each one?
1 Travel abroad > malaria
Travelling abroad increases the risk of catching malaria.
2 Recycling > save money
3 Low temperatures > car accidents
4 Language learning > cultural awareness
Remember
It is important to be specific in your research question.
You need to define and clearly state your question early on in the research process.
Sampling can have a significant impact on your research and should be done carefully.
It is important to choose the most appropriate research methods.
You can use hypotheses as part of your research process.
3
Research Methods (#ulink_9b25ea1f-8e20-5769-b6b4-9b590bef71fd)
Aims
understand some common research methods
understand when to use interviews, questionnaires and focus groups
understand the advantages and disadvantages of common research methods
Quiz
Self-evaluation
Read the statements below. Circle the answers that are true for you.
A wide range of research methods is available for you to choose from when you conduct a research project. The key is to choose the most appropriate method or methods for your research aims. In Social Sciences, particularly with projects at undergraduate level, three of the most common methods are interviews, questionnaires and focus groups. This, of course, does not mean you need to limit yourself to these methods.
This chapter looks at some of the main research methods, at some of their main advantages and disadvantages and gives a brief overview of some other methods of research. The following two chapters look in more detail at how to produce a questionnaire and conduct an interview.
For more information on other research methods, see Further reading.
Choosing your research method
A research method is the way in which you choose to collect your data. A wide range of research methods can be used to gather data. This section will give you an overview before looking in more detail at some of the main advantages and disadvantages of four key research methods: questionnaires, focus groups, interviews and experiments. This is then followed by a brief overview of some other methods to consider. When you select your method it is important to choose one that will effectively help you to answer your research question or test your hypothesis. It is also important to be aware of the advantages and disadvantages of each method.
Questionnaires
Many students choose to do a survey using a questionnaire as it is commonly believed that the method is easy. A questionnaire doesn’t involve the pressure of an interview, and the answers are conveniently written down for future analysis. However, it can be challenging to write an effective questionnaire.
Questionnaires can be distributed in a variety of ways and there is a varying amount of success in getting responses back. The questions are typically predominantly aimed at gathering quantitative data, but an element of qualitative data can also be gathered.
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Dawn Willoughby
Louis Rogers
Statistics and data for the non-specialist*The Collins Academic Skills Series - winner of the ELTon 2014 Innovation in Learner Resources Award.*At university you may be expected to analyse complex data and present your findings, whatever your area of study. Collins Academic Skills Series: Numbers gives you the skills you need to make sense of data and numbers and the confidence to use them effectively in your work.Learn how to• interpret statistics and data• conduct surveys• evaluate and question results• present numerical information clearlyCollins Academic Skills Series: Numbers will help you to make the most of your time at university.• Clear information and practical exercises• Information on academic expectations – understand the requirements of studying at university• Helpful tips and summaries• Answer key and glossaryNumbers is part of a new six-book series to help international students achieve academic success at college or university. It is designed to support students who are studying, or preparing to study, at an English-speaking institution.Suitable for students whose level of English is Upper Intermediate / CEF level B2 / IELTS 5.5 and higher.Other titles in the Collins Academic Skills Series:Group Work • Lectures • Presenting • Writing • Research
Collins (#ulink_b55acb4b-5349-5da2-baeb-3b0be120c2ca)
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First edition 2013
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You can trust Collins COBUILD
The 4.5-billion-word Collins Corpus is the world’s largest database of the English language. It is updated every month and has been at the heart of Collins COBUILD publishing for over 20 years. All definitions provided in the glossary boxes in this book have been taken from the Collins COBUILD Advanced Dictionary.
Source ISBN: 9780007507153
Ebook Edition © April 2014 ISBN 9780008101848
Version: 2014-07-01
Contents
Title Page (#u67c88dfa-2ecc-5f02-a33d-e251dc67759c)
Copyright (#ue45b060d-c031-53ed-9c77-3749c49db958)
Introduction (#ub83f7cde-9273-519a-a9fe-4147506d7578)
Chapter 1 Getting started (#u3799d65a-9258-5ee7-b7c0-e9a46035ec4b)
look at numbers in everyday life
understand the purpose and use of statistics
learn key terms for working with numbers
learn the basics about spreadsheets
practice referring to and labelling graphics in writing
Chapter 2 Starting primary research (#ufaeb31f1-ac0c-5871-9a0b-9619d8aa91d1)
practise formulating research questions
understand the principles of sampling
learn how to formulate a hypothesis
Chapter 3 Research methods (#udb663fdc-bdaa-57c3-a6ec-001ec0d1efae)
understand some common research methods
understand when to use interviews, questionnaires and focus groups
understand the advantages and disadvantages of common research methods
Chapter 4 Questionnaires (#litres_trial_promo)
understand how to write a questionnaire
practise forming polite question forms
understand different sampling techniques
understand the pros and cons of distribution methods
Chapter 5 Interviews (#litres_trial_promo)
understand how to ask good interview questions
learn how to structure different questions
learn about the interviewer effect
learn how to use reported speech
Chapter 6 Percentages and fractions (#litres_trial_promo)
learn how to work with percentages
learn how to understand fractions
compare fractions and percentages
use verbs and nouns and dependent prepositions
Chapter 7 Averages (#litres_trial_promo)
learn why we use averages
learn about different types of averages
learn when to use frequency tables to find averages
learn how to choose the right average to use
Chapter 8 Presenting your data (#litres_trial_promo)
understand the use of different visual information
use the present simple, past simple and present perfect to describe graphics
use the active and passive voice to describe graphics
Chapter 9 Describing change (#litres_trial_promo)
represent change visually
use verbs of change
use adverbs describing change
use adjective and noun combinations to describe change
Chapter 10 Making comparisons (#litres_trial_promo)
use graphics to compare information
use comparative structures
use superlative structures and cautious language
Chapter 11 Making connections (#litres_trial_promo)
understand correlation
understand the effect of sample size
express links and connections
describe facts and data
Chapter 12 Working with collected data (#litres_trial_promo)
learn how to present survey results
avoid producing misleading results from diagrams
describe cause and effect
express generalizations and specifics
use language of argumentation
use evaluative language
learn how to write conclusions
Further reading (#litres_trial_promo)
The grammar of fractions (#litres_trial_promo)
Glossary
(#litres_trial_promo)
Answer key (#litres_trial_promo)
About the Author (#litres_trial_promo)
About the Publisher (#litres_trial_promo)
Introduction (#ulink_ac99a9cf-ae8e-5583-bfd5-cac0479ebcba)
Collins Academic Skills Series: Numbers will give you the skills you need for doing research, collecting data, presenting it, using numbers and appropriate language to describe it, and working with the collected data.
Designed to be used on a self-study basis to support English for Academic Purposes or study skills courses, it is intended for students on pre-sessional or foundation courses as well as for first-year undergraduate students.
The book has twelve chapters covering the key stages of the research process from start to finish. You will learn how to:
choose the right research methods
use basic maths skills
present your data
analyse your data
At the back of the book there is:
a list of useful books in Further reading
helpful information in The grammar of fractions
a Glossary of key terms
a comprehensive Answer key
Chapter structure
Each chapter includes:
Aims – These set out the skills covered in the chapter.
A self-evaluation quiz – By doing this you are able identify what you already know on the subject of the chapter and what you need to learn.
Information on academic guidelines on how to develop academic skills – These sections will help you understand university practices and expectations so you know what is required.
Practical exercises – These help you to develop the skills to succeed at university. You can check your answers at the back of the book.
Tips – Key points are highlighted for easy reference and provide useful revision summaries for the busy student.
Glossary – Difficult words are glossed in boxes next to where the word appears in the chapter. There is also a comprehensive Glossary at the back of the book.
Remember sections – This is a summary of key points for revision and easy reference.
Glossary boxes
Where we feel that a word or phrase is difficult to understand, we have glossed this word/phrase. All definitions provided in the glossary boxes have been taken from the COBUILD Advanced Dictionary. At the end of the book there is a full alphabetical list of the most difficult words from the book for your reference.
Using Numbers
You can either work through the chapters from Chapter 1 (#u3799d65a-9258-5ee7-b7c0-e9a46035ec4b) to Chapter 12 (#litres_trial_promo) or you can choose the chapters and topics that are most useful to you. The Contents page will help in your selection.
Study tips
Each chapter will take between one and three hours. Take regular breaks and do not try to study for too long. Thirty to sixty minutes is a sensible study period.
Regular study is better than occasional intensive study.
Read the chapter through first to get an overview without doing any exercises. This will help you see what you want to focus on.
Try the exercises before checking the Answer key.
After doing the exercises in the book, try them again using your own research topic and reading materials. If possible, ask a more experienced colleague or friend to give you feedback on your work.
All university departments are different. Use the information in the book as a guide to investigating your own university department.
Write questions you can ask to find out how your department expects you to do research and collect and present data.
There is no one correct way of doing research and working with collected data. Use your experience of doing the exercises to learn what works best for you. Adapt the suggestions in this book to suit your learning style and context.
Learning to do research and work with data is an on-going process, which means you need to practise the same skills many times. Revise regularly.
Other titles
Also available in the Collins Academic Skills Series: Writing, Lectures, Research, Presenting, and Group Work.
1
Getting Started (#ulink_5a5bc926-baf0-54b8-9d68-8b36d8b2d97e)
Aims
look at numbers in everyday life
understand the purpose and use of statistics
learn key terms for working with numbers
learn the basics about spreadsheets
practise referring to and labelling graphics in writing
Quiz
Self-evaluation
Read the statements below. Circle the answers that are true for you.
Numbers and mathematics are very important in our everyday lives because we use them frequently when we manage our finances, go shopping, make travel plans, convert currency, follow instructions for a recipe or take measurements when we are building and creating things. If we carry out an academic study or investigation, then we need to use a branch of mathematics known as statistics which involves collecting and organizing data, making sense of our information and presenting findings.
Glossary
data You can refer to information as data, especially when it is in the form of facts or statistics that you can analyse. In American English, data is usually a plural noun. In technical or formal British English, data is sometimes a plural noun, but at other times, it is an uncountable noun.
This chapter begins by reminding us of the calculations and vocabulary that are used when we are working with money and taking measurements. It then provides an introduction to statistics, explaining where data is used in different subject areas and describing different categories of data. With a more technical focus, the chapter then describes how to use a computer program known as a spreadsheet which can help with storing and presenting data. Finally, an explanation is given of the use of graphics in academic writing, highlighting ways to refer to graphics in your text so that you can comment on your data and findings effectively.
Numbers in everyday life
In this section, we will explore some of the ways in which numbers are used in everyday situations. We will investigate taking measurements and working with money.
Money
It is important to know how to work with money so that you can:
Recognize the value of amounts of money
Estimate your expenditure
Often money calculations will involve the use of percentages and fractions. You will learn about these in Chapter 6 (#litres_trial_promo).
Glossary
estimate If you estimate a quantity or value, you make an approximate judgement or calculation of it.
expenditure Expenditure is the spending of money on something, or the money that is spent on something.
value In mathematics, the value of a symbol or letter is the amount represented by it.
The value of a digit in a number depends on its position in the number. In the following amounts of money, the digit 4 has a different meaning:
A place value diagram may help to remind you how to recognize the value of amounts of money. The highest number in the group is the maximum and the lowest is the minimum.
Estimating can be a useful skill when you are calculating your monthly expenditure because you can work out approximately how much your total bill will be without adding up all of the individual values. Estimating involves rounding prices up or down to the nearest ten pounds, dollars or euros so that you can work out the total more easily.
This list shows the actual expenditure with the estimated value for each cost:
So, when we add up the actual prices the aggregate total price for our shopping is £835.85 and the estimated cost is £840.
Glossary
round up/down If you round an amount up or down, you change it to the nearest whole number or the nearest multiple of 10, 100, 1,000, and so on.
aggregate An aggregate amount or score is made up of several smaller amounts or scores added together.
Measurements
Taking measurements is about finding a number that shows the amount or size of something. We are most often interested in measuring temperature, length, speed, time, capacity and mass. To make an accurate measurement, you would need to choose an appropriate measuring device and use the correct type of units on a scale. Here are some examples:
Glossary
capacity The capacity of a container is its volume, or the amount of liquid it can hold, measured in units such as litres or gallons.
mass In physics, the mass of an object is the amount of physical matter that it has.
Exercise 1
Match the correct unit of measurement with each item to be measured.
There are a number of key terms that are useful to learn when working with numbers and data. Test your knowledge of these by completing the following exercises.
Exercise 2
Use the words in the box to complete these sentences. You might need to change the form of the word.
accurate calculation fraction measurement
aggregate / total capacity mass percentage
approximately estimated maximum / minimum round up / down
1 The ________of 9, 10, 24, 6, 8, 5 is 62. It is also known as the ________.
2 The ________of the lecture theatre is 200 people.
3 Economic forecasters have ________that the economy will grow by 0.5% next year.
4 There are ________300,000 international students studying in the UK.
5 The spreadsheet automatically ________or ________to the nearest whole number.
6 The ________loan available is £5,000 and the ________loan available is £500.
7 The ________of a bowling ball is 7.25 kilograms.
8 ________measurements are essential in many scientific experiments.
Exercise 3
Use another word in the box in Exercise 2 to describe each item below.
1 1/3 ________
2 245 × 6 ________
3 98% ________
4 100 ml ________
Exercise 4
Put the word in brackets into the correct form in each of these sentences.
1 The closest ________was 2 years 4 months. (estimate)
2 There are a number of different ways to ________an average. (calculate)
3 There are ________1.3 billion people in China. (approximate)
4 The ________of another variable completely changed the outcome of the experiment. (add)
5 The values were ________and then used to find the average. (total)
6 The answers were cross-checked to ________predict the outcome. (accurate)
What is statistics?
Every day in our lives, we hear and read about many different types of information in the form of data. Data can tell us interesting and important details about the world around us but it can be challenging to understand the facts and figures.
Statistics is a mathematical science that helps us to make sense of data that has been counted, measured, asked about or observed. It involves four main activities:
Glossary
method A method is a particular way of doing something.
technique A technique is a particular method of doing an activity, usually a method that involves practical skills.
Collecting data – first of all, we decide what type of data we are interested in, which method we shall use to collect the data, and where we would like to collect it from.
Organizing data – we use a range of different techniques to summarize the data we have collected so that we can see interesting features or patterns in the information.
Interpreting data – we use the results of calculations to help us make comparisons about different sets of data, to answer questions and make decisions about the world around us.
Glossary
feature A feature of something is an interesting or important part or characteristic of it.
Presenting data – when we have found out interesting facts about our data, then we will need to display and present the information to other people so that they can understand our conclusions.
Exercise 5
Choose a newspaper or news-related website and look for reports that use statistics to help explain the main points of the article. Think about these questions:
How was the data collected?
What type of organization is using the statistics?
What interesting features or patterns were found in the data?
How is the data presented?
Statistics is important in many different subject areas. The following diagram lists some examples of the type of data that might be collected and used:
Some terminology
In statistics, we use two key words: variable and observation. It is important to understand the difference in their meanings. A variable is a characteristic or an attribute that can have different values; an observation is the value of a variable that has actually been counted, measured or observed. Some variables are shown below, with a list of possible observations next to each one.
Glossary
variable A variable is a factor that can change in quality, quantity, or size, which you have to take into account in a situation.
characteristic The characteristics of a person or thing are the qualities or features that belong to them and make them recognizable.
attribute An attribute is a quality or feature that someone or something has.
The observations for a variable can be described as quantitative or qualitative, depending on what the information is about. Quantitative data is something which can be measured or counted using a number. Qualitative data represents a characteristic that uses words to describe it but does not use any numbers.
Examples of quantitative variables are:
time taken to complete a test
the number of books in a library
the highest temperature in a month
Examples of qualitative variables are:
the nationality of people in a cinema
the favourite sport of children in a school
the colours of balloons at a party
Exercise 6
Match the words on the left to their definitions on the right.
Exercise 7
State whether each of the following variables is quantitative or qualitative:
1 number of pages in a book
2 names of students in a class
3 hair colour
4 weight of apples in a bag
5 height of trees in a park
Exercise 8
Answer these questions.
1 Explain the difference between a quantitative and a qualitative variable.
2 Give an example of each type of variable.
3 Explain why:
‘type of tree’ is a qualitative variable
‘number of pupils in a class’ is a quantitative variable
Exercise 9
Without looking back at the section ‘What is statistics?’, put these statistical stages into the correct order.
1 organize data
2 present data
3 collect data
4 interpret data
Exercise 10
Use the words in the box to complete these questions about the stages above.
data features patterns sets of data
display method present technique
1 What type of ________are we interested in?
2 Which data collection ________shall we use?
3 What ________shall I use to summarize my data?
4 What interesting ________or ________can I see?
5 What questions do my ________answer?
6 What is the clearest way to ________and ________my data?
Exercise 11
Match the questions in Exercise 10 to the stages in Exercise 9.
Using spreadsheets
You can store, organize and present your data in a computer program called a spreadsheet.
Glossary
grid A grid is something which is in a pattern of straight lines that cross over each other, forming squares. On maps the grid is used to help you find a particular thing or place.
row A row of things or people is a number of them arranged in a straight line.
intersection An intersection is a place where lines or roads meet or cross.
cell A cell is one of the small squares in a chart or spreadsheet into which you can add a single piece of data.
A spreadsheet appears as a table or grid containing a set of rows and columns. Rows are displayed horizontally on the grid and each one is labelled with a number (1, 2, 3 …); the label for each column is a letter (A, B, C …) and columns are displayed vertically across the grid.
The empty spreadsheet grid shown below has eight rows and five columns, but a spreadsheet in a computer program will have many, many more rows and columns.
The intersection of a row and a column is called a cell. Each cell has its own name, which consists of the letter of the column followed by the number of the row. The highlighted cell in the spreadsheet grid shown above is called C5 – it is where column C and row 5 meet.
Tip
Use the glossaries to help you with some of the key words in this book. Consider making similar lists for your modules to help you learn key words.
Exercise 12
Look at the section of a spreadsheet below, and answer the questions.
1 What is contained in the following cells?
a A6
b B3
2 What is the reference for the cells that contain the following?
a The number ‘53%’
b The word ‘Statistics’
The data values in each spreadsheet cell can be displayed in different ways depending on how the information is described. You can use:
text
numbers
currency
dates and times
The spreadsheet opposite records the food purchased by a shopper at a supermarket. Row 1 in this grid is used to show the names of the columns so that it is easy to understand what information is being stored.
A spreadsheet is very useful for performing simple calculations. It uses formulae to perform operations such as addition, subtraction and multiplication.
The following spreadsheet shows the different nationalities of students enrolled on an English course. It includes a formula which uses the individual numbers of each nationality to calculate the total number of students enrolled on the course. The formula is usually hidden from view and only the result is displayed.
Glossary
formula A formula is a group of letters, numbers or other symbols which represents a scientific or mathematical rule.
The formula SUM(B2:B8) is used to calculate the total of number of students enrolled on the course. It adds up the numbers in cells B2 to B8. If a number in one of these cells is changed, then the result of the formula is automatically updated by the spreadsheet.
So, if another French student enrols on the course, then the cell B5 becomes 4 and the total in cell B10 is changed automatically to 44 to include the new student.
Once you have organized your data in a spreadsheet, it is then possible to use the computer program to create graphs and charts to display the information in a visual way. The bar chart below has been created using the data in the previous example.
For more information on graphics, see Chapter 8 (#litres_trial_promo).
Tip
When using spreadsheets, you can click on the Help button in the computer program to search for advice on how to use formulae for calculations.
Using graphics
A number of different visuals are used in academic writing to present data or information. In academic texts they are often referred to as figures, but sometimes a wider range of terms such as chart and table are used as well. A pie chart is used to show the proportion of something in different segments. A key is used to label a pie chart when there are many sections. A bar chart is used to compare different amounts of something. A line graph is used to show trends or patterns. The axes are labelled to show what data is being presented. The x axis is horizontal and the y axis is vertical. A table is a grid with columns and rows of numbers. Diagrams are often used to describe functions. For example, they may show the organization of a company or the stages in the process involved in manufacturing or in decision-making.
Glossary
proportion A proportion of a group or an amount is a part of it.
trend A trend is a change or development towards something new or different.
Exercise 13
Look at the pictures below and label them with words from the box.
Exercise 14
Put the words in brackets into the correct position and form in each sentence.
1 The x axis goes ________and the y axis goes ________. (horizontal / vertical)
2 A ________goes vertically and a ________goes horizontally. (row / column)
3 A ________is used to ________a ________. With a ________the ________needs to be labelled. (label / key / pie chart / line graph / axis)
4 How many ________are there in the ________above? (segment / pie chart)
5 Graphics in academic writing are often referred to as ________but sometimes as ________or tables. (chart / figure)
6 Pie charts are generally used to show the ________of something and line graphs to show ________. (trend / proportion)
Referring to graphics in writing
Although graphics generally speak for themselves, it is common to make a brief reference to them in writing to introduce what they show. This can be done with a range of basic phrases, for example:
As can be seen in Figure 12.1, …
From Table 2.1, it can be concluded that …
Language: relative clauses
Relative clauses can be a useful structure for summarizing or referring to key information in a graphic. For example:
The graph shows the number of students from India who were given visas in 2010 was 58,000.
The table shows that the number of students who come from the USA is getting bigger.
In academic writing, relative clauses are often used for defining; in the case of data, they are used to describe or define exactly who or what you are referring to. Note that the relative pronoun (who, whose, which, that) will change depending on what you are defining. For people, use who, that or whose (possessive):
The graph shows people who are motivated by goals often have short-term satisfaction.
The graph shows that people that set realistic goals often enhance their performance.
The chart demonstrates that companies whose managers are not aware of employee motivation are less likely to be successful.
For most things or ideas, use that or which:
The table shows companies that use money as a means to motivate employees.
The table shows teams which use a sports psychologist to motivate teams.
For more information on describing graphics, see Chapters 8 (#litres_trial_promo) and 9 (#litres_trial_promo).
Exercise 15
Complete the table with words from the box.
As is shown graph 2.3 in It can be seen from
Exercise 16
Match 1–5 with a–e to form sentences including a relative clause.
Tip
Try to record all new vocabulary in a similar way and regularly test yourself on the new words.
Remember
You might have to use spreadsheets to analyse your data.
The main purpose and use of statistics.
Relative clauses are useful for referring to and labelling graphics in writing.
The different stages from collection to presentation of data.
2
Starting Primary Research (#ulink_47c38016-2279-5e6d-81f1-dc9dee32f096)
Aims
practise formulating research questions
understand the principles of sampling
learn how to formulate a hypothesis
Quiz
Self-evaluation
Read the statements below. Circle the answers that are true for you.
Early planning and good organization are key to a successful research project. What you decide to research can vary greatly depending on the field you are in, but there are two main starting points: formulating research questions, or formulating a hypothesis to test. Whether you choose one, the other or both, there are some important points to consider:
Does this area interest you enough? After all, this project will become a large part of your life for quite some time.
Has this area been researched before? If so, what new things are you hoping to add with this study?
How does this build on previous research in the area?
Are the research aims focused and limited enough? You will have a limited amount of time and words to complete the project, so it needs to be realistic.
Do you have access to a reasonable cross-section of the population you wish to study?
This chapter will help you to consider some of these key issues. It gives you practical steps to formulate research questions, and helps you understand the basic principles of sampling and to understand the cause and effect nature of hypotheses.
Formulating research questions
Doing a research project is both exciting and challenging at the same time. Research projects at the end of a Bachelor’s or Master’s (BA, BSc, MA, MSc) degree are commonly called a dissertation or a thesis. You usually have a lot of freedom to choose the area you want to research, although sometimes you may be given a choice of questions about a broad area of research to look into. You can start to think about the area you want to research very early on, but try not to narrow it down too soon before you are ready to begin.
It is a good idea to choose a topic or area that interests you, perhaps from a module you enjoyed or a topic that has stimulated your interest in a new area. Sometimes it can be a challenge to think of an area, so talk about it with tutors, friends or other students and perhaps look at some previous projects in your area of study.
Exercise 1
Follow these steps to help find an area that interests you.
1 Brainstorm the different subjects from your degree.
2 Think about particularly interesting modules.
3 Think of an interesting area from that module.
4 Which of these topics particularly interests you?
Once you have a range of topics that interest you, the next step is to narrow it down. This is something that should be done quite quickly as you often have limited time. Thinking about your motivation is important because you will be spending a lot of time on the project. It is also important to try to think about how practical the project is.
Being specific
One of the biggest challenges is choosing a research question that is specific enough. The idea of writing 15,000 or 20,000 words in your own language can make people feel quite worried, and doing it in another language for your Bachelor’s or Master’s degree can seem even more challenging. Many of the English exams to gain entry to a university only require students to write 250 words in English. So when, in perhaps just nine months of completing that test, you have to write 20,000 words, very few people worry about being specific. Many think – can I write that much? When people choose a topic that is too broad it can be difficult to answer in 15,000 to 20,000 words as there are too many things to cover. It can create problems conducting the literature review as you will have too many things to read. It could also mean that you do not have the time or resources to conduct your own research and write it up. Try to build on topics. Think about the following: has this area already been well researched? Is there a clear research methodology I could use? Can I bring a slightly new perspective to the topic? How specific you need to be will vary between courses, but it is essential you think about these questions in order to make your project realistic.
Glossary
specific If someone is specific, they give a description that is precise and exact.
Exercise 2
Which of these research questions sounds specific enough?
1 Does regular exercise reduce stress levels in men aged 18–25?
2 Will a high-fibre and low-fat diet be sufficient to reduce cholesterol levels in middle-aged women?
3 Does exercise improve mental health?
4 Does motivation affect levels of effort?
Tip
Try to be as focused as you can from the start. Look at as many previous students’ dissertations as possible to help guide you. Ask your supervisor for help and guidance when you feel you need it.
Exercise 3
Think about your possible research question and ask yourself these questions.
1 Can you answer your question in just a few months?
2 Is your question specific enough? Brainstorm all the different things you might include and then imagine how many words it might take to cover each.
3 Have you read previous students’ projects? How long was each section?
4 Once you have collected your data how will you analyse it? How long do you think this might take? If you are doing something that requires you to write down what was said, for example an interview, practise this by recording a friend and writing down what they say. Time yourself and then imagine how long this might take once you have interviewed the number of people you want to interview.
5 Can you get access easily to people you want to interview, use in a focus group or give your questionnaire to?
Exercise 4
Decide if the following statements are true or false.
Sampling
Population: when you carry out an investigation to find out information about a group of things or people, this group is known as the population.
Some examples of different populations are:
all the people who live in New York
all the books in a library
all the trees in a forest
all the nurses in a hospital
Glossary
population If you refer to a particular type of population in a country or area, you are referring to all the people or animals of that type there.
Census: you would need to carry out a census if you want to find out information about every member of a population. It is easier to carry out a census if you have a small number of people or things in your population, but if the population is very large then it is usually time-consuming, often expensive and sometimes impractical.
For example, if a biscuit manufacturer that bakes thousands of biscuits every day decided to find out how easily their biscuits break, a census would involve breaking every biscuit that they make. This would be impractical because the population is too big and it would be very time-consuming to test each biscuit individually.
Sampling: instead of carrying out a census of the whole population, you could decide to ask questions or observe just a small group of the things or people within that population. This is called sampling. Using a sample can be a lot less expensive, quicker and much easier than carrying out a census. When you have collected information from a sample, it is then possible to draw conclusions and make estimates about the entire population.
For example, the biscuit manufacturer in the previous example could use a sample to find out how easily their biscuits break by choosing 100 biscuits of different varieties for testing.
Glossary
census A census is an official survey of the population of a country that is carried out in order to find out how many people live there and to obtain details of such things as people’s ages and jobs.
sample A sample of people or things is a number of them chosen out of a larger group and then used in tests or surveys, or used to provide information about the whole group.
Exercise 5
For the investigations listed in the table below, describe the population and decide if it would be practical or impractical to carry out a census to find out information on the whole population.
Avoiding bias
Using sample data, you can only draw conclusions and make estimates about the entire population if you choose a sample of things or people that represents the whole population fairly. If your sample is not representative of the population, then it is known as a biased sample.
The table below describes some samples taken for different investigations, and explains why these samples are not representative of the population. Can you work out why the sample is biased for the last two investigations?
Glossary
biased If someone is biased, they prefer one group of people to another, and behave unfairly as a result. You can also say that a process or system is biased.
Tip
Ask someone else to look at your planned sample before you start your research and ask them if they can see any bias. It can be difficult to look at it objectively yourself, so help and guidance will be useful here.
Exercise 6
Match the words or phrases on the left to a definition on the right.
Exercise 7
Complete these sentences with words from Exercise 6. You may need to change the form of some words.
1 The sample was not large enough to be ________of the whole population.
2 Poor ________meant that it was difficult to draw conclusions.
3 The study was ________over a three-month period.
4 The study aimed to ________the effects of advertising on children.
5 The sample was ________towards middle aged men.
6 The ________net spend per month was £500.
7 A national ________is carried out in the UK every few years.
8 The ________under investigation was international students in the UK.
9 We can ________the ________that advertising has a significant impact on children’s spending patterns.
Formulating a hypothesis
A hypothesis is something that you plan to test in your research and is related to forming your research question. The hypothesis usually states that something will or will not happen. It is something that you would write before starting your research; you plan to see if it is true or not after doing your research.
Glossary
construct In the area of research, a construct is an idea, belief, or subject which is based on evidence which may not be true, and which you want to test and measure.
objectively If you look at something objectively, you base your opinions on facts rather than on your personal feelings.
Examples of hypotheses:
Language is the main challenge in adapting to another culture.
Low income is the main reason for job dissatisfaction.
Blueberries have a positive impact on the mind.
Each of these hypotheses is formed from two or more constructs and often makes a claim for cause and effect. For example:
A construct is something that can be tested or questioned objectively. For example, in the first hypothesis above we could ask:
How can culture be defined?
How can adaptation be measured?
What factors affect adaptation?
How are language and culture related?
Does language impact on adaptation?
Exercise 8
What is the purpose of a hypothesis and what should it clearly state?
Exercise 9
Look at the other two hypotheses from the previous page. What questions could you ask yourself about these hypotheses?
Low income is the main reason for job dissatisfaction.
1How is job satisfaction defined?
2 ________
3 ________
4 ________
5 ________
6 ________
Blueberries have a positive impact on the mind.
1What foods have a positive impact on the mind?
2 ________
3 ________
4 ________
A piece of research may contain more than one hypothesis that will be tested. Another common thing other than cause and effect that is tested is a comparison between two groups or classes.
Example:
Single sex schools produce better academic results than other schools. They are also more of an advantage for girls than boys.
Here the hypothesis is looking at the cause and effect relationship between single sex schools and academic success but it is also making a comparison between boys and girls.
Exercise 10
Which of the following hypotheses make a comparison?
1 People who regularly use computers suffer from more health issues than those who do not use them.
2 Men make more impulse purchases than women.
3 It is more difficult to learn a second language after the age of 20 than before it.
4 Independent study increases academic success.
5 Three minutes’ intensive exercise is enough to maintain fitness levels.
Exercise 11
Look at these possible causes and their effects. Can you join them together to write a hypothesis for each one?
1 Travel abroad > malaria
Travelling abroad increases the risk of catching malaria.
2 Recycling > save money
3 Low temperatures > car accidents
4 Language learning > cultural awareness
Remember
It is important to be specific in your research question.
You need to define and clearly state your question early on in the research process.
Sampling can have a significant impact on your research and should be done carefully.
It is important to choose the most appropriate research methods.
You can use hypotheses as part of your research process.
3
Research Methods (#ulink_9b25ea1f-8e20-5769-b6b4-9b590bef71fd)
Aims
understand some common research methods
understand when to use interviews, questionnaires and focus groups
understand the advantages and disadvantages of common research methods
Quiz
Self-evaluation
Read the statements below. Circle the answers that are true for you.
A wide range of research methods is available for you to choose from when you conduct a research project. The key is to choose the most appropriate method or methods for your research aims. In Social Sciences, particularly with projects at undergraduate level, three of the most common methods are interviews, questionnaires and focus groups. This, of course, does not mean you need to limit yourself to these methods.
This chapter looks at some of the main research methods, at some of their main advantages and disadvantages and gives a brief overview of some other methods of research. The following two chapters look in more detail at how to produce a questionnaire and conduct an interview.
For more information on other research methods, see Further reading.
Choosing your research method
A research method is the way in which you choose to collect your data. A wide range of research methods can be used to gather data. This section will give you an overview before looking in more detail at some of the main advantages and disadvantages of four key research methods: questionnaires, focus groups, interviews and experiments. This is then followed by a brief overview of some other methods to consider. When you select your method it is important to choose one that will effectively help you to answer your research question or test your hypothesis. It is also important to be aware of the advantages and disadvantages of each method.
Questionnaires
Many students choose to do a survey using a questionnaire as it is commonly believed that the method is easy. A questionnaire doesn’t involve the pressure of an interview, and the answers are conveniently written down for future analysis. However, it can be challenging to write an effective questionnaire.
Questionnaires can be distributed in a variety of ways and there is a varying amount of success in getting responses back. The questions are typically predominantly aimed at gathering quantitative data, but an element of qualitative data can also be gathered.
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Dawn Willoughby и Louis Rogers
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Жанр: Иностранные языки
Язык: на английском языке
Издательство: HarperCollins
Дата публикации: 17.04.2024
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О книге: Statistics and data for the non-specialist*The Collins Academic Skills Series – winner of the ELTon 2014 Innovation in Learner Resources Award.*At university you may be expected to analyse complex data and present your findings, whatever your area of study. Collins Academic Skills Series: Numbers gives you the skills you need to make sense of data and numbers and the confidence to use them effectively in your work.Learn how to• interpret statistics and data• conduct surveys• evaluate and question results• present numerical information clearlyCollins Academic Skills Series: Numbers will help you to make the most of your time at university.• Clear information and practical exercises• Information on academic expectations – understand the requirements of studying at university• Helpful tips and summaries• Answer key and glossaryNumbers is part of a new six-book series to help international students achieve academic success at college or university. It is designed to support students who are studying, or preparing to study, at an English-speaking institution.Suitable for students whose level of English is Upper Intermediate / CEF level B2 / IELTS 5.5 and higher.Other titles in the Collins Academic Skills Series:Group Work • Lectures • Presenting • Writing • Research