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MEASURING ASSOCIATION 531 found and, as we shall see, most coefficients of correlation in social research are around +0.50 or less. The correlation coefficient may be seen then as an indication of the predictability of one variable given the other: it is an indication of covariation. The relationship between two variables can be examined visually by plotting the paired measurements on graph paper with each pair of observations being represented by a point. The resulting arrangement of points is known as a scatterplot and enables us to assess graphically the degree of relationship between the characteristics being measured. Box 24.25 gives some examples of scatterplots in the field of educational research (see http://www.routledge.com/textbooks/ 9780415368780 – Chapter 24, file 24.14.ppt). While correlations are widely used in research, and they are straightforward to calculate and to interpret, the researcher must be aware of four caveats in undertaking correlational analysis: Do not assume that correlations imply causal relationships (i.e. simply because having large hands appears to correlate with having large feet does not imply that having large hands causes one to have large feet). There is a need to be alert to a Type I error – not supporting the null hypothesis when it is in fact true. There is a need to be alert to a Type II error – supporting the null hypothesis when it is in fact not true. Statistical significance must be accompanied by an indication of effect size. In SPSS a typical printout of a correlation coefficient is given in Box 24.26. In this fictitious example using 1,000 cases there are four points to note: The cells of data to the right of the cells containing the figure 1 are the same as the cells to the left of the cells containing the figure 1, i.e. there is a mirror image, and, if very many more variables were being correlated then, in fact, one would have to decide whether to look at only the variables to the right of the cell with the figure 1 (the perfect correlation, since it is one variable being correlated with itself), or to look at the cells to the left of the figure 1. In each cell where one variable is being correlated with a different variable there are three figures: the top figure gives the correlation coefficient, the middle figure gives the significance level, and the lowest figure gives the sample size. SPSS marks with an asterisk those correlations which are statistically significant. All of the correlations are positive, since there are no negative coefficients given. What these tables give us is the magnitude of the correlation (the coefficient), the direction of the correlation (positive and negative), and the significance level. The correlation coefficient can be taken as the effect size. The significance level (as mentioned earlier) is calculated automatically by SPSS, based on the coefficient and the sample size: the greater the sample size, the lower the coefficient of correlation has to be in order to be statistically significant, and, by contrast, the smaller the sample size, the greater the coefficient of correlation has to be in order to be statistically significant. In reporting correlations one has to report the test used, the coefficient, the direction of the correlation (positive or negative), and the significance level (if considered appropriate). For example, one could write: Using the Pearson-product moment correlation, a statistically significant correlation was found between students’ attendance at school and their examination performance (r = 0.87, ρ = 0.035). Those students who attended school the most tended to have the best examination performance, and those who attended the least tended to have the lowest examination performance. Alternatively, there may be occasions when it is important to report when a correlation has not been found, for example: There was no statistically significant correlation found between the amount of time spent on homework and examination performance (r = 0.37, ρ = 0.43). Chapter 24
532 QUANTITATIVE DATA ANALYSIS Box 24.25 Correlation scatterplots Academic achievement Socio-economic status r 0.90 r 0.30 IQ IQ Weight r 00 IQ Absenteeism r 0.30 Visual acuity r 0.90 IQ IQ Source:Tuckman1972 In both of these examples of reporting, exact significance levels have been given, assuming that SPSS has calculated these. An alternative way of reporting the significance levels (as appropriate) are: ρ
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Research Methods in Education This
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First published 2007 by Routledge 2
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Contents List of boxes xiii Acknowl
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CONTENTS ix Searching for research
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CONTENTS xi Part 5 Data analysis 22
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xiv BOXES 13.1 Independent and depe
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xvi BOXES 24.54 Frequencies and per
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xviii ACKNOWLEDGEMENTS Springer,for
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2 INTRODUCTION Package for the Soci
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1 The nature of inquiry - Setting t
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TWO CONCEPTIONS OF SOCIAL REALITY 7
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POSITIVISM 9 Box 1.1 The subjective
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THE ASSUMPTIONS AND NATURE OF SCIEN
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THE ASSUMPTIONS AND NATURE OF SCIEN
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THE SCIENTIFIC METHOD 15 an educate
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CRITICISMS OF POSITIVISM AND THE SC
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ALTERNATIVES TO POSITIVISTIC SOCIAL
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A QUESTION OF TERMINOLOGY: THE NORM
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PHENOMENOLOGY, ETHNOMETHODOLOGY AND
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CRITICISMS OF THE NATURALISTIC AND
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CRITICAL THEORY AND CRITICAL EDUCAT
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CRITICISMS OF APPROACHES FROM CRITI
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CRITICAL THEORY AND CURRICULUM RESE
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THE EMERGING PARADIGM OF COMPLEXITY
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FEMINIST RESEARCH 35 deconstructin
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FEMINIST RESEARCH 37 respecting d
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FEMINIST RESEARCH 39 Research must
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RESEARCH AND EVALUATION 41 particul
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RESEARCH AND EVALUATION 43 The age
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RESEARCH AND EVALUATION 45 to exten
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METHODS AND METHODOLOGY 47 too easi
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Part Two Planning educational resea
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52 THE ETHICS OF EDUCATIONAL AND SO
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3 Planning educational research Int
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80 PLANNING EDUCATIONAL RESEARCH t
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82 PLANNING EDUCATIONAL RESEARCH de
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84 PLANNING EDUCATIONAL RESEARCH Bo
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96 PLANNING EDUCATIONAL RESEARCH Or
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98 PLANNING EDUCATIONAL RESEARCH Pa
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4 Sampling Introduction The quality
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102 SAMPLING sample of 200 might be
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104 SAMPLING Box 4.1 Sample size, c
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106 SAMPLING would be insufficient
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108 SAMPLING The formula assumes th
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110 SAMPLING school governors, scho
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112 SAMPLING terms of sex, a random
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114 SAMPLING the required sample si
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116 SAMPLING Snowball sampling In s
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118 SAMPLING the kind of sample (d
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120 SENSITIVE EDUCATIONAL RESEARCH
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134 VALIDITY AND RELIABILITY It is
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136 VALIDITY AND RELIABILITY using
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138 VALIDITY AND RELIABILITY includ
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140 VALIDITY AND RELIABILITY leadin
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142 VALIDITY AND RELIABILITY social
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144 VALIDITY AND RELIABILITY this i
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146 VALIDITY AND RELIABILITY prese
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148 VALIDITY AND RELIABILITY by ass
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150 VALIDITY AND RELIABILITY Validi
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152 VALIDITY AND RELIABILITY typica
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154 VALIDITY AND RELIABILITY people
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156 VALIDITY AND RELIABILITY
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158 VALIDITY AND RELIABILITY sensit
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160 VALIDITY AND RELIABILITY certif
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162 VALIDITY AND RELIABILITY how m
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164 VALIDITY AND RELIABILITY operat
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7 Naturalistic and ethnographic res
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ELEMENTS OF NATURALISTIC INQUIRY 16
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PLANNING NATURALISTIC RESEARCH 171
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CRITICAL ETHNOGRAPHY 187 Relatio
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SOME PROBLEMS WITH ETHNOGRAPHIC AND
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8 Historical and documentary resear
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DATA COLLECTION 193 One can see fro
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WRITING THE RESEARCH REPORT 195 Ext
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THE USE OF QUANTITATIVE METHODS 197
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LIFE HISTORIES 199 Box 8.2 Atypolog
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DOCUMENTARY RESEARCH 201 Documentar
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DOCUMENTARY RESEARCH 203 What are
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9 Surveys, longitudinal, cross-sect
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SOME PRELIMINARY CONSIDERATIONS 207
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PLANNING A SURVEY 209 structured or
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LONGITUDINAL, CROSS-SECTIONAL AND T
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LONGITUDINAL, CROSS-SECTIONAL AND T
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STRENGTHS AND WEAKNESSES OF LONGITU
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STRENGTHS AND WEAKNESSES OF LONGITU
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POSTAL, INTERVIEW AND TELEPHONE SUR
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EVENT HISTORY ANALYSIS 225 may be p
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INTERNET-BASED SURVEYS 227 packages
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INTERNET-BASED SURVEYS 229 instruc
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INTERNET-BASED SURVEYS 231 Box 10.1
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INTERNET-BASED SURVEYS 237 Witte et
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INTERNET-BASED EXPERIMENTS 239 requ
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INTERNET-BASED INTERVIEWS 241 ‘ne
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SEARCHING FOR RESEARCH MATERIALS ON
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COMPUTER SIMULATIONS 245 autho
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COMPUTER SIMULATIONS 247 computer s
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COMPUTER SIMULATIONS 249 On the oth
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GEOGRAPHICAL INFORMATION SYSTEMS 25
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11 Case studies What is a case stud
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WHAT IS A CASE STUDY 255 (providing
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WHAT IS A CASE STUDY 257 argue that
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EXAMPLES OF KINDS OF CASE STUDY 259
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PLANNING A CASE STUDY 261 accounts
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CONCLUSION 263 In the narrativ
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CO-RELATIONAL AND CRITERION GROUPS
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CHARACTERISTICS OF EX POST FACTO RE
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DESIGNING AN EX POST FACTO INVESTIG
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PROCEDURES IN EX POST FACTO RESEARC
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INTRODUCTION 273 Box 13.1 Independe
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TRUE EXPERIMENTAL DESIGNS 275 motor
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TRUE EXPERIMENTAL DESIGNS 277 2 Sub
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TRUE EXPERIMENTAL DESIGNS 279 textb
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TRUE EXPERIMENTAL DESIGNS 281 Facto
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A QUASI-EXPERIMENTAL DESIGN: THE NO
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PROCEDURES IN CONDUCTING EXPERIMENT
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EXAMPLES FROM EDUCATIONAL RESEARCH
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EVIDENCE-BASED EDUCATIONAL RESEARCH
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14 Action research Introduction Act
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PRINCIPLES AND CHARACTERISTICS OF A
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PRINCIPLES AND CHARACTERISTICS OF A
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ACTION RESEARCH AS CRITICAL PRAXIS
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PROCEDURES FOR ACTION RESEARCH 305
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SOME PRACTICAL AND THEORETICAL MATT
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CONCLUSION 313 3 Actionresearchreso
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15 Questionnaires Introduction The
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APPROACHING THE PLANNING OF A QUEST
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TYPES OF QUESTIONNAIRE ITEMS 321 If
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TYPES OF QUESTIONNAIRE ITEMS 323 de
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TYPES OF QUESTIONNAIRE ITEMS 325 Ra
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TYPES OF QUESTIONNAIRE ITEMS 327 Ve
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TYPES OF QUESTIONNAIRE ITEMS 329 I
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TYPES OF QUESTIONNAIRE ITEMS 331 Fu
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ASKING SENSITIVE QUESTIONS 333 and
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AVOIDING PITFALLS IN QUESTION WRITI
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QUESTIONNAIRES CONTAINING FEW VERBA
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COVERING LETTERS OR SHEETS AND FOLL
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PILOTING THE QUESTIONNAIRE 341 Nove
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PRACTICAL CONSIDERATIONS IN QUESTIO
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ADMINISTERING QUESTIONNAIRES 345 is
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PROCESSING QUESTIONNAIRE DATA 347 B
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16 Interviews Introduction The use
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PURPOSES OF THE INTERVIEW 351 appli
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TYPES OF INTERVIEW 353 closed quant
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TYPES OF INTERVIEW 355 One can clus
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PLANNING INTERVIEW-BASED RESEARCH P
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GROUP INTERVIEWING 373 an intro
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INTERVIEWING CHILDREN 375 taking pl
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THE NON-DIRECTIVE INTERVIEW AND THE
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TELEPHONE INTERVIEWING 379 By mean
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TELEPHONE INTERVIEWING 381 questi
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ETHICAL ISSUES IN INTERVIEWING 383
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PROCEDURES IN ELICITING, ANALYSING
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PROCEDURES IN ELICITING, ANALYSING
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DISCOURSE ANALYSIS 389 completeness
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ACCOUNT GATHERING IN EDUCATIONAL RE
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STRENGTHS OF THE ETHOGENIC APPROACH
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A NOTE ON STORIES 395 instruments t
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INTRODUCTION 397 the physical s
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STRUCTURED OBSERVATION 399 Box 18.1
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STRUCTURED OBSERVATION 401 Box 18.2
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STRUCTURED OBSERVATION 403 or event
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NATURALISTIC AND PARTICIPANT OBSERV
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NATURALISTIC AND PARTICIPANT OBSERV
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ETHICAL CONSIDERATIONS 409 Box 18.3
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SOME CAUTIONARY COMMENTS 411 ob
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CONCLUSION 413 the data mean. This
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NORM-REFERENCED, CRITERION-REFERENC
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COMMERCIALLY PRODUCED TESTS AND RES
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CONSTRUCTING A TEST 419 achieveme
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CONSTRUCTING A TEST 421 Select the
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CONSTRUCTING A TEST 423 where A = t
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CONSTRUCTING A TEST 425 true/fal
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CONSTRUCTING A TEST 427 short-answe
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CONSTRUCTING A TEST 429 demonstrate
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CONSTRUCTING A TEST 431 (e.g. to as
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COMPUTERIZED ADAPTIVE TESTING 433 H
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20 Personal constructs Introduction
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ALLOTTING ELEMENTS TO CONSTRUCTS 43
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PROCEDURES IN GRID ANALYSIS 439 inv
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PROCEDURES IN GRID ANALYSIS 441 Box
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SOME EXAMPLES OF THE USE OF REPERTO
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GRID TECHNIQUE AND AUDIO/VIDEO LESS
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FOCUSED GRIDS, NON-VERBAL GRIDS, EX
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INTRODUCTION 449 Box 21.1 Dimension
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ROLE-PLAYING VERSUS DECEPTION: THE
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THE USES OF ROLE-PLAYING 453 of
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ROLE-PLAYING IN AN EDUCATIONAL SETT
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EVALUATING ROLE-PLAYING AND OTHER S
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22 Approaches to qualitative data a
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TABULATING DATA 463 data set reprod
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TABULATING DATA 465 Box 22.4 Studen
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FIVE WAYS OF ORGANIZING AND PRESENT
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SYSTEMATIC APPROACHES TO DATA ANALY
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SYSTEMATIC APPROACHES TO DATA ANALY
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METHODOLOGICAL TOOLS FOR ANALYSING
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23 Content analysis and grounded th
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HOW DOES CONTENT ANALYSIS WORK 477
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HOW DOES CONTENT ANALYSIS WORK 479
Page 500 and 501: HOW DOES CONTENT ANALYSIS WORK 481
Page 502 and 503: A WORKED EXAMPLE OF CONTENT ANALYSI
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Page 506 and 507: COMPUTER USAGE IN CONTENT ANALYSIS
Page 508 and 509: COMPUTER USAGE IN CONTENT ANALYSIS
Page 510 and 511: GROUNDED THEORY 491 data, thereby c
Page 512 and 513: GROUNDED THEORY 493 fragments are t
Page 514 and 515: INTERPRETATION IN QUALITATIVE DATA
Page 520 and 521: 24 Quantitative data analysis Intro
Page 522 and 523: DESCRIPTIVE AND INFERENTIAL STATIST
Page 524 and 525: DEPENDENT AND INDEPENDENT VARIABLES
Page 526 and 527: EXPLORATORY DATA ANALYSIS: FREQUENC
Page 534 and 535: STATISTICAL SIGNIFICANCE 515 alongt
Page 536 and 537: STATISTICAL SIGNIFICANCE 517 hands
Page 538 and 539: HYPOTHESIS TESTING 519 selection fr
Page 540 and 541: EFFECT SIZE 521 differential measur
Page 542 and 543: EFFECT SIZE 523 Box 24.17 The Leven
Page 544 and 545: THE CHI-SQUARE TEST 525 The Effect
Page 546 and 547: DEGREES OF FREEDOM 527 Box 24.22 A2
Page 548 and 549: MEASURING ASSOCIATION 529 Box 24.23
Page 552 and 553: MEASURING ASSOCIATION 533 Box 24.26
Page 554 and 555: MEASURING ASSOCIATION 535 Many usef
Page 556 and 557: REGRESSION ANALYSIS 537 we know or
Page 558 and 559: REGRESSION ANALYSIS 539 Box 24.32 S
Page 560 and 561: REGRESSION ANALYSIS 541 Box 24.35 S
Page 562 and 563: MEASURES OF DIFFERENCE BETWEEN GROU
Page 578 and 579: 25 Multidimensional measurement and
Page 580 and 581: FACTOR ANALYSIS 561 Box 25.1 Rank o
Page 582 and 583: FACTOR ANALYSIS 563 Box 25.3 The st
Page 584 and 585: FACTOR ANALYSIS 565 Box 25.5 Ascree
Page 586 and 587: FACTOR ANALYSIS 567 Box 25.7 The ro
Page 588 and 589: FACTOR ANALYSIS 569 The school
Page 590 and 591: FACTOR ANALYSIS: AN EXAMPLE 571 sco
Page 592 and 593: FACTOR ANALYSIS: AN EXAMPLE 573 Box
Page 594 and 595: FACTOR ANALYSIS: AN EXAMPLE 575 Box
Page 596 and 597: EXAMPLES OF STUDIES USING MULTIDIME
Page 598 and 599: MULTIDIMENSIONAL DATA: SOME WORDS O
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MULTIDIMENSIONAL DATA: SOME WORDS O
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MULTILEVEL MODELLING 583 Degrees of
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CLUSTER ANALYSIS 585 Box 25.22 Clus
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→ → → → HOW MANY SAMPLES 58
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HOW MANY SAMPLES 589 Box 26.4 Choos
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ASSUMPTIONS OF TESTS 591 Box 26.5 c
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Notes 1 THE NATURE OF INQUIRY - SET
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NOTES 595 Gender and Careers. Lewes
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NOTES 597 is widespread, indeed the
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Bibliography Acker, S. (1989) Teach
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BIBLIOGRAPHY 601 Bannister, D. and
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BIBLIOGRAPHY 603 Brenner, M., Brown
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BIBLIOGRAPHY 605 Cohen, L. and Holl
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BIBLIOGRAPHY 607 or case-based Euro
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BIBLIOGRAPHY 609 Fendler, L. (1999)
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BIBLIOGRAPHY 611 the Powerful in Ed
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BIBLIOGRAPHY 613 Hanna, G. S. (1993
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BIBLIOGRAPHY 615 Jones, S. (1987) T
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BIBLIOGRAPHY 617 IL: Bureau of Econ
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BIBLIOGRAPHY 619 McNiff, J., Lomax,
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BIBLIOGRAPHY 621 Morrison, K. R. B.
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BIBLIOGRAPHY 623 Patton, M. Q. (198
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BIBLIOGRAPHY 625 Muliak and J. H. S
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BIBLIOGRAPHY 627 Smith, M. L. and G
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BIBLIOGRAPHY 629 Thorne, B. (1994)
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BIBLIOGRAPHY 631 Whyte, W. F. (1993
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INDEX Absolutism 51, 61-2 Access 51
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INDEX 635 face validity see validit
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INDEX 637 qualitative research 19-2
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