Tianjiin Medical University

Theoretical Teaching Syllabus 《Medical statistics》

开课单位：公共卫生学院 2015

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《医学统计学》供临床五年制留学生和医学研究生留学生使用大纲

Preface

Good medical doctors should also be considered scientists and artists. They encounter numerous questions raised by their patients, colleagues and even themselves. In addition, they are faced with a lot of data from patients as well as from laboratory tests. They need to learn to evaluate the information obtained from these tests as well as the journals or medical books. How does one use these data to answer questions? Statistical skills are required to understand and address these questions.

This book is an introductory level textbook designed for medical students as well as students from other healthcare related professions such as nursing, dentistry, pharmacy, and public health services. It can also be used as a reference book for the clinician or other healthcare professionals. It does not require any background knowledge in statistics, and its mathematical level assumes only some knowledge of algebra. In this book, we try to minimize the amount of mathematical formulation but focus more on the applications using relevant examples.

It is important to learn statistics through continuous practice. The study questions listed at the end of each chapter are designed to help to learn and practice topics explained in the book. .

It is worth noting that this text book serves as an introduction of medical statistics only. It does not provide answers to all of the questions in statistics. However, it would be a good start to learn statistics. We would very much appreciate any comments and suggestions on what and how the contents of this book can be improved.

We would like to express our sincere gratitude to all of the contributors who wrote or edited chapters of this textbook.

The support of the institution, International College, Tianjin Medical University, was essential for this book. We especially want to acknowledge Professor Guo Fenglin, the dean of the college, and his colleagues, for their encouragement and substantive support.

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We also thank the publisher for their helpful advice.

We would like to acknowledge many professors and their great works from which we have learned a lot.

Finally, we would like to acknowledge all of the families of the contributors for their support.

Chapter 1 Introduction

Purpose and Requirement:

1. To master the concepts of statistics.

2. To understand the purpose of the course.

Teaching Contents: 1. Definition of statistics: descriptive statistics and inferential statistics 2. The Purpose of the Text 3. Introduction to Some Basic Terms and Notation

Chapter 2 Descriptive Statistics

Purpose and Requirement:

1. To understand the different types of data.

2. To study tables and graphs of data.

3. To master measures of central tendency and dispersion. Teaching Contents: 1. Types of data: nominal data, ordered categorical or ranked data and numerical or quantitative data. 2. Measures of central tendency and dispersion: the arithmetic mean, the median, the geometric mean, and the mode; the range, deviation from the mean, the variance, the standard variation, the coefficient of variation and the interquartile range. 3. Tabular and graphical presentation of data: tables, histograms, stem-and-leaf plots, dot plots, box plots, line graphs, bar charts, pie chart and scatter plot.

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Chapter 3 Probability Distributions

Purpose and Requirement: 1. To understand the definitions and basic ideas related to probability 2. To study binomial distribution and Poisson distribution. 3. To master the normal probability distribution Teaching Contents: 1. Definitions and Basic Ideas Related to Probability: probability, properties of probability, discrete and continuous random variables, discrete probability distribution, Expected value of a discrete random variable and the variance of a discrete random variable. 2. The Binomial Distribution: assumptions and the binomial probability distribution. 3. The Poisson Distribution: assumptions and the poisson probability distribution. 4. The Normal Probability Distribution: probabilities of the normal distribution, the standard normal distribution, the standard normal tables, applications of the normal

distribution, the Zp notation and normal approximation to the binomial.

Chapter 4 Introduction to Statistical Inference

Purpose and Requirement: 1. To Understand the Important Definitions and Concepts of Statistical Inference. 2. To Study Concepts of Hypothesis Testing. 3. To Master the Interval Estimation. Teaching Contents: 1. The important definitions and concepts of statistical inference: sampling, sampling distributions, central limit theorem and unbiased, minimum variance estimators. 2. Concepts of hypothesis Testing: type I and type II errors, the effect of sample size, one sided vs. two sided tests, the test statistic and the P-value. 3. The general hypothesis testing procedure. 4. Interval estimation.

Chapter 5 One Sample Statistical Inference

Purpose and Requirement:

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1. To Understand One Sample Test for the Mean of a Normal Distribution with Known Variance. 2. To Study Hypothesis Testing. 3. To Master the one sample t test. Teaching Contents: 1. One Sample Test for Mean of a Normal Distribution with Known Variance: Hypothesis testing, confidence intervals, sample size determination. 2. One Sample t Test: The student’s t distribution, Hypothesis testing. 3. One Sample Test for the Variance of a Normal Distribution

Chapter 6 Two Sample Statistical Inferences

Purpose and Requirement: 1. To Understand the Paired t Test. 2. To Study Two Sample t Test’s Hypothesis Testing for Independent Means. 3. To Master the Two Sample Test for Binomial Proportions. Teaching Contents: 1. The Paired t Test: Two sample paired t test for the mean of normal distributions. 2. Two sample t test for Independent Means: inferences when variances are equal and unequal. 3. Two sample test for binomial proportions, testing for the equality of two variances.

Chapter 7 Nonparametric Statistical

Purpose and Requirement: 1. To understand the advantages and Disadvantages of nonparametric statistical 2. To studythe nonparametric methods Teaching Contents: 1. Advantages and Disadvantages: Nonparametric methods have several appealing characteristics but also some shortcomings 2. The Wilcoxon Sign-rank Test for One Test of Central Tendency 3. Wilcoxon Sign-rank Test for Paired Data 4. Two Sample Test of Central Tendency 5. The Kruskal-Wallis Test

Chapter 8 Chi-square Test

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Purpose and Requirement: 1. To understand the definitions and basic ideas related to Chi-square test 2. To study the comparison of proportion in independent samples 3. To master the Fisher’s exact test Teaching Contents: 1. Comparison of Proportion in Dependent Samples:Chi-square test for r×c contingency table,Chi-square test for two contingency table. 2. Comparison of Proportion in Related Samples - McNermar’s Test 3. Chi-square Goodness-of-fit Test 4. Tests for Association in contingency tables - Measuring Independence 5.The Fisher’s Exact Test

Chapter 9 Correlation and Regression

Purpose and Requirement: 1. To understand the definitions and calculation of correlation and regression 2. To study the differences and similarities between correlation and regression 3. To master Spearman’s rank correlation coefficient Teaching Contents: 1.Simple Linear Regression:general concepts, the method of least squares, the standard error of the estimate, test for a significant regression, interval estimation for prediction made from regression lines. 2 .Multiple Regression 3. Linear Correlation: Pearson’s product-moment correlation coefficient, hypothesis test for correlation, Spearman’s rank correlation coefficient.

Chapter 10 Analysis of Variance Techniques

Purpose and Requirement: 1. To understand the definitions and basic ideas related to analysis of variance 2. To study F test for overall comparison of group means 3. To master ANOVA for randomized block design Teaching Contents:

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1. One Way Analysis of Variance： the mathematical model, the null hypothesis, model assumptions, F test for overall comparison of group means, multiple comparisons. 2. ANOVA for Randomized Block Design 3. Factorial Designs: the mathematical model, the null hypothesis, the analysis of variance table.

Chapter 11 Research Designs Purpose and Requirement: 1. To understand the sampling techniques also their advantages and disadvantages 2. To study the three elements of designed experiment 3. To study the two observational study designs 4. To master the types of designed experiment Teaching Contents: 1. Sample and Sample Techniques: Probability sampling - simple random sampling(SRS), systematic sampling,stratified random sampling,cluster sampling. 2. Design of Experiments: (1) Concepts of a designed experiments:control, randomization, replication, confounding (2) Completely randomized design (3) Randomized block design (4) Matched pairs design 3. Observational Study Design: case-control design, cohort study.

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