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Seyed Hassan Saneii
Hassan Doosti
Practical
Biostatistics
for Medical and
Health Sciences
Practical Biostatistics for Medical and Health
Sciences
Seyed Hassan Saneii · Hassan Doosti
Practical Biostatistics
for Medical and Health
Sciences
Seyed Hassan Saneii
School of Rehabilitation Science
Iran University of Medical Sciences
Tehran, Iran
Hassan Doosti
Macquarie University
Arncliffe, NSW, Australia
ISBN 978-981-97-3082-7 ISBN 978-981-97-3083-4 (eBook)
https://doi.org/10.1007/978-981-97-3083-4
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature
Singapore Pte Ltd. 2024
This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether
the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse
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does not imply, even in the absence of a specific statement, that such names are exempt from the relevant
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The publisher, the authors and the editors are safe to assume that the advice and information in this book
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This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd.
The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721,
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If disposing of this product, please recycle the paper.
Preface
Statistics permeates nearly every aspect of our lives. Its significance has particularly
grown in the biological, medical, and health sciences, spanning from opinion polls to
clinical trials in medicine, as well as the analysis of big data from health applications.
The influence of statistics shapes the world around us. In Practical Biostatistics for
Medical and Health Sciences, we, as authors, establish a strong connection between
statistics and our reality by employing a diverse range of real-life applications that
bring theory and methods to life.
This book is specifically designed for students majoring in the medical,
biological, and health sciences, catering to a wide variety of learners who are
taking their first biostatistics course. Recognizing that some students may not have
completed advanced mathematical and algebraic courses beforehand, we have
minimized the use of algebra and calculus. As a result, the book does not demand a
higher level of mathematical rigor than what students have typically covered in
high school, where their mathematical background is limited to basic algebra.
The primary audience for this biostatistics book comprises medical and health
science researchers, whether in clinical or non-clinical fields. Additionally, students
and clinicians seeking an understanding of research design and analysis, as well as
those attending postgraduate courses in medical and health science statistics, will find
it useful. Our intention, as authors, is to start from a beginner level and progress to a
research level, with a strong focus on the interpretation and presentation of results.
Throughout the book, we adopt a non-theoretical approach, omitting formal proofs
and instead explaining concepts intuitively, supported by ample examples.
Our motivation for writing this book stemmed from the belief that any writing
style can be understood by a portion of its audience. However, we observed that most
introductory texts fail to sufficiently explain the underlying concepts of statistics and
often detach from the reality of conducting and evaluating medical research.
The book comprises 13 chapters, each accompanied by detailed solved
examples. In Chap.
1, we elucidate the measurement scales, types of data, and the
application of statistics in medical and health sciences. Chapter
2 offers guidance
on tabulating raw data and creating various plots. Chapter
3 focuses on data
summarization, including measures of central tendency, measures of dispersion,
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vi Preface
and the impact of constant changes on these measures. Chapter 4 delves into the
principles of probability, conditional probability, Bayes’ theorem, epidemiology,
odds and probability, and counting principles. Chapter
5 explores discrete
distributions such as binomial, multinomial, geometric, hypergeometric, and
Poisson distributions. Chapter
6 is dedicated to normal and standard normal
distributions, as well as t and Chi-squared distributions. Chapter
7 primarily
discusses sampling techniques, emphasizing probabilistic approaches and sample
size calculations. Chapter
8 delves into estimation (point and interval) and
statistical inference. Chapter
9 focuses on health and disease measures, particularly
relevant to epidemiological studies. Chapter
10 introduces the foreground toolbox
for hypothesis testing, while Chap.
11 delves further into hypothesis testing.
Chapter
12 covers correlations, including Pearson, Spearman, and point-biserial
correlations, as well as linear correlation. Finally, Chap.
13 centers around one-way
ANOVA and post-hoc tests. All the procedures are meticulously calculated step by
step and have been validated using SPSS.
Tehran, Iran
Arncliffe, Australia
Seyed Hassan Saneii
Hassan Doosti
https://t.me/med1917
Contents
1 Measuring Scales .............................................. 1
1.1 Statistics and Its Applications ............................. 1
1.2 Type of Data ........................................... 2
1.3 Exercises .............................................. 8
2 Tables and Charts ............................................. 11
2.1 Introduction ............................................ 11
2.2 How to Construct a Frequency Table ....................... 11
2.3 Types of Frequencies .................................... 17
2.4 Features of Table Classification ........................... 20
2.5 Graphs ................................................ 22
2.6 Exercises .............................................. 33
3 Summarizing Data ............................................ 37
3.1 Introduction ............................................ 37
3.2 Measures of Central Tendency ............................ 37
3.3 Measures of Dispersion .................................. 50
3.4 The Effect of Constant Changes on Measures of Central
Tendency and Dispersion ................................. 61
3.5 Exercises .............................................. 64
4 Probability ................................................... 67
4.1 Introduction ............................................ 67
4.2 Definitions ............................................. 67
4.3 Principles of Probability .................................. 70
4.4 Conditional Probability .................................. 73
4.5 Bayes’ Theorem ........................................ 75
4.6 Bayes’ Theorem and Epidemiology ........................ 80
4.7 Odds and Probability .................................... 83
4.8 Counting Principle ...................................... 84
4.9 Expected Value ......................................... 87
4.10 Exercises .............................................. 89
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viii Contents
5 Discrete Distributions .......................................... 95
5.1 Introductions ........................................... 95
5.2 Binomial Distribution .................................... 96
5.3 Multinomial Distribution ................................. 100
5.4 The Limit of the Binomial Distribution ..................... 103
5.5 Geometric Distribution ................................... 104
5.6 Hypergeometric Distribution .............................. 106
5.7 Poisson Distribution ..................................... 108
5.8 Exercises .............................................. 111
6 Normal Distribution ........................................... 115
6.1 Normal Distribution ..................................... 115
6.1.1 Distribution Function and Density Function ........ 116
6.1.2 The Properties of the Normal Distribution .......... 117
6.2 The Standard Normal Distribution ......................... 118
6.2.1 Skewness and Kurtosis of Normal Distributions ..... 123
6.2.2 Assessing Normality of a Distribution ............. 127
6.3 t Distribution ........................................... 130
6.4 Chi-Square Distribution .................................. 133
6.5 Exercises .............................................. 136
7 Sampling and Sample Size ..................................... 139
7.1 Introduction ............................................ 139
7.2 Definitions ............................................. 139
7.3 Sampling Techniques .................................... 141
7.4 Sample Size ............................................ 147
7.4.1 Sample Size Determination for Estimating
a Single Population Mean ........................ 149
7.4.2 Sample Size Determination to Estimate
the Proportion .................................. 150
7.4.3 Sample Size Determination for Comparing
the Mean of Two Populations ..................... 152
7.4.4 Sample Size Determination to Compare
the Proportion of Two Populations ................ 154
7.5 Exercises .............................................. 156
8 Estimation and Statistical Inference ............................. 159
8.1 Introduction ............................................ 159
8.2 Estimation ............................................. 160
8.3 Estimation of the Mean .................................. 162
8.3.1 Point Estimate of the Mean ...................... 162
8.3.2 Interval Estimate of the Mean .................... 163
8.4 Point and Interval Estimation of a Population Proportion ...... 166
8.5 Central Limit Theorem ................................... 170
8.6 Estimation of Variance and Standard Deviation .............. 174
8.7 Exercises .............................................. 176
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Contents ix
9 Health and Disease Measures ................................... 177
9.1 Introduction ............................................ 177
9.2 Difference Between Ratios, Rates, and Proportions ........... 177
9.3 Rates .................................................. 178
9.3.1 Incidence ...................................... 179
9.3.2 Prevalence ..................................... 183
9.3.3 Mortality Rate ................................. 184
9.4 Standardization ......................................... 185
9.4.1 Procedure for Direct Standardization .............. 186
9.4.2 Procedure for Indirect Standardization ............. 186
9.5 Screening Tests ......................................... 187
9.5.1 Confidence Interval for Screening Tests ............ 191
9.6 Cohen’s Kappa Coefficient ............................... 192
9.6.1 Confidence Interval for Cohen’s Kappa ............ 194
9.7 Relative Risk (RR) ...................................... 200
9.8 Odds Ratio (OR) ........................................ 204
9.9 Risk Difference or Excess Risk ............................ 209
9.10 Exercises .............................................. 211
10 Foreground Toolbox for Hypothesis Testing ...................... 215
10.1 Introduction ............................................ 215
10.2 Definitions ............................................. 216
10.3 The Steps for Testing Hypotheses .......................... 223
10.4 Applications of Statistical Tests ........................... 224
10.5 Common Statistical Tables ............................... 225
11 Hypothesis Testing ............................................ 227
11.1 Introduction ............................................ 227
11.2 Comparing the Mean of a Population with a Fixed Value ...... 228
11.3 Comparing the Mean of Two Populations ................... 233
11.4 Comparison of the Mean of the Two Paired Samples ......... 238
11.5 Comparing Population Proportion with a Fixed Proportion .... 242
11.6 Comparison the Proportions in Two Independent Groups ...... 247
11.7 Testing the Equality of Variance of Two Groups ............. 250
11.8 Goodness-Of-Fit Tests ................................... 252
11.9 Association and Dependence of Variables in Contingency
Tables ................................................. 255
11.10 Fisher’s Exact Test for Small Samples ...................... 259
11.11 Tests of Homogeneity .................................... 260
11.12 Chi-Squared Test for Trend ............................... 262
11.13 McNemar’s Test for Paired Proportions ..................... 265
11.14 Confidence Intervals and Hypothesis Tests? ................. 268
11.15 How to Present the Results of a Statistical Test .............. 269
11.16 Exercises .............................................. 269
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x Contents
12 Correlation and Regression .................................... 273
12.1 Introduction ............................................ 273
12.2 Correlation ............................................. 274
12.2.1 Pearson Correlation Coefficient ................... 277
12.2.2 Confidence Interval for Pearson Correlation
Coefficient ..................................... 280
12.2.3 The Significant Test of the Pearson Correlation
Coefficient ..................................... 281
12.2.4 Running Correlation Coefficient on SPSS .......... 285
12.2.5 The Spearman Rank Correlation Coefficient ........ 286
12.2.6 Confidence Interval for Spearman Correlation
Coefficient ..................................... 290
12.2.7 Kendall’s Rank Correlation Coefficient ............ 293
12.2.8 Test Statistic and Confidence Interval
for Kendall’s Tau Correlation Coefficient ........... 295
12.2.9 Point-Biserial Correlation ........................ 297
12.2.10 Running Point-Biserial Correlation on SPSS ........ 300
12.2.11 Partial Correlation Coefficient .................... 301
12.2.12 Comparing Two Correlation Coefficients ........... 302
12.2.13 Precautions .................................... 305
12.3 Regression ............................................. 306
12.3.1 Assumptions for Linear Regression ............... 308
12.3.2 Confidence Interval and Significant Test
for Regression Coefficient ....................... 311
12.3.3 Running Simple Linear Regression in SPSS ........ 313
12.4 Coefficient of Determination .............................. 316
12.5 Exercises .............................................. 317
13 Analysis of Variance ........................................... 321
13.1 Introduction ............................................ 321
13.2 Multiple t-TestsorANOVA ............................... 321
13.3 Mechanism of ANOVA .................................. 323
13.4 Commonly Used Definitions in ANOVA .................... 326
13.5 Assumptions for One-Way ANOVA ........................ 327
13.6 Hypotheses in ANOVA .................................. 328
13.7 The ANOVA Table ...................................... 328
13.8 Running ANOVA on SPSS ............................... 333
13.9 Identifying Which Means is Different ...................... 335
13.10 Exercises .............................................. 339
Appendix A: Selected Statistical Function in Excel .................... 341
Appendix B: Common Statistical Tables ............................. 345
Answer to Exercises ............................................... 377
References ........................................................ 383
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