1: Biostats Chapter 1: Intro & Graphs

Course Information

• The course is BMS 511 Biostats & Statistical Analysis, Chapter 1: Intro & Displaying Data with Graphs
• The instructor is Guang Xu, PhD, MPH
• The instructor is an assistant professor of Biostatistics and Public Health at the College of Osteopathic Medicine, Marian University
• The course provides a comprehensive introduction to statistical practices relevant to biomedical and clinical research
• The course covers experimental questions and approaches to data collection, statistical analysis, basic statistical concepts, and appropriate statistical methodology
• The course emphasizes the relationship between statistics and medical research
• Examples from healthcare and research are used to illustrate statistical concepts and methodology.

Required Texts

• The required textbook is "The practice of statistics in the life sciences" by Baldi, Brigitte, and David S. Moore, 4th edition, Macmillan Higher Education
• Required supplementary textbook is "Epidemiology: With Student Consult Online Access," 5e, by Gordis, L., WB Saunders Co., Philadelphia (5th edition, 2013), ISBN: 978-1455737338

Recommended (Optional Texts)

• "Intuitive Biostatistics: a nonmathematical guide to statistical thinking" by Motulsky, Harvey, 4th edition, Oxford University Press
• "Statistics in Medicine" by Robert H. Riffenburgh, 3rd edition, Elsevier

Course Grades

• Exam I: 16%
• Exam II: 16%
• Exam III: 16%
• Exam IV: 16%
• In-class Quizzes: 16%
• Homework (10 total): 10%

Group Project

• The group project gives students a chance to apply the learned statistics and to think critically
• The project necessitates an understanding of the story, methods, results, conclusions, future, and personal thoughts.

Office Hours

• Instructor: Guang Xu, PhD, MPH
• Email: [email protected]
• Phone: 317-955-6496
• Office Hours: Tuesday 10:00 – 11:30 (Time may change due to other duties)
• WebEx Meeting Room: https://mu.webex.com/meet/guangxu

Learning Objectives

• Determine and apply methods for depicting data distributions using graphs.
• Define and utilize individuals and variables.
• Understand the various types of data: categorical and quantitative
• Understand different ways to display categorical data (e.g., bar graphs, pie charts)
• Understand different ways to display quantitative data (e.g., histograms, dot plots)
• Interpret histograms.
• Graph time series using time plots.

Variable Types

• Quantitative Variables: Variables that measure or assess a quantity, allowing for calculating an average for all individuals. Examples include age, blood pressure, leaf length.
• Categorical Variables: Variables that describe a characteristic or quality of an individual, allowing for counting or calculating the proportion of individuals with that characteristic. Examples include gender, blood type, flower color

Classifying Variables

• Identify the individuals being studied.
• Define what is being recorded about those individuals.
• Determine whether the recorded information is a number (quantitative) or a description (categorical).

Graphing Categorical Data

• Bar graphs: Each category is represented by a bar. The bar's height represents the frequency or relative frequency of individuals in that category.
• Pie charts: The whole pie represents all individuals. Each slice represents a category, and the size of the slice corresponds to the proportion of individuals in that category.

Graphing Quantitative Data

• Histograms: A summary graph for a single numerical variable, useful for understanding variability, especially with large datasets.
• Dot plots: A graph of raw data, useful to clarify variation patterns, primarily with small datasets.
• Time plots: A graph employing time on the horizontal axis and a variable on the vertical axis, highlighting changes over time.

Making Histograms

• Divide the range of the quantitative variable into equal-size intervals.
• The vertical axis represents either frequency (counts) or relative frequency (percentages of total).
• For each interval, create a column whose height corresponds to the count or percentage of data points in that interval.

Choosing Histogram Classes

• The process of selecting classes is iterative (repeated)
• Avoid too many classes with values of 0 or 1 (pancake graph).
• Avoid overly summarized classes (skyscraper graph); data is no longer informative.
• Begin by selecting 5 to 10 intervals, then adjust accordingly.

Interpreting Histograms

• Shape: Examine the overall pattern and deviations. Look for patterns like unimodal (single peak), bimodal (two peaks), symmetric (similar shape on both sides), skewed (one tail longer).
• Center: Estimate the approximate midpoint of the data.
• Spread: Determine the range of values observed.
• Outliers: Identify values that deviate significantly from the overall pattern and try to explain them.

Common Distribution Shapes

• Symmetric: The graph of the left half of the data and right half looks identical.
• Left-Skewed: The left side of the graph, containing extreme values, extends further than the right side.
• Right-Skewed: The right side of the graph, containing extreme values, extends further than the left side.

Outliers

• An outlier is a data point that falls outside the overall distribution pattern.
• Look for outliers and try to explain them.
• Note that the largest observation isn't always an outlier. It must not be consistent with the rest of the data.

Making Dot Plots

• Create a single axis representing the variable's range.
• Place a dot for each data point, positioned according to its value on the axis.
• Stack dots when multiple data points have the same value.

Graphing Time Series

• Time plots usually involve plotting a variable against time.
• Look for overall trends and cyclical variability in the data.

Homework

• Homework is available under the "Modules" section on Canvas.