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E-raamat: Understanding Quantitative Data in Educational Research

  • Formaat: 376 pages
  • Ilmumisaeg: 11-Nov-2020
  • Kirjastus: Sage Publications Ltd
  • Keel: eng
  • ISBN-13: 9781529743920
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Understanding Quantitative Data in Educational ResearchSuurem pilt
  • Formaat: 376 pages
  • Ilmumisaeg: 11-Nov-2020
  • Kirjastus: Sage Publications Ltd
  • Keel: eng
  • ISBN-13: 9781529743920
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This book is designed to help Education students gain confidence in analysing and interpreting quantitative data and using appropriate statistical tests, by exploring, in plain language, a variety of data analysis methods.



This book is designed to help Education students gain confidence in analysing and interpreting quantitative data and using appropriate statistical tests, by exploring, in plain language, a variety of data analysis methods.

Highly practical, each chapter includes step-by-step instructions on how to run specific statistical tests using R, practical tips on how to interpret results correctly and exercises to put into practice what students have learned.

It also includes guidance on how to use R and RStudio, how to visualise quantitative data, and the fundamentals of inferential statistics, estimations and hypothesis testing.

Nicoleta Gaciu is Senior Lecturer in Education at Oxford Brookes University.

About the author xiii
About the online resources xv
Acknowledgements xvii
Introduction xix
Part One Understanding quantitative data and R
1(2)
1 Introduction to information, knowledge and quantitative data
3(1)
1.1 Quantitative data, information and knowledge in education
4(2)
1.1.1 What is quantitative data?
5(1)
1.2 Measurement and scales of measurement
6(2)
1.2.1 What is a measurement? What is a scale?
6(2)
1.3 From concepts to constructs and variables
8(1)
1.4 Types of variables
9(1)
1.5 Quantitative data and R
10(1)
1.5.1 Why use R?
10(1)
Further reading
11(2)
2 An introduction to R and RStudio
13(24)
2.1 Installing R
14(1)
2.2 Upgrading R
14(1)
2.3 Installing and using RStudio
15(3)
2.4 Functions, packages and libraries
18(4)
2.5 Working with data in R
22(6)
2.5.1 Data structures and value types in R
24(4)
2.6 Importing and exporting data sets
28(5)
2.6.1 Importing data sets in R
29(3)
2.6.2 Exporting data sets from R
32(1)
2.7 Getting help on R and RStudio
33(1)
Further reading
34(3)
Part Two Data visualisation
37(24)
3 Graphical representation of data
39(22)
3.1 Using tables
42(2)
3.2 Using graphs
44(14)
3.2.1 Bar graph
45(2)
3.2.2 Pareto graph
47(2)
3.2.3 Pie graph
49(2)
3.2.4 Histogram
51(1)
3.2.5 Box and whisker graph
52(1)
3.2.6 Line graph
53(2)
3.2.7 Scatter graph
55(3)
Further reading
58(3)
Part Three Providing information about data
61(78)
4 Descriptive statistics
63(20)
4.1 From raw data to frequency distributions
64(6)
4.2 Measures of location or central tendency
70(6)
4.2.1 Mode
71(1)
4.2.2 Median
72(1)
4.2.3 Mean
73(3)
4.3 Advantages and disadvantages of using the mode, median and mean
76(1)
4.4 Measures of location and graphical display
77(5)
Further reading
82(1)
5 Measures of dispersion and distributions
83(34)
5.1 Range
84(3)
5.2 Percentiles, deciles and quartiles
87(7)
5.3 Interquartile range
94(2)
5.4 Mean deviation
96(3)
5.5 Standard deviation
99(5)
5.6 Coefficient of variation
104(2)
5.7 Shape of distributions and skewness
106(4)
5.8 Advantages and disadvantages of using the range, mean deviation and standard deviation
110(1)
5.9 Measures of dispersion and graphical display
111(5)
Further reading
116(1)
6 Normal distribution and standardised scores
117(22)
6.1 From histogram to normal distribution curve
118(3)
6.2 Other visual methods for assessing normality of data
121(2)
6.2.1 The boxplot and the normal distribution
122(1)
6.2.2 The QQ plot and the normal distribution
123(1)
6.3 Normal distribution and standard deviation
123(2)
6.4 Statistical tests for normality
125(4)
6.5 Standard normal distribution and z-scores
129(2)
6.6 Transforming data values into z-scores
131(7)
Further reading
138(1)
Part Four Making estimations and predictions from data
139(42)
7 Fundamentals of inferential statistics
141(20)
7.1 What is inferential statistics and how does it work?
142(1)
7.2 From sample to population
143(1)
7.3 Sampling strategies
144(8)
7.3.1 Random sampling methods
145(6)
7.3.2 Non-random sampling methods
151(1)
7.4 Making decisions about the population based on the information about the sample
152(2)
7.5 Standard distributions
154(6)
7.5.1 Standard normal distribution
154(1)
7.5.2 R-distributions
154(3)
7.5.3 Chi-squared distributions
157(3)
Further reading
160(1)
8 Estimation and hypothesis testing
161(20)
8.1 Making estimations
162(7)
8.1.1 Standard error
162(2)
8.1.2 Sample size
164(2)
8.1.3 Confidence interval and confidence level
166(3)
8.2 Statistical hypothesis testing process
169(7)
8.2.1 Null and alternative hypotheses
169(3)
8.2.2 Directional and non-directional hypotheses
172(1)
8.2.3 Decisions about the null hypothesis: statistical levels, types of error and power
173(1)
8.2.4 Regions of rejection
174(2)
8.3 Selection of statistical tests
176(3)
Further reading
179(2)
Part Five From sample to population
181(110)
9 One-sample tests
183(26)
9.1 Parameter hypothesis testing using sample statistics
184(1)
9.2 One-sample statistical tests for interval/ratio data
185(13)
9.2.1 Z-test
187(2)
9.2.2 F-test
189(6)
9.2.3 Sign test
195(3)
9.3 One-sample statistical tests for ordinal data
198(2)
9.3.1 Wilcoxon signed-rank test
198(2)
9.4 One-sample statistical tests for nominal data
200(8)
9.4.1 Binomial test
200(3)
9.4.2 Pearson chi-squared goodness-of-fit test
203(5)
Further reading
208(1)
10 Differences between two independent or dependent samples
209(20)
10.1 Differences between two independent samples
210(10)
10.1.1 Mann-Whitney test (or Wilcoxon rank-sum test)
211(3)
10.1.2 Independent samples t-test
214(3)
10.1.3 Chi-squared test
217(3)
10.2 Differences between two dependent samples
220(7)
10.2.1 Wilcoxon signed-rank test
220(4)
10.2.2 Paired samples t-test
224(1)
10.2.3 McNemar's test
225(2)
Further reading
227(2)
11 Differences between more than two independent samples
229(32)
11.1 The analysis of variance (ANOVA)
230(3)
11.2 One-way ANOVA
233(13)
11.2.1 Calculating one-way ANOVA by hand
234(3)
11.2.2 Computing one-way ANOVA in R
237(4)
11.2.3 Post-hoc tests for one-way ANOVA
241(2)
11.2.4 Measuring the effect size in a one-way ANOVA
243(3)
11.3 Two-way ANOVA
246(8)
11.3.1 Computing a two-way ANOVA in R
247(3)
11.3.2 Interaction plot for two-way ANOVA test results
250(1)
11.3.3 Post-hoc analysis in two-way ANOVA
251(2)
11.3.4 Measuring the effect size in two-way ANOVA
253(1)
11.4 Kruskal-Wallis ANOVA test
254(5)
11.4.1 Post-hoc analysis for the Kruskal-Wallis test
256(3)
Further reading
259(2)
12 Differences between more than two dependent samples
261(30)
12.1 Repeated measures ANOVA
262(2)
12.2 One-way repeated measures ANOVA
264(9)
12.2.1 Checking assumptions for one-way repeated measures ANOVA
265(4)
12.2.2 Computing one-way repeated measures ANOVA and Mauchly's test of sphericity
269(2)
12.2.3 Post-hoc analysis for one-way repeated measures ANOVA
271(1)
12.2.4 Measuring the effect size in a one-way repeated measures ANOVA
272(1)
12.3 Two-way repeated measures ANOVA
273(5)
12.3.1 Checking assumptions for two-way repeated measures ANOVA
274(3)
12.3.2 Computing two-way repeated measures ANOVA in R
277(1)
12.4 Friedman's test
278(4)
12.4.1 Computing Friedman's test in R
278(2)
12.4.2 Post-hoc analysis for Friedman's test
280(1)
12.4.3 Measuring the effect size in Friedman's test
281(1)
12.5 Cochran's Q-test
282(8)
12.5.1 Manual calculation of Q-statistic
284(1)
12.5.2 Computing Cochran's Q-test in R
285(1)
12.5.3 Post-hoc analysis for Cochran's Q-test
286(2)
12.5.4 Effect size for Cochran's Q-test
288(2)
Further reading
290(1)
Part Six Relationships and predictions
291(54)
13 Relationships between variables
293(24)
13.1 Covariance and correlation between two variables
294(6)
13.1.1 Visual representation of the correlation
297(2)
13.1.2 Coefficient of determination
299(1)
13.1.3 Errors of the correlation coefficient
299(1)
13.2 Correlations for more than two variables
300(3)
13.2.1 Visual representation of the correlation matrix
302(1)
13.3 Correlations and scales of measurement
303(12)
13.3.1 Pearson's correlation coefficient
303(4)
13.3.2 Spearman's correlation coefficient
307(3)
13.3.3 Lambda, phi and Cramer's V correlation coefficients
310(5)
Further reading
315(2)
14 Predictions for independent and dependent variables
317(28)
14.1 Linear regression models
319(2)
14.2 Ordinary least squares regression
321(12)
14.2.1 Creating the OLS regression model
325(2)
14.2.2 Checking for statistical significance
327(3)
14.2.3 Assessing the assumptions of the linear regression model
330(3)
14.3 Multiple linear regression
333(10)
14.3.1 Creating the multiple linear regression model
334(1)
14.3.2 Checking statistical significance
335(2)
14.3.3 Assessing the assumptions of the multiple linear regression model
337(6)
Further reading
343(2)
Bibliography 345(4)
Index 349
Dr Nicoleta Gaciu is Senior Lecturer in Education at Oxford Brookes University, UK. Her academic and research specialisations in disciplines such as physics, statistics, computer sciences, research methods and business have given her the best opportunities to make connections across disciplines, to view real-life phenomena through different lenses and to take different perspectives, knowledge, logical and methodological approaches for interdisciplinary research.
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