NUMBERS, HYPOTHESES & CONCLUSIONS
A COURSE IN STATISTICS FOR THE SOCIAL SCIENCES
Third edition
Colin Tredoux & Kevin Durrheim
(Editors)
, Numbers, Hypotheses
& Conclusions
A course in statistics for the
social sciences
Third edition
Editors
Colin Tredoux (University of Cape Town)
Kevin Durrheim (University of KwaZulu-Natal)
NumHyp&Con_3e_Book.indb 1 2018/07/12 2:43:39 PM
, Numbers, Hypotheses & Conclusions — A course in statistics for the social sciences
First published 2002
Second edition 2013
Third edition 2019
Juta and Company (Pty) Ltd
First floor, Sunclare building, 21 Dreyer street, Claremont 7708
PO Box 14373, Lansdowne 7779, Cape Town, South Africa
www.juta.co.za
© 2019 Juta and Company (Pty) Ltd
ISBN 978 1 48512 544 0 (Print)
ISBN 978 1 48512 984 4 (WebPDF)
All rights reserved. No part of this publication may be reproduced or transmitted in any
form or by any means, electronic or mechanical, including photocopying, recording, or
any information storage or retrieval system, without prior permission in writing from
the publisher. Subject to any applicable licensing terms and conditions in the case of
electronically supplied publications, a person may engage in fair dealing with a copy of
this publication for his or her personal or private use, or his or her research or private
study. See section 12(1)(a) of the Copyright Act 98 of 1978.
Project manager: Edith Viljoen and Carlyn Bartlett-Cronje
Editor: Jyoti Singh
Proofreader: Jyoti Singh
Cover designer: Zach Viljoen
Typesetter: Anton Stark
Indexer: Michel Cozien
Typeset in Minion Pro 10.5pt
The author and the publisher believe on the strength of due diligence exercised that
this work does not contain any material that is the subject of copyright held by another
person. In the alternative, they believe that any protected pre-existing material that
may be comprised in it has been used with appropriate authority or has been used in
circumstances that make such use permissible under the law.
NumHyp&Con_Prelims.indd 2 2018/07/13 9:28:51 AM
, Table of contents
Section 1 Statistics
Tutorial 1: Numbers, variables, and measurement.................................................... 2
The advantages of quantitative methods................................................................................ 3
Functions of quantification...................................................................................................... 7
Some basic concepts.................................................................................................................. 9
Problems with the quantitative approach............................................................................... 14
Summary.................................................................................................................................... 14
Exercises..................................................................................................................................... 15
Tutorial 2: Displaying data.......................................................................................... 16
Bar graphs................................................................................................................................... 17
Histograms................................................................................................................................. 24
Cumulative frequency diagrams............................................................................................. 29
Line graphs................................................................................................................................. 32
Basic rules for creating graphs................................................................................................. 40
Worked example........................................................................................................................ 41
Summary.................................................................................................................................... 43
Exercises..................................................................................................................................... 44
Further reading.......................................................................................................................... 46
Tutorial 3: Central tendency and variation................................................................ 47
Measures of central tendency.................................................................................................. 48
Measures of variability.............................................................................................................. 55
Estimating population parameters from sample data.......................................................... 64
Worked example........................................................................................................................ 69
Summary.................................................................................................................................... 73
Exercises..................................................................................................................................... 74
Tutorial 4: Probability and theoretical distributions................................................. 76
Probability as frequency........................................................................................................... 76
Probability and games of chance............................................................................................. 77
The multiplication and addition rules of probability........................................................... 79
Probabilities of multiple outcomes.......................................................................................... 82
Worked example........................................................................................................................ 90
Summary.................................................................................................................................... 93
Exercises..................................................................................................................................... 93
Tutorial 5: The standard normal distribution............................................................ 95
The standard normal distribution........................................................................................... 96
Two worlds: the statistical world and the real world............................................................ 101
Worked example........................................................................................................................ 106
Summary.................................................................................................................................... 108
Exercises..................................................................................................................................... 109
NumHyp&Con_3e_Book.indb 3 2018/07/12 2:43:39 PM
A COURSE IN STATISTICS FOR THE SOCIAL SCIENCES
Third edition
Colin Tredoux & Kevin Durrheim
(Editors)
, Numbers, Hypotheses
& Conclusions
A course in statistics for the
social sciences
Third edition
Editors
Colin Tredoux (University of Cape Town)
Kevin Durrheim (University of KwaZulu-Natal)
NumHyp&Con_3e_Book.indb 1 2018/07/12 2:43:39 PM
, Numbers, Hypotheses & Conclusions — A course in statistics for the social sciences
First published 2002
Second edition 2013
Third edition 2019
Juta and Company (Pty) Ltd
First floor, Sunclare building, 21 Dreyer street, Claremont 7708
PO Box 14373, Lansdowne 7779, Cape Town, South Africa
www.juta.co.za
© 2019 Juta and Company (Pty) Ltd
ISBN 978 1 48512 544 0 (Print)
ISBN 978 1 48512 984 4 (WebPDF)
All rights reserved. No part of this publication may be reproduced or transmitted in any
form or by any means, electronic or mechanical, including photocopying, recording, or
any information storage or retrieval system, without prior permission in writing from
the publisher. Subject to any applicable licensing terms and conditions in the case of
electronically supplied publications, a person may engage in fair dealing with a copy of
this publication for his or her personal or private use, or his or her research or private
study. See section 12(1)(a) of the Copyright Act 98 of 1978.
Project manager: Edith Viljoen and Carlyn Bartlett-Cronje
Editor: Jyoti Singh
Proofreader: Jyoti Singh
Cover designer: Zach Viljoen
Typesetter: Anton Stark
Indexer: Michel Cozien
Typeset in Minion Pro 10.5pt
The author and the publisher believe on the strength of due diligence exercised that
this work does not contain any material that is the subject of copyright held by another
person. In the alternative, they believe that any protected pre-existing material that
may be comprised in it has been used with appropriate authority or has been used in
circumstances that make such use permissible under the law.
NumHyp&Con_Prelims.indd 2 2018/07/13 9:28:51 AM
, Table of contents
Section 1 Statistics
Tutorial 1: Numbers, variables, and measurement.................................................... 2
The advantages of quantitative methods................................................................................ 3
Functions of quantification...................................................................................................... 7
Some basic concepts.................................................................................................................. 9
Problems with the quantitative approach............................................................................... 14
Summary.................................................................................................................................... 14
Exercises..................................................................................................................................... 15
Tutorial 2: Displaying data.......................................................................................... 16
Bar graphs................................................................................................................................... 17
Histograms................................................................................................................................. 24
Cumulative frequency diagrams............................................................................................. 29
Line graphs................................................................................................................................. 32
Basic rules for creating graphs................................................................................................. 40
Worked example........................................................................................................................ 41
Summary.................................................................................................................................... 43
Exercises..................................................................................................................................... 44
Further reading.......................................................................................................................... 46
Tutorial 3: Central tendency and variation................................................................ 47
Measures of central tendency.................................................................................................. 48
Measures of variability.............................................................................................................. 55
Estimating population parameters from sample data.......................................................... 64
Worked example........................................................................................................................ 69
Summary.................................................................................................................................... 73
Exercises..................................................................................................................................... 74
Tutorial 4: Probability and theoretical distributions................................................. 76
Probability as frequency........................................................................................................... 76
Probability and games of chance............................................................................................. 77
The multiplication and addition rules of probability........................................................... 79
Probabilities of multiple outcomes.......................................................................................... 82
Worked example........................................................................................................................ 90
Summary.................................................................................................................................... 93
Exercises..................................................................................................................................... 93
Tutorial 5: The standard normal distribution............................................................ 95
The standard normal distribution........................................................................................... 96
Two worlds: the statistical world and the real world............................................................ 101
Worked example........................................................................................................................ 106
Summary.................................................................................................................................... 108
Exercises..................................................................................................................................... 109
NumHyp&Con_3e_Book.indb 3 2018/07/12 2:43:39 PM
