Set Datang di SMAN 8 Batam Analysing data

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Getting and analysing

quantitative data

A3

MODULE

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course in research and evaluation skills and six handbooks in specific research areas of ODL.There is an accompanying user guide. A full list appears on the back cover.

The print-based materials are freely downloadable from the Commonwealth of Learning (COL) website (www.col.org/prest). Providers wishing to print and bind copies can apply for camera-ready copy which includes colour covers ([email protected]).They were developed by the International Research Foundation for Open Learning (www.irfol.ac.uk) on behalf of COL.

The PREST core team

Charlotte Creed (Programme coordinator)

Richard Freeman (Instructional designer, editor and author) Bernadette Robinson (Academic editor and author) Alan Woodley (Academic editor and author)

Additional members

Terry Allsop (Critical reviewer) Alicia Fentiman (Basic education adviser) Graham Hiles (Page layout)

Helen Lentell (Commonwealth of Learning Training Programme Manager) Santosh Panda (External academic editor)

Reehana Raza (Higher education adviser)

Steering group

The PREST programme has been guided by a distinguished international steering group including: Peter Cookson, Raj Dhanarajan,Tony Dodds,Terry Evans, Olugbemiro Jegede, David Murphy, Evie Nonyongo, Santosh Panda and Hilary Perraton.

Acknowledgements

We are particularly grateful to Hilary Perraton and Raj Dhanarajan who originally conceived of the PREST programme and have supported the project throughout. Among those to whom we are indebted for support, information and ideas are Honor Carter, Kate Crofts, John Daniel, Nick Gao, Jenny Glennie, Keith Harry, Colin Latchem, Lydia Meister, Roger Mills, Sanjaya Mishra, Ros Morpeth, Rod Tyrer, Paul West and Dave Wilson. In developing the materials, we have drawn inspiration from the lead provided by Roger Mitton in his handbook, Mitton, R. 1982 Practical research in distance education_{, Cambridge:}

International Extension College.

Handbook A3: Getting and analysing quantitative data

Author:Alan Woodley

Critical reviewers: Richard Freeman, Santosh Panda and Bernadette Robinson.

Permission is granted for use by third parties on condition that attribution to COL is retained and that their use is strictly for non-commercial purposes and not for resale. Training providers wishing to version the materials must follow COL's rules on copyright matters.

Permissions

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Getting and analysing quantitative data . . . .1

Aims of the module . . . .1

Module objectives . . . .2

Module organisation . . . .2

Requirements . . . .3

Resources . . . .4

Unit 1: Introduction . . . .5

Unit overview . . . .5

Learning outcomes . . . .5

The rules of quantitative methods and how to apply them: an introductory case study . . . . .6

Summary . . . .13

Feedback to selected activities . . . .13

Unit 2:What do we mean by quantitative methods? . . . .17

Introduction . . . .17

Which questions can be answered with a quantitative approach? . . . .18

Summary . . . .21

The rest of the module . . . .21

Unit 3: Analysing other people’s data . . . .23

The data . . . .23

Raw numbers . . . .24

Percentages . . . .25

Excel for beginners: calculating totals . . . .26

The open schools case study . . . .33

Conclusions . . . .43

Summary . . . .45

Unit 4: Quantitative institutional data . . . .55

Types of data . . . .56

Types of institutional data . . . .59

Dealing with quantitative data . . . .59

Summarising . . . .60

Averages . . . .65

Spread, dispersion and deviation . . . .68

Are we getting more young students? . . . .73

Patterns and trends . . . .77

Summary . . . .86

Unit 5: Doing institutional research ‘from scratch’ . . . .89

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The dimensions of data collection methods . . . .91

The range of quantitative research methods . . . .94

Designing good questions to ask people . . . .94

Guidelines for good question writing . . . .97

Forms of questions . . . .100

Designing good questionnaires . . . .108

Designing for disability . . . .113

Carrying out a survey . . . .116

Summary . . . .125

Unit 6: Analysing your research results . . . .133

Exploring relationships using correlation . . . .155

Looking back and looking forward . . . .163

Summary . . . .164

References . . . .165

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quantitative data

Module overview

You have seen in the earlier modules that there are two broad approaches to collecting research data: qualitative methods and quantitative methods.This module looks at the latter type.Through studying the module you will gain an overview of some of the key issues in collecting and analysing quantitative data.

You will also learn some of the common methods of statistical analysis of numerical data, although this is not a module on statistical methods in general – that is far too large a topic to treat here. Instead, I have concentrated on showing you how to use some of the basic analytical tools that you can find in Microsoft Excel.

During the module you will explore and learn about:

䉴 deciding what data you need in order to answer given research questions 䉴 interpreting quantitative data

䉴 types of quantitative data

䉴 methods of summarising quantitative data

䉴 methods of describing patterns and trends in data

䉴 methods of collecting quantitative data, including questionnaire design 䉴 some methods of analysing quantitative data.

Aims of the module

The overall aim of this module is to introduce you to the concepts and techniques of quantitative research methods in the context of open and distance learning.

A second aim is to demonstrate that facts involving quantitative data are ‘socially constructed’ and to examine the underlying processes involved. Our third aim is to enable you to analyse other people’s data and to appreciate how and why secondary analysis of external quantitative data

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needs to be done with care if you are to extract meaningful information from such data.

Our fourth aim is to enable you to analyse quantitative institutional data (e.g. data on students, their courses and their marks) that already exist in order to extract meaning and information from that data, using methods such as averages, measures of spread and trend analysis.

Our final aim is to help you develop the skills of doing institutional research from scratch.You will look at how to decide what data to collect, which methods to use and how to design your data collection instruments so that they will yield valid and reliable results.

Module objectives

When you have worked through this module, you should be able to: 1 Identify the sorts of research questions that can be answered by a

quantitative approach.

2 Calculate percentages as a means of comparing data. 3 Calculate averages as a means of summarising data. 4 Calculate some common measures of dispersion for data. 5 Explain the ideas of validity and reliability and identify methods of

maximising these in your research.

6 Design effective instruments for collecting quantitative data.

Module organisation

The module is structured is in seven parts: this introduction and six units, as follows.

This introduction: (1 hr) Unit 1: Introduction (2 hrs)

Unit 2: What do we mean by quantitative data? (1 hr) Unit 3: Analysing other people’s data (10 hrs)

Unit 4: Quantitative institutional data (9 hrs) Unit 5: Doing institutional data ‘from scratch’ (9 hrs) Unit 6: Analysing your research results (9 hrs) Each unit is made up of the following components:

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䉴 a range of activities for you to engage in, many based on Excel

spreadsheets 䉴 unit summary

䉴 feedback on your responses to the questions or problems posed in each activity.

Requirements

In order to make your learning more interactive, and hence more efficient, we have included lots of practical exercises.These use numerical data and we take you through all of the necessary calculations.

We do not assume any great mathematical knowledge. If you understand the concepts of addition, subtraction, multiplication and division then you should be able to manage.

However the activities will use the general piece of office software called Microsoft Excel.This is normally built into desktop computers as standard nowadays. It will be possible to work through the module without Excel, but you are strongly advised to get access to it.

Excel

To carry the activities out exactly as laid down you will need access to Excel

Version 4 or above. However you should be able to open the data in earlier versions and still carry out the exercises. Some of the instructions might have to be interpreted and adapted.

If you are fairly experienced in Excel, you will be able to carry out the tasks relatively quickly.

For novice Excel users we have tried to spell out what you need to do. If you get stuck you can turn to the Model worksheet in each workbook where we have carried out all of the stages.The letters in brackets, e.g. (W1) tell you where to look on the relevant Model sheet.

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Resources

The following resources are used in this module:

Teaching boxes

We have used two types of ‘teaching boxes’ in the text as follows:

Provides additional explanations of some of the statistical terms and methods that I discuss.

Provides additional information and explanation on how to use Excel. Excel note:

Statistical note:

Resource Name when referred to in our text Location

Excelworkbook Women Women Resources File

Excelworkbook M101 M101 Resources File

Excelworkbook Summarising Summarising Resources File

Excelworkbook Analysing 1 Analysing 1 Resources File

Excelworkbook Analysing 2 Analysing 2 Resources File

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Unit overview

We live in an age where it is claimed that policy decisions are based on facts rather than hunches, prejudices and rumours.This is commonly referred to as ‘evidence-based decision-making’.The field of education is no exception, where it is felt that this ‘evidence’ is needed both to decide between policy options and also to evaluate the success or failure of past policies.

Furthermore, this ‘evidence’ tends to be ‘facts and figures’ or ‘statistics’. I think it is fairly uncontentious to say that managers, bosses, civil servants, politicians prefer quantitative data to qualitative. Faced with an argumentative audience they like to be armed with charts, spreadsheets and survey results.

This unit will introduce you to:

䉴 some of the difficulties of deciding just what a fact is

䉴 some of the issues that arise when we try to describe a system or a situation using statistical data.

Learning outcomes

When you have worked through this unit, you should be able to: 1 Discuss the difficulties of deciding just what a fact is.

2 Explain why all knowledge can be seen to be provisional.

3 Illustrate some of the difficulties of using statistical data to describe a situation such as course enrolments in an ODL institution.

I want you to begin with a fairly light-hearted activity to get you thinking about ‘facts and figures’

Activity 1 10 mins

Which of these statements are ‘facts’ and why? 1 Paris is the capital city of France.

2 The author of this module is 21 years old and 2 metres (approximately 6 ft 7 ins) tall. 3 Mount Everest is the world’s tallest mountain at 8848 metres high.

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4 In 2003 The Sukhothai Thammathirat Open University (STOU) in Thailand, with over 300,000 students, was the biggest university in the world.

The feedback to this activity is at the end of the unit 䉴

One thing that we can conclude from this last activity is that good research should tell you something about precision levels and how much confidence you should place in the results.

Accuracy and rounding

Numbers are frequently ‘rounded’ before being made public. For example, the number 7.98 may be ‘rounded up’ to 8 and the number 632 may be rounded down to 600. In the case of Everest the height has been rounded to the nearest metre. The actual result would have been somewhere between 8847.50001 and 8848.49999.

The measurement method may have been such that this was the greatest level of accuracy that could have been claimed. The actual result may have been 8848.234632 and this was then ‘rounded down’ by the scientists because they knew that the instrument used was not really that accurate. For example, on a hotter day it may have given a slightly higher reading. In reality they have probably made lots of measurements and then calculated a middle or ‘average’ value which they then published as their best estimate. (Statistical averages will be covered later in this module.)

You will frequently see results being presented in social research that exaggerate the accuracy of the measurement tool. Do not be impressed if the results say that 10.256% of students disliked the course when in reality it refers to a survey of 100 students where 19 replied and only 2 gave this answer.

The provisional nature of knowledge

Karl Popper, a 20th century philosopher (but one who repeated and expanded on the ideas of his predecessors) maintained that a theory could never be completelyverified. Even if it has been rigorously tested over a long period of time, the most that one could say was that the theory has received a high measure of corroboration. It can be provisionally retained as the best available theory until it is finally falsified (if indeed it is ever falsified), and/or is superseded by a better theory.

In my opinion, a strong case can be made for the view that ‘all knowledge is provisional’ in the Popperian sense. However, I think it is undeniable that all knowledge, including ‘facts and figures’, is socially constructed.This has led people like Henry Ford (the founder of the US car company) to proclaim that ‘there are lies, damn, lies and statistics’. Many people in the general public share his feelings, namely that figures can be manipulated to prove anything and that they should not be trusted.

I do not take such a negative, cynical view. My position is more a sceptical, questioning one:

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䉴 while all knowledge is provisional, some forms of knowledge can be relied upon more than others

䉴 the trust one places in a piece of knowledge depends to a great extent upon whether appropriate research methods have been used and how clearly these have been documented

䉴 arguments in favour of quantitative methods rather than qualitative methods, or vice versa, will never be conclusive

䉴 in general, the ‘truth’ about a social situation is best approached by a combination of methods, both quantitative and qualitative

䉴 there are certain rules for constructing and presenting knowledge 䉴 one must be cautious when interpreting knowledge.

Now let’s move on to learning the rules of quantitative methods and how to apply them.

The rules of quantitative methods and how to

apply them: an introductory case study

Rather than beginning with a long list of the ‘whys?, ‘hows?’ and ‘whens?’ of quantitative research, I am going to begin with a case study in open and distance learning that I hope you will find realistic. I thought that this would be more interesting for you, and more like the reality of practitioner research. At this stage I will not go into the details of the statistical techniques that I am using.The important things at the moment are the processes involved in doing this type of research.

Case studies

The term ‘case study’ is used in many areas and has several meanings. For example, it can mean the selection and in-depth study of a single ‘case’ – perhaps one particular ODL institution. By looking intensely at one, complex example it is intended to give an insight into the context of a problem as well as illustrating the main point.

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government departments, evaluations of programmes and research projects that come from abroad.

The Vice-chancellor wants to present findings to the Minister of Education to show how successful AOU has been in enrolling students on its teacher training programme. He gives her the data on enrolments on the programme for the last three semesters and asks the ERG to produce a graph to illustrate the rise in numbers (Table 1).

Table 1 Enrolments on the teacher training programme at AOU (Semesters 8 to 10)

Abidagoes ahead and constructs the graph shown in Figure 1and submits it to the Vice-chancellor. He, being an astute person, suggests that it be re-drawn as in Figure 2 because he feels that this shows the growth in numbers better.The second graph is then sent off to the Ministry.

Figure 1 Enrolments on the teacher training programme at AOU (Semesters 8–10)

0 50 100 150 200 250 300 350

Semester8 Semester9 Semester10

Semester 8 Semester 9 Semester 10

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Figure 2 Enrolments on the teacher training programme at AOU (Semesters 8-10)

Imagine that you are the Minister of Education. 1 What would you make of Abida’sgraph (Figure 2)?

2 Would you be impressed by AOU’s performance in teacher training?

Graphs

Graphs (or charts as they tend to be called in Excel) are important and powerful tools. The horizontal line is called the x-axis and tends to be used for the categories being looked at such as age, gender, semester, etc. The vertical line is called the y-axis and tends to be used for the numbers in each category.

The plural of axis is axes.

There are generally accepted rules for the shape of graphs. The default shape produced by

Excelis usually in line with these rules.

Statistical note: 0

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The role of the researcher in presenting data

Now, what about Abida? Did she behave appropriately?

Well as a junior researcher she is probably not in a very powerful position.To some extent she has to do exactly what she is told. However, I believe that it is part of Abida’sprofessionalrole to raise questions. She might only be able to raise them with her line manager, who might block them or produce convincing counter-arguments. On the other hand her ideas might go further up the chain and actually effect what goes to the Minister.

Let’s proceed by suggesting some of the questions Abidamight have asked. What should have been her concerns?

Just like the Minister, she should have been concerned about constructing a graph based on just three data points.

Let’s imagine that in this case she was able to access the information for the previous eight semesters and that the full data set is in Table 2.

Table 2 Enrolments on the teacher training programme at AOU (Semesters 1 to 10)

The numbers from Table 2 are plotted in Figure 3.

Figure 3 Enrolments on the teacher training programme at AOU (Semesters 1-10)

What does Figure 3 tell you about the growth of enrolments over the ten semesters?

The feedback to this activity is at the end of the unit 䉴 0

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1 2 3 4 5 6 7 8 9 10

Semester

Semester 1 2 3 4 5 6 7 8 9 10

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In order to discover underlying trends Abidacould use statistical techniques to smooth out this graph.These tools attempt to remove random fluctuations in the data.This topic is covered in more detail later in this module. Here we just illustrate the concept in Figure 4 where we have added the ‘linear trend line’ – that is the straight line that best represents all of the data mathematically.

Figure 4 Enrolments on the teacher training programme at AOU with trend line added (Semesters 1–10)

What does the trend line in Figure 4 tell you about the growth of enrolments over the ten semesters?

Other factors behind the enrolment pattern

Abidamight also have the time, the intellectual curiosity and the necessary data, to investigate other factors that lie behind the enrolment patterns. Let’s say that the programme consisted of three courses. Course A ‘Curriculum Design’ run in semesters 1, 2, 3, 9 and 10. Course B ‘Developmental Psychology’ run through semesters 3 to 10. Course C ‘Teaching Methods’ only started in semester 10.The enrolments for each course in each semester are shown in Table 3.

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Table 3 Enrolments on the teacher training programme at AOU (Semesters 1 to 10)

Now, if we graph these numbers (Figure 5) we see that each course is different.

Figure 5 Enrolments on the teacher training programme at AOU (Semesters 1–10)

Describe the different enrolment patterns of three courses, as shown in Figure 5.

Looked at in this way we can see that the peak in enrolments in Semester 3 was because Course B started then with a lot of students.The peak in Semester 10 occurred because it was the only semester in which all three courses were running. In fact if you calculate the average number of

enrolments per course (these number are shown in Table 3) then you can see that there were six semesters that had a higher number of enrolments per course than Semester 10. Growth at AOU does not seem to be due to

0 20 40 60 80 100 120 140 160 180

1 2 3 4 5 6 7 8 9 10

Semester

Course A Course B Course C

Semester 1 2 3 4 5 6 7 8 9 10

Course A 97 122 127 97 98

Course B 158 133 137 144 122 94 100 112

Course C 110

Total 97 122 285 133 137 144 122 94 197 320

Average enrolments per course

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greater student demand for each course, but merely the provision of more courses.

Summary

In the case study we have been looking at quantitative data. We have not infringed any methodological rules (except, perhaps, when we ‘squeezed’ Figure 2) but we have come up with some different stories and explanations. This shows that little if anything is self-evident from quantitative data. It has to be assembled, arranged, presented and interpreted by people – or ‘socially constructed’.

Secondly, how it is done can depend a great deal on the skills and interests of the researcher.

Thirdly, the context of the data is important.Abidahas shown that by adding in data from more semesters and breaking it down into courses, we gain a richer understanding and a more sceptical view of enrolment growth.

However, if the Vice-chancellor knows that there are more courses coming on stream, and that they seem to attract about one hundred students each, then his optimism may well be justified.

Finally, there are clearly issues of power involved when it comes to decisions about what questions are asked, what data is collected, and how it is analysed, presented and interpreted.

Feedback to selected activities

Feedback to Activity 1

1 Paris is the capital city of France.

This seems like a ‘fact’ to me because that is what my book on France says. (Pedantically you could say that it is a ‘partial fact’.There is a town in the USA called Paris that is notthe capital of France.) So ‘facts’ don’t necessarily contain ‘figures’.

2 Alan Woodley is 21 years old and 2 metres (approximately 6 ft 7 ins) tall.

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3 Mount Everest is the world’s tallest mountain at 8848 metres high.

Well I looked this up on my computer using GOOGLE, the web-based search engine. In the first reference that I went to, it said that Everest was 8848 metres high, so I was fairly sure that this was a ‘fact’, but:

䉴 it is not a very precise ‘fact’. All we know here is that, to the nearest metre, the height is 8848.You could measure a pile of books with your ruler more precisely than that! However, this apparent lack of precision does not necessarily mean bad research

䉴 the scientists may have much more precise results but have chosen to present them in a simplified fashion

䉴 they should not be presenting results to several decimal places if the measurement techniques do not justify it.

Strictly speaking, even if this ‘fact’ was accurate to several decimal places, it should have a date attached to it! Apparently Mount Everest is very slowly getting taller at the rate of two inches (5 centimetres) per year as the geological movements that created the mountain range continue to force it upwards.

I have trusted what I have found on my computer but people can put up any ‘facts’ they want to on a website.You need to know whether the source is reliable, or you should check several sources. In this instance I went to a second website and it said that the latest estimate using satellite technology was 8872 metres.

A case could be made that the tallest mountain isn’t Everest but Hawaii’s Mauna Kea, which rises to a height of 9500 metres from the seabed. It just happens that most of it is under water and mountains are traditionally measured from sea level. (Of course, this also raises the question of ‘sea-level’ – how do we measure it and is it a constant?) A third contender is

Chimborazo in Ecuador. Because of the ‘equatorial bulge’ its peak is actually the furthest from the centre of the earth. My point is that you need to know the assumptions and definitions that lie behind the ‘facts’.

There are also cultural aspects to this ‘fact’. When asked to name the tallest mountain you may get different answers depending upon where you are. In Tibet the local name for the mountain that most of us know as Everest is Chomolungma. In Nepal it is called Sagarmatha. Early British surveyors labelled it Peak XV and in 1856 Surveyor General Andrew Waugh, unaware of local names, named the mountain after his predecessor, George Everest.

4 In 2003 The Sukhothai Thammathirat Open University (STOU) in Thailand, with over 300,000 students, was the biggest university in the world

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However, given the variety of ways that students are counted in different institutions, I would like to know what definition of ‘student’ they were using. For example, if a person is registered simultaneously on four courses, do they count as one or four students? Is this the number of students studying at one point in time, or the number who studied over a given time period such as a year?

To compare STOU with other universities one needs a standard form of measurement. One such system is full-time equivalent students (FTE’s). Many of STOU’s students are studying part-time so it can be argued that they should only count as a fraction of a student.This fraction would depend upon what proportion of a full-time load they were carrying.

I would also want to check out which other universities had been included and how. For example, if the Chinese Central Radio and Television University and its Regional Television Universities were considered to be one university then it might be bigger than STOU.Then there is the growing number of virtual universities such as the University of Phoenix that would need to be looked at.

Feedback to Activity 2

Well, as a busy Minister, I would be pleased to receive the information in the form of a graph. Most people find them easier to digest than tables of figures. They enable you to see patterns and trends in the data.

However, I don’t think that I would be convinced by a graph that only has three points on it. I would not be confident that you could extend that line into the future to predict a similar rate of growth.

I would also be suspicious of the shape of the graph. It looks as though the lower axis has been shortened to make the line on the graph steeper. I would like to see some comparative figures from other institutions.

Even if I was impressed by the growth in enrolments, I would like to see some figures on student progress as well.

Feedback to Activity 3

You can see immediately that the graph does not show a pattern of continuous growth over the ten semesters. In fact, there was also a peak in the third semester that was almost as big as that in the tenth semester.

Feedback to Activity 4

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Feedback to Activity 5

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quantitative methods?

Unit overview

This unit introduces you to the idea of quantitative research methods by considering the types of questions such methods could be used to answer.

Learning outcomes

When you have worked through this unit, you should be able to:

1 Describe the basic difference between quantitative and qualitative research in terms of their outcomes.

2 List the types of questions that are suited to the quantitative approach.

Introduction

As you have seen earlier in this series, the stages of a research project are typically:

䉴 Design the research question. 䉴 Identify the population to be studied. 䉴 Select the research tools for data collection. 䉴 Collect the research data.

䉴 Analyse the research data. 䉴 Interpret the results. 䉴 Present the results.

These stages are the same, whatever the size of the project; and regardless of whether the project is essentially qualitative or quantitative.

The essential difference between the qualitative and quantitative approaches is in their outputs. Put at its simplest, quantitative research is about measuring things in a way that can give meaningfulnumericalresults. It is what researchers in the physical sciences do all of the time. Qualitative research aims for a subjective understanding of a situation using non-numerical results.

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However, while just about any research question in ODL could be formulated in a way that could be answered by using quantitative orqualitative methods, there are certain types of question that lend themselves more to a

quantitative approach.

Which questions can be answered with a

quantitative approach?

As we outlined in Module 1, the range of topics and areas of inquiry that can involve institutional or practitioner research is huge. It is also the case that just about any research question in ODL could be formulated in a way that could be answered by using quantitative or qualitative approaches, or a combination of the two. However, there are certain types of question that lend themselves more to a quantitative approach and there are certainly situations where numerical answers are expected and are more appropriate.

To give you some idea of the typesof question that quantitative methods can be used to answer, we list some examples below.To keep things simple, they all relate to the subject of student age. For each one, we will describe how a quantitative researcher might set about the task and we will introduce some of the technical language involved. (These are the words in bold. Don’t worry if you do not understand some of them.Their meaning will become clear later in the module.)

Descriptive questions

Example How old are our students this year? Purpose To provide descriptive data.

Source Probably our institutional database.

Pre-collection issues We will need to establish working definitions.For example, do we mean all students registered at a particular date. Is it age on January 1st?

Post-collection issues We will probably need to groupthe datainto age bands. We will use descriptive statistics such as frequencies.

The data will be tabulated in order to condenseand summarisethe information. We will probably draw agraph orchart based onraw numbers or

percentages.

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Comparative questions

Trend questions

Relationship questions

Example Do young people perform as well as older students?

Purpose To find out whether one factor (e.g. performance) seems to be linked to another factor (e.g. age).

It is important to note that, even when we can show that a link exists, that does not necessarily mean that there is a causal relationship between the two factors. Source Additional institutional data will be required on student performance.This might be

whether the student dropped out or not (a nominal scalevariable), what position in the class they came (an ordinal scalevariable) or what exam score they gained (an interval scalevariable). (Age is a ratio scalevariable.)

Pre-collection issues Do we need to control forother variablessuch as previous educational qualifications which may disguise the true relationship?

Post-collection issues Depending upon the type of performance variable used, an appropriate correlation or contingency tabletechnique would be selected.

Example Is the age distribution of our students changing over time?

Purpose To identify the long-term direction in which the data is moving, e.g. is the average age growing? declining?

Source Historical data will be needed to be extracted from the institutional database. Pre-collection issues Which should be our baseyear?

Post-collection issues This question requirestrend analysis.

Regressionor other curve-fittingtechniques will be used. Example How is this age distribution different from other institutions like us? Purpose To compare. e.g. in this case to compare a number of different student

populations.

Source Comparative datamay be gained from the government publications, from published research, from direct collaboration with other institutions both inside and outside one’s own country.

Pre-collection issues We will need to decide which institutions are appropriate for comparisons.

Post-collection issues Furtherdata manipulation may be necessary if, for example, other institutions have used different age bands.

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Explaining questions

Attitude questions

Predictive questions

Example What will happen if we become more attractive to young people?

Purpose What are the implications for the institution and its various subsystems if this happens? Source The institutional database.

Pre-collection issues None.

Post-collection issues Statistical modelling techniques can be used to predict effects on course numbers in different areas, drop-out rates, the demand on financial assistance funds, etc Example Do young people like studying our courses?

Purpose To find out how people feel about a particular issue.

Source Acourse feedback survey across the age range could be carried out as described in the previous question.

Pre-collection issues What is meant by ‘like’? We need to operationalizeour terms so that people can answer in numerical terms.

Post-collection issues Crosstabulationsand correlationaltechniques could be used to see whether there is a relationship between age and attitudes to some or all of the courses. Example Why do so many young people drop out of our courses?

Purpose To look for the reasons for an effect that we have already observed, e.g. differential drop-out rates.

Source A postal surveyusing a self-completion questionnairemight be made of young students who had dropped out, asking them for their reasons.

Pre-collection issues A random or stratified sampleof young students who had dropped out would be drawn from the institutional database.

A control groupof older students who had dropped out might also be used for comparison purposes.

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Summary

In this unit, you have explored some of the types of question that can be answered using quantitative techniques.

The rest of the module

This is the end of the introductory part of the module.The rest of the module has been structured in a particular way that we hope will improve your learning and retain your interest.

It is in three broad sections:

1 The first is about you carrying out secondary analysis of external data. 2 The second chiefly concerns institutional data that is based on information

collected on a regular basis; the third is where you collect data for a specific research purpose.

3 The third and last section will help you to plan your own study in which you wish to collect quantitative data.

We introduce particular research methods and statistical techniques as we go along whenever they become relevant.

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Unit overview

This unit is designed to introduce you to: 䉴 the basics of using Excel

䉴 some simple methods of analysing student data using Excel.

Learning outcomes

When you have worked through this unit, you should be able to: 1 Calculate percentages with and without Excel.

2 Calculate totals using Excel.

3 Copy formulae in Excelby dragging. 4 Copy and paste values in Excel. 5 Copy and paste formats in Excel. 6 Sort data in Excel.

7 Apply these methods to a case study on enrolments and exam passes.

Introduction

While most books on research methods concentrate on how to collect and analyse your own data, a large part of your work is likely to involve dealing with data that has been collected and compiled by others. In this section we are going to look at ways to interpret and further analyse such information. We begin with a basic example for you to work through. Please remember that the actual numbers are not important here. It is more important to concentrate on the thought processes involved and the techniques that you will be able to use elsewhere.

The data

One of our pen portrait learners in Module 1and the User Guide was Abida Quuyaam, a researcher at Auranzeb Open University (AOU) She is

particularly interested in improving access for women and so she is pleased when the Vice-chancellor asks for a short report on how well AOU is doing

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in this area compared to the rest of higher education.Abidabegins by consulting a table of figures published by the Ministry of Education for 2003 that covers the country’s five universities, four teacher training colleges and two open universities.This is shown below as Table 4.

Table 4 Students registered on higher education courses by institution and gender (2003)

Raw numbers

We will start by looking at the raw numbers– that means numbers that have not been processed in any way.

Table 4 contains raw numbers.This is signified by the letter nat the top of each column.

Sometimes numbers will contain commas to indicate thousands, millions, etc. For example, 2357854 could be written as 2,357,854.

If numbers are very big they may be given in other units such as thousands. If the column heading had been n‘000s, the first number would have been written as 2.387.

How many women were registered at AOU in 2003?

The feedback to this activity is at the end of the unit 䉴 Registered students

Men (n) Women (n)

University 1 2387 1432

Teacher Training College 1 2231 2487

AOU 2879 3556

BOU 1236 984

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Percentages

I think you will agree that Table 4 is a very compact way of displaying a lot of data. It tells you about the gender of thousands of students spread across eleven institutions. As the activity showed, it is easy to look up certain kinds of data. However, it is difficult to get an overall picture of what is really going on by just looking at the figures. We are going to make things much easier by using percentages.

Percentages are probably the most used statistical technique in institutional and practitioner research, so you must feel comfortable with them. Percentages enable us to make comparisons between groups.

Let’s take the example of a group of 25 people, 5 of whom are women and 20 of whom are men (Table 5).The second column of the table shows us the raw numbers. In the third column, we have expressed the raw numbers as fractions of the total, e.g. there are 5 women out of 25 people.

However, the third column still expresses the data in terms of the raw numbers. What we need is a way of showing the proportion of women in a standard way so that we can make comparisons with other groups. We do this using percentages.

Fractions remain the same if you multiply the top figure and the bottom figure by the same number or divide the top and bottom figure by the same number. In the fourth column, we have multiplied both the top and the bottom number by four.This figure (20/100) is called 20 per cent (or 20%). 20% tells us the proportion of the group that is women, and it tells us in a way that gets gets us away from the raw data. It says that 20 in every 100 are women.

Percentages

Why are percentages so good? Because they allow us to make instant comparisons. Imagine that you had two groups of people. In the first there were 18 women out of a total of 72. In the second there were 123 women out of 492. Which group contains a higher proportion of women?

With percentages you can say that the proportion is the same in each group, i.e. 25%.

Table 5 Expressing a group as percentages

Group n Fraction of total Fraction of 100

Women 5 5 out of 25 20 out of 100 = 20%

Men 20 20 out of 25 75 out of 100 = 75%

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Formula for percentages

A general formula to calculate a percentage is as follows.

Percentage=

冤

ᎏNu

T m ota b l er nu in m g b r e o r up

ᎏ

冥

⫻₁₀₀

So, for our example, we have:

Percentage of women =

冤

ᎏ 2 5

5

ᎏ

冥

⫻_{100 = 20%}

We are now going to use the data from Table 4 in a series of activities that will simulate the sorts of processes that Abidamight go through when compiling her report on the situation of women at AOU.

Excel for beginners: Calculating totals

In this section you will work through a number of activities, that will introduce you to some of the basic techniques for using Excel.

Creating a copy of a worksheet

1 Open the ExcelWorkbook Women– see the Resources File. It should open on Sheet 1

which contains Table 4. If it does not, just click the Sheet 1tab at the bottom of the screen.

2 Copy and paste Table 4 into Sheet 2 by following these instructions:

䉴 highlight the whole of Sheet 1by clicking on the cell in the top left hand corner – that is the cell above 1 and to the left of A

䉴 from the menu at the top of the screen select Edit ➞_Copy_{. (i.e. First select}_Edit_and

then select Copy.)

䉴 click on Sheet 2at the bottom to open it

䉴 click on cell A1

䉴 from the menu select Edit ➞_Paste_.

You will now have a copy of the data on Sheet 2. If you corrupt it in any way you can always go back to Sheet 1and copy and paste another copy.

There is no feedback to this activity

Checking screen settings

You will need to check your Excelscreen settings in order to make sure that your screen is displaying both the Formula bar and the Standard toolbar.

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Formula bar

Select View from the menu items at the top of the screen. When the options drop down there should be a tick by the side of Formula bar. If there is no tick, scroll down to

Formula barthen release the mouse button – this will add a tick.

Standard toolbar

Select View from the menu items at the top of the screen. When the options drop down, scroll to Toolbars. This will produce another menu where there should be a tick by the side of both Standardand Formatting. If not, drag to each in turn and release the mouse button.

Adding numbers in rows and columns

To start, we are going to calculate the number of students at each institution.

Adding two columns of numbers

In this activity you will insert a formula to calculate the total number of students at each of the institutions in Table 4. The process is in two steps.

Step 1: Create the formula in one cell

1 Make sure that you are in Sheet 2, where you have your working copy of Sheet 1. 2 Click on cell D6 and type in the formula = B6 + C6. (This will appear in the Formula

barabove the worksheet as you type.)

3 Click the green arrow to the left of the Formula bar. Square D6 should now contain 10804. (W1) (Check your answers as you go against those on the Model worksheet. These answers are numbered W1, W2, etc.)

Step 2: Copy the formula to all the other cells

4 Click and drag from D6 to D17 so as to highlight the cells to be filled. (W1a). 5 Then from the menu bar use Edit➞ _Fill➞_Down_{. This will calculate the total for all}

the institutions. (W2)

Writing your own formulae and using the sigma symbol

Writing your own formulae

There are quicker ways to add cells together. You can write your own formula like = SUM (C3:C45) that will produce a total for the array of cells specified.

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The sigma symbol

Or, you can use the sigma symbol (pronounced sigma), which appears as Σ in the Standard toolbar. In our example if you had clicked on cell D6 then clicked on the sigma symbol, Excel would have guessed and entered = SUM (B6:C6). (If it guesses wrong, you just alter it manually.) Clicking a second time and Excelwill complete the sum.

You can copy a formula in a given cell to a range of other cells as follows:

䉴 grab the cell containing the formula by putting the cursor over the bottom right-hand corner of the cell

䉴 a square with arrow heads in opposite corners will appear

䉴 drag the square over the cells that you wish to fill with the same formula.

Calculating percentages

We are now going to calculate the percentage of women at each institution.

Calculating a percentage

We will start by calculating the percentage of women at University 1. 1 Click on cell E6 and type in = C6/D6*100. Press Enter. (W2a and W3) 2 You should see the result (19.72 …) in cell E6.

/ and *

You should have recognised the formula that you typed in from our earlier explanation of percentages

In Excel:

/ means divide * means multiply.

Copying your percentage formula

Copying the formula

1 Enter the results for all of the other institutions by using Edit➞_Fill➞_Down_{as you}

did before.

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2 You now have the percentages but you probably have some very long figures in the cells, since Exceldoes not know the degree of precision that you wish to see displayed. (W3a and W4)

Specifying the degree of precision

3 We will display these percentages as whole numbers.

4 Highlight cells E6 to E17 (W4a) then Format➞_Cells ➞_Number➞_{Decimal places} ➞_Zero_{. This will simplify the column to whole numbers. (W5)}

How Excel stores and displays numbers

Excelstores number with up to 30 decimal places. Even when you display a number to zero decimal places, that number is still stored in its original form.

Conclusion

As a result of this analysis Abidais now in a position to offer preliminary findings to her Vice-chancellor. In a short note, she might say something like this:

‘Slightly over a half (55%) of AOU students are women. This compares favourably with the overall figure of 40% for higher education generally in our country.’

What more could she tell the Vice-chancellor? Vice-chancellors always like to know how well they are doing as an individual institution. ‘League tables’ are now a very common method of ranking institutions according to a variety of ‘performance indicators’. So, we will now try to make some comparisons between the various institutions.

Pasting a copy of a block of cells

When you copy a block of cells, you can choose which characteristics you wish to be copied, e.g. the values in the cells, the formulae, the formatting of the cells.

In this activity you are going to copy rows 4 to 16 to a position lower down on your worksheet. In doing this, you will copy the values and the format, but no other cell characteristics.

Your version of Excelmay allow you to do this in one step. The instructions below are for the two-step process.

Step 1: Copy rows 4-16 with their values

1 Highlight the wholeof rows 4 through 16 by clicking and dragging from the 4 of Row 4 to the 16 of Row 16. (W5a)

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2 Click on cell A20 – this is where you are going to paste the rows. 3 Click on Edit ➞_{Paste special}_{and select}_Values.

4 ClickOK.

5 Repeat steps 2-4, but this time select Formats.

You now have a copy of rows 4-16, but without their formulae.

Paste special

This the first time that we have used Paste special. This is because if we had used Paste here it would have pasted in the formulae that were in the copied cells, and the specified cells would have changed and hence the results.

Try Copy and Paste in a spare part of the worksheet to the right and you will see the difference.

Here we just want the values (the results produced by the formulae) and the formats from the original cells.

Sorting a list of numbers

We now wish to re-order the list of institutions by their percentages of women students.The next activity shows you how to do this.

Sorting the institutions

Remove redundant data

1 First we will get rid of the raw data. Click/Hold on the centre of cell B20 then drag the cursor to cell D32 to highlight a rectangle of cells. (W6a)

2 Use Edit ➞_Delete_{to delete the data in the cells. At the same time, use the option}

Shift cells left. (W7)

Sort the remaining data

3 Now Click/Hold on the centre of A22 then drag the cursor to cell B32 to highlight a rectangle of cells. (W7a)

4 Now use Data➞ _Sort_{to arrange the institutions in order by % women students. You}

can choose ascending or descending order. (W8)

By examining the sorted data you can see that AOU was the fourth most successful institution in attracting women and it outperformed all of the other universities.

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Sorting by raw data

In this activity you will again sort the institutions, but this time by number of women rather than by the percentage of women.

1 Sort the data using cells C6 to C16.

2 What do you conclude from the new rank ordering?

More practice with percentages

Since it is important to be very comfortable with percentages, I have added an extra activity here to give you more practice.

More percentages

The Vice-chancellor is fairly happy with AOU’s numbers of women students, but she wants three more figures. She wants to know the percentage of women students among:

1 All conventional university students (University 1-5).

2 All teacher training college students (Teacher Training Colleges 1-4). 3 All open university students (AOU and BOU).

Calculate these, by hand, with a calculator or with Excel.

We are now going to move on to another example using a different set of data.You may remember from Module 1that one of our pen-portraits was

Agathawho has been asked by the Minister of Education of the Republic of Nuime to look at the case for using ODL methods to provide ‘open schooling’ rather than traditional classrooms in order to achieve universal schooling.The Minister wants to know the extent of the needs and whether open schooling would be an effective and cost-effective way of addressing this issue.

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Table 6 Students in ten open schools on the basic maths course M101 (1998-2002)

Reading data from tables

This activity is just to help you to check that you can read data accurately from tables. Use Table 6 to answer these two questions:

1 How many registrations were there on M101 at open school F in 2001? 2 How many passes on M101 were there in total in 1999?

The feedback to this activity is at the end of the unit 䉴 Passes

Open school 1998 1999 2000 2001 2002 Total

A 174 183 194 198 208 956

B 276 302 321 324 335 1558

C 54 47 62 59 74 296

D 289 294 311 325 251 1470

E 111 128 136 137 140 652

F 213 224 237 242 256 1172

G 376 376 392 423 431 1998

H 243 303 322 325 398 1591

I 233 225 206 200 190 1054

J 154 162 175 173 177 840

Total 2123 2244 2355 2405 2460 11587

Registrations

Open school 1998 1999 2000 2001 2002 Total

A 286 272 298 324 355 1535

B 354 322 377 381 385 1818

C 122 140 123 124 125 635

D 435 432 422 411 276 1976

E 143 156 167 169 170 805

F 298 304 325 329 332 1588

G 467 488 476 506 523 2460

H 432 411 439 409 485 2176

I 306 230 210 208 195 1149

J 192 222 216 218 220 1068

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The open schools case study

Exploring the open school data

Firstly, I want you to put yourself in the position of Agatha. Imagine that as part of her research she has been given Table 6 and has been asked to summarise the results for the Minister. He wants to know whether the M101 course has been a success or not.

Well, she could of course simply say that almost twelve thousand pupils have passed M101 in the last five years through the open school programme.That is a summary and in some circumstances this might be sufficient. However, I don’t think that the Minister would be satisfied with this ‘summary’. A thorough practitioner researcher would do some further analysis, even if it were never actually used by the Minister. She would ask herself questions such as the following:

䉴 Are registrations going up over the five years? 䉴 Are pass rates going up?

䉴 Are some of the schools doing better than others? You will explore these questions in the next few activities.

Prepare the M101 workbook

In this activity you will prepare the M101workbook, ready for the following activities. 1 Open the Excelworkbook M101. It will open on Sheet 1, which contains Table 6. If it

does not open at Sheet 1, click the Sheet 1tab at the bottom of the worksheet.

2 Copy and paste the table into Sheet 2 into a new worksheet, Just as you did at the start of the activities on the Women worksheet.

Is important to copy the tables so that they are in exactly the same cells as they were in

Sheet 1. e.g. ‘a) Registrations’ should appear in cell A5. (If you put the data into different cells, then you will not be able to follow the instructions for the next few activities.) 3 Check your answers as you go against those on the model worksheet. These answers

are numbered M1, M2, etc.

4 The feedback to this activity is M1 on the model worksheet. 5 Do all of your own calculations on Sheet 2.

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Are registrations going up over the five years?

Firstly we are going to look at whether registrations on M101 have been going up or not.You can of course just look at the total figures in each of the five years in Row 18, but it is hard to get a mental image of what is happening with such big raw numbers.To make it easier we are going to indexthe numbers.

Indexing

Indexing is very similar to calculating percentages.

We are going to select 1998 as our ‘base’ year and give it the value of 100.

Then for each of the other four years we are going to calculate their totals as a percentage of the 1998 total.

We could have picked any year as our base year and we could have used some other figure than 100 as the starting point.

Indexing the registrations (base year 1998)

1 First of all, type in 100 in square B19 – we are going to use this as our base.

2 Then in cell C19, type the formula = (C18/$B$18*100) and click Enter. The result should be 98. (M1)

3 We now want to apply this formula to the other squares, so click and drag from C19 to F19 to highlight this block of cells. Then use Edit➞_Fill➞_Right_{. (M2 )}

Choosing a baseline year

It is clearly critical which year you pick as your baseline year.

Watch out for cases where people have picked a particular baseline point to exaggerate growth, or lack of it.

the $ sign

You can use the dollar signs ‘$’ to make a formula’s reference to a cell into a constant, i.e. to stop it changing as you drag a formula.

This means that in our example when we are filling right, the cells will change from C18 to C19 to C20 etc, but the divisor will be cell B18 in all cases.

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Are the number of passes going up?

We now want to explore what is happening to the number of passes.

Apply the same procedure that you used in the Indexing the registrationsactivity, but this time apply it to the number of passes.

What about pass rates?

Pass rates

A pass rate is just another percentage. It converts a given number of passes into a number of passes per 100 students.

The formula to calculate a pass rate is:

Pass rate =

冤

冥

⫻₁₀₀

So, for our example, we have: Percentage of women =

冤

ᎏ1

2 2 4

ᎏ

冥

⫻ _{100 = 20%}

For example:

Now you can practise some pass rates.

M101 pass rates

You are now going to calculate the overall pass rate for M101 in each of the years. 1 In cell B38 type the formula = B34/B18*100.

2 Now apply this formula to the other squares, so click and drag from B38 to F38 to highlight this block of cells. Then use Edit➞_Fill➞_Right_{. (M3)}

Are some of the schools doing better than others?

Now we are going to look at whether some open schools are doing better than others.

Firstly we must decide on what we mean by ‘doing better’. I can think of at least six ways in which we can interpret this question, even with such a basic set of data. In the activities that follow we are going to look at all six.

Number of passes

ᎏᎏᎏ

Number of registrations

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In real life somebody senior to you might have strong views as to which of these measures, if any, is the most appropriate to use.You, on the other hand, as a conscientious researcher, should be aware of the other possibilities.You should be prepared to make the other possibilities known and to argue or negotiate over their various merits.

Three of the proposed measures are related to size, or the number of registrations:

䉴 Total registrations over the five-year period (TotReg). Which school has offered the most opportunities for M101 students over the period? 䉴 Registrations in the most recent year (RecReg). Which school is currently

teaching the most M101 students?

䉴 Growth in registrations over the five-year period (GroReg). Which school seems to be growing fastest in terms of M101 registrations?

The other three refer to performance, or pass rates.

䉴 The average pass rate over the five-year period (AvePass). Which school has averaged the highest M101 pass rate over the period?

䉴 Pass rate in the most recent year (RecPass). Which school currently has the highest M101 pass rate?

䉴 Changes in pass rates over the five-year period (ChaPass). In which school is the M101 pass rate growing fastest?

Variable names

You will see that we have given abbreviated titles for each of the measures, e.g. AvePass. These are variable namesand they are a useful shorthand in Exceland packages such as

SPSS.

The variable names can be anything, but it is best to choose a name that will remind you what it stands for and that makes sense to the next person to use your data.

Some types of software do not like spaces in variable names, so it best to avoid them, or to use the ‘underscore’. For example, ‘Ave_Pass’.

Also the software may be ‘case sensitive’. If this is so, and you ask it to search for ‘ave_pass’ it will not find it. You might want to avoid this by consistently using upper OR lower case. (e.g. AVE_PASS or ave_pass).

Total registrations

We are now going to calculate the values of these six measures, beginning with total registrations.

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Calculating total registrations

Step 1: Delete the cells that you don’t need

1 Click and drag to highlight the whole of rows 7 to 17, then Edit➞_Copy_.

2 Click on cell A40, then Edit ➞_{Paste. (M4)}

3 Click and drag from B40 to F50 to highlight a block of cells (M4a). Then use Edit ➞

Delete and OKthe Shift cells leftoption. (M5)

Step 2: Sort the remaining cells

4 Highlight all the remaining cells by clicking and dragging from A40 to B50. (M5a) 5 Go to Data➞_Sort_{. In the}_Options_{box select}_{Sort by total}_{(rather than by open}

school) and select Descending. Ensure that My list has header rowis checked. Then click OK. (M6)

Step 3: Show the ranking

6 Type in the numbers 1 to 10 in cells C41 to C50. (M7) This has now given you a ‘rank ordering’. School G had the most registrations and is ranked 1, School H is next and ranked 2, etc.

7 Type in ‘TotReg’ in cell C40 to keep track of what these figures are.

Step 4: Put the data back into school order

8 For convenience we will now put them back in school order. Highlight the block from A40 to C50, and then go to Data➞_Sort_{. In the}_Options_{box select}_{Sort by open}

schooland Ascending. Ensure that My list has header row is checked. Click OK. (M8)

9 So we end up with Table 7 below. This shows, for example, that School H had the second highest number of M101 registrations over the period.

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Table 7 Open School M101 total registrations 1998-2002 with rank ordering

Typing in numerical sequences

There is a useful way of getting Excelto type in numerical sequences for you.

For example, when you needed to type in 1, 2, 3, …10 for the TotReg activity, you could have done as follows:

䉴 Type 1 in cell C41 and 2 in cell C42.

䉴 Select the two cells.

䉴 Drag from the bottom right corner of C42 to C50.

Excelwill complete the sequence.

The method will also work for sequences with fixed gaps e.g. 2, 4, 6, 8, 10 It will not work for letters.

Registrations in 2002

Next we need to do exactly the same but for registrations in 2002 (RecReg), rather than total registrations.

Registrations in 2002

Repeat the process that you used in the Calculating total registrations, but this time do it for Registrations in 2002, i.e. produce a table to show the schools in rank ordering by registrations in 2002.

The feedback to this activity is at the end of the unit 䉴 Excel note:

Open School Total Rank

A 1535 6

B 1818 4

C 635 10

D 1976 3

E 805 9

F 1588 5

G 2460 1

H 2176 2

I 1149 7

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Growth in registrations

The third measure concerns growth in registrations. We have already seen that there has been very little overall change but now we want to look at the change in individual schools.

Growth in registrations

Use Excelto produce indexed figures for each school similar to those produced in M2 for the total figures.

Interpreting the figures

The figures in the table (Table 11 in the feedback to Activity 17) are very interesting. We had already noted that the overallsituation had changed little, but there had been a lot of fluctuation in certain individual schools. You might be able to look at Table 11 and see the patterns. However, most people prefer pictures to numbers, so we are going to construct a graph.The following activity will take you through the steps.

Constructing a graph of growth in registrations

1 First, we need to tell Excelthat the year numbers (1998, 1999, …) are to be treated as labels and not as numbers. To do this, put an apostrophe before each year. So 1998 becomes ‘1998, 1999 becomes ‘1999, etc.

2 Highlight the whole block of cells from ‘Open School’ to ‘220’, (cells A7 to F17). 3 Click Insert ➞_Chart_.

Excelwill now take you through the stages of Chart wizard. These are straightforward but the details may vary between different versions of Excel.

4 Under Chart type select Line. Select the first of theChart sub-types. Click Next. 5 Under Chart source data select Series in Rows. Click Next.

6 Under Chart options: Chart title: type in Open School M101 registrations 1998-2002 (Base = 1998 = 100).

7 Under Category (X) axis type in Year. Click Next.

8 Under Chart location click on As new sheetand type in a name for your chart. Click

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[image:44.595.72.403.171.369.2]

You should now have produced a graph like Figure 6. (If not see M101 and Figure 6 that was produced from it and saved as a new worksheet.) The figure is a bit complicated because it has data for five years for ten schools. However, look at it for a few moments and see what patterns emerge.

Figure 6 Open school M101 registrations 1998-2002 (Base: 1998 = 100)

(Note: a larger version of this chart appears in Workbook M101, Figure 6.)

Commentary

While we have seen little change in the overallregistration figures, no individual school seems to have behaved in this way. School C comes the closest but it actually grew in 1999 when the total went down.

Eight out of ten schools show a reasonable growth in registrations over the period.

Schools D and E show a marked decline in registrations. With D the major decline took place in 2002 but for E it was in 1999.

Growth patterns using a single figure

Now we want to summarise these growth patterns using just a single figure. Here we are going to use the 2002 index figure GroReg as our measure. So for open school A the value will be 124 (the 2002 figure is 24% greater than the 1998 figure) and for open school D it will be 63 (the 2002 figure is 63% of the 1998 figure).

0 20 40 60 80 100 120 140

1998 1999 2000 2001 2002

Year

A

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Ranking by growth

Sort and rank the ten schools in terms of their growth (GroReg).

Pass rates

We turn now to pass rates and we begin with the school’s average pass rate for M101(AvePass).This is defined as the total number of passes divided by the total number of registrations, multiplied by 100.

Pass rates

You should be able to calculate the average pass rate (AvePass) for each school as we did for average registration numbers and then rank them (if not see M13 a-c).

Recent pass rates

Now do the same for the most recent pass rates (RecPass).

The sixth and last measure concerns changes in pass rates. We have already seen that there has been a year-on-year improvement in the overall pass rate for M101, but now we consider individual schools.

Pass rates

1 Calculate indexed pass rates as we did for registration numbers.

2 Produce a line graph similar to Figure 6, but this time for indexed pass rates. 3 Study the new graph and prepare a short commentary on it.

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Changes in pass rates using a single figure

We