# MATH07036 2019 STATISTICS FOR SCIENTISTS

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**Description**

This course is designed to provide an introduction to a range of statistical tools of relevance to scientists. Specific topics include an overview of statistical distributions, significance testing, uncertainty determination, linear regression and experimental design. The application of statistics for quality control and practical experience in the application of statistical features in the widely available Microsoft Excel is particularly emphasised.

The teaching methods used will be a combination of lectures, self-study, labs, tutorials, and any combination of discussion, case study, problem-solving exercises and computer-based learning.

### Learning Outcomes

*On completion of this module the learner will/should be able to;*

**1.**

Describe basic statistical terms which are of relevance to the area of analytical science.

**2.**

Graphically display and numerically summarise data using appropriate tables, graphs and measures of centre, spread and position.

**3.**

Explain and apply concepts of basic probability including, conditional probability, Bayes' theorem, independent events and counting formulae;

**4.**

Make interferences about population parameters using sample statistics using confidence interval estimates and tests of statistical hypotheses

**5.**

Describe the application of statistics to sampling, quality control, analytical method validation and experimental design.

**6.**

Use an appropriate method for analysing relationships between variables in a dataset

### Teaching and Learning Strategies

The teaching methods used will be a combination of lectures, self-study, labs, tutorials, and any combination of discussion, case study, problem-solving exercises and computer-based learning.

The practical element of the course will be delivered separately to students in their various class groups (Biomedical Science/Medical Biotechnology, Forensic Science, Pharmaceutical Science) so that the examples used in the practical application of statistics can be tailored to their field of study.

### Module Assessment Strategies

This module will be assessed by both summative and formative means. The student will be assessed by means of both summative and formative assessment. The summative assessment will consist of continuous assessments where the student will be examined on both their theoretical knowledge of statistics and their use of statistical analysis software to apply this knowledge with the emphasis on the practical application of statistics. They will also take an end of module exam which will concentrate further on their knowledge of the application of statistics to scientific related problems and in the area of experimental design.

The formative assessment will be by means of a number of self assessment quizzes which the student can attempt in order to track their progress on the module and identify any gaps they may have or areas that they need further clarification in.

### Repeat Assessments

Where the student fails to achieve the pass mark in the module, they may be asked to repeat the final exam or complete a practical laboratory assessment or a combination of both.

The repeat practical laboratory assessment will be held in the first week of September prior to the autumn exam boards taking place.

### Module Dependencies

**Co-requisites**

**Incompatibles**

### Indicative Syllabus

**1. Describe basic statistical terms which are of relevance to the area of analytical science**

- Introduction to Statistical Terms
- Populations and Samples
- Data Types
- Introduction to Sampling Methods

**2. Graphically display and numerically summarise data using appropriate tables, graphs and measures of centre, spread and position.**

- Graphical Representation of data including frequency tables and charts
- Measures of Central Tendency, Position and Dispersion.

**3. Explain and apply concepts of basic probability including, conditional probability, Bayes' theorem, independent events and counting formulae;**

- Probability Experiments
- Probability Trees
- Classical Probability
- Experimental Probability
- Addition and Multiplication Rules of Probability
- Counting Rules
- Bayes Theorem
- Discrete Probability Distributions
- Binomial Distribution
- Poisson Distribution

- The Normal Distribution
- Applications of the standard Normal Distribution
- Assessing Normality
- The Central Limit Theorem

**4. Make interferences about population parameters using sample statistics using confidence interval estimates and tests of statistical hypotheses**

- Introduction to Hypothesis Testing
- Writing hypotheses for statistical tests
- One Sample, Independent Samples and Paired Samples t-tests
- One-Way ANOVA and related Post Hoc Tests
- Repeated Measures ANOVA and related Post Hoc Tests
- z-tests for proportion size

**5. Describe the application of statistics to sampling, quality control, analytical method validation and experimental design**

- Sample Size Calculations
- Quality of Analytical Measurements
- Uncertainty
- Method Validation.
- Calibration Methods
- Experimental Design and Optimisation

**6. Use an appropriate method for analysing relationships between variables in a dataset**

- Relationship Modelling
- Pearson's Correlation Co-efficient
- Significance of the correlation co-efficient
- Simple Linear Regression
- Chi Square test for association
- Chi Square test of goodness of fit

During the Practical element of the course, students will use the Data Analysis ToolPak in Microsoft Excel to carry out the various types of analysis listed in the syllabus above.

### Coursework & Assessment Breakdown

**Coursework & Continuous Assessment**

**End of Semester / Year Formal Exam**

### Coursework Assessment

Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
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1 | Descriptive Statistics - Practical Exam | Continuous Assessment | Practical Evaluation | 15 % | Week 5 | 2 |

2 | Inferential Statistics - Practical Exam | Continuous Assessment | Practical Evaluation | 20 % | Week 13 | 4,5,6 |

3 | Theory Assessment | Continuous Assessment | Multiple Choice | 15 % | Week 8 | 1,3,5 |

### End of Semester / Year Assessment

Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
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1 | End of Term Exam | Final Exam | Closed Book Exam | 50 % | End of Term | 1,2,3,4,5,6 |

### Full Time Mode Workload

Type | Location | Description | Hours | Frequency | Avg Workload |
---|---|---|---|---|---|

Lecture | Tiered Classroom | Lecture | 2 | Weekly | 2.00 |

Laboratory Practical | Computer Laboratory | Laboratory Practical | 1 | Weekly | 1.00 |

Independent Learning | UNKNOWN | Self Study | 4 | Weekly | 4.00 |

### Required & Recommended Book List

**Recommended Reading**

2009

*Practical Statistics for the Analytical Scientist*Royal Society of Chemistry

ISBN 9780854041312 ISBN-13 0854041311

"Completely revised and updated, the second edition contains new sections on method validation, measurement uncertainty, effective experimental design and proficiency testing."--pub. desc.

**Recommended Reading**

2017-10

*Statistics and Chemometrics for Analytical Chemistry*

ISBN 1292186712 ISBN-13 9781292186719

Introduction -- Statistics of repeated measurements -- Significance tests -- The quality of analytical measurements -- Calibration methods in instrumental analysis : regression and correlation -- Non-parametric and robust methods -- Experimental design and optimisation -- Multivariate analysis

**Recommended Reading**

2009-06-22

*Essential Mathematics and Statistics for Science*Wiley

ISBN 0470694483 ISBN-13 9780470694480

This book is a completely revised and updated version of this invaluable text which allows science students to extend necessary skills and techniques, with the topics being developed through examples in science which are easily understood by students from a range of disciplines. The introductory approach eases students into the subject, progressing to cover topics relevant to first and second year study and support data analysis for final year projects. The revision of the material in the book has been matched, on the accompanying website, with the extensive use of video, providing worked answers to over 200 questions in the book plus additional tutorial support. The second edition has also improved the learning approach for key topic areas to make it even more accessible and user-friendly, making it a perfect resource for students of all abilities. The expanding website provides a wide range of support material, providing a study environment within which students can develop their independent learning skills, in addition to providing resources that can be used by tutors for integration into other science-based programmes. Hallmark Features: Applied approach providing mathematics and statistics from the first to final years of undergraduate science courses. Second edition substantially revised to improve the learning approach to key topics and the organisation of resources for ease of use in teaching. Companion website at www.wiley.com/go/currellmaths2 providing: Over 200 videos showing step-by-step workings of problems in the book. Additional materials including related topic areas, applications, and tutorials on Excel and Minitab. Interactive multiple-choice questions for self-testing, with step-by-step video feedback for any wrong answers. A developing resource of study plans for useful topics and applications. Figures from the book for downloading.

**Recommended Reading**

2005-12-16

*Introduction to Statistics for Forensic Scientists*Wiley

ISBN 0470022019 ISBN-13 9780470022016

Introduction to Statistics for Forensic Scientists is an essential introduction to the subject, gently guiding the reader through the key statistical techniques used to evaluate various types of forensic evidence. Assuming only a modest mathematical background, the book uses real-life examples from the forensic science literature and forensic case-work to illustrate relevant statistical concepts and methods. Opening with a brief overview of the history and use of statistics within forensic science, the text then goes on to introduce statistical techniques commonly used to examine data obtained during laboratory experiments. There is a strong emphasis on the evaluation of scientific observation as evidence and modern Bayesian approaches to interpreting forensic data for the courts. The analysis of key forms of evidence are discussed throughout with a particular focus on DNA, fibres and glass. An invaluable introduction to the statistical interpretation of forensic evidence; this book will be invaluable for all undergraduates taking courses in forensic science. Introduction to the key statistical techniques used in the evaluation of forensic evidence Includes end of chapter exercises to enhance student understanding Numerous examples taken from forensic science to put the subject into context

**Recommended Reading**

2014-01-03

*Elementary Statistics*McGraw-Hill Higher Education

ISBN 9780077665807 ISBN-13 0077665805

Elementary Statistics: A Step By Step Approach is for introductory statistics courses with a basic algebra prerequisite. The text follows a nontheoretical approach, explaining concepts intuitively and supporting them with abundant examples. In recent editions, Al Bluman has placed more emphasis on conceptual understanding and understanding results, which is also reflected in the online homework environment, Connect Math Hosted by ALEKS. Additionally step-by step instructions on how to utilize the TI-84 Plus graphing calculator, Excel, and Minitab, have also been updated to reflect the most recent editions of each technology.

**Recommended Reading**

2016-02-18

*Elementary Statistics Using Excel*Pearson

ISBN 9780134429816 ISBN-13 0134429818

This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. From SAT scores to job search methods, statistics influences and shapes the world around us. Marty Triolas text continues to be the bestseller because it helps students understand the relationship between statistics and the world, bringing life to the theory and methods. Elementary Statistics Using Excel raises the bar with every edition by incorporating an unprecedented amount of real and interesting data that will help instructors connect with students today, and help them connect statistics to their daily lives. The Fifth Edition contains more than 1,800 exercises, 89% of which use real data and 85% of which are new. Hundreds of examples are included, 91% of which use real data and 84% of which are new.

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