Introduction to statistics for biomedical engineers

1. Introduction ........................................................................................................1 2. Collecting Data and Experimental Design ............................................................5 3. D ata Summary and Descriptive Statistics .............................................................9 3.1 Why Do We Collect Data? ................................................................................. 9 3.2 Why Do We Need Statistics? .............................................................................. 9 3.3 What Questions Do We Hope to Address With Our Statistical Analysis? ...... 10 3.4 How Do We Graphically Summarize Data? ..................................................... 11 3.4.1 Scatterplots ............................................................................................ 11 3.4.2 Time Series ........................................................................................... 11 3.4.3 Box-and-Whisker Plots ........................................................................ 12 3.4.4 Histogram ............................................................................................. 13 3.5 General Approach to Statistical Analysis .......................................................... 17 3.6 Descriptive Statistics ......................................................................................... 20 3.6.1 Measures of Central Tendency .............................................................. 21 3.6.2 Measures of Variability .......................................................................... 22 4. Assuming a Probability Model From the Sample Data ......................................... 25 4.1 The Standard Normal Distribution ................................................................... 29 4.2 The Normal Distribution and Sample Mean..................................................... 32 4.3 Confidence Interval for the Sample Mean ........................................................ 33 4.4 The t Distribution ............................................................................................. 36 4.5 Confidence Interval Using t Distribution........................................................... 38 5. Statistical Inference ........................................................................................... 41 5.1 Comparison of Population Means ..................................................................... 41 5.1.1 The t Test .............................................................................................. 42 5.1.1.1 Hypothesis Testing ................................................................. 42 5.1.1.2 Applying the t Test ................................................................. 43 5.1.1.3 Unpaired t Test ....................................................................... 44 5.1.1.4 Paired t Test ............................................................................ 49 5.1.1.5 Example of a Biomedical Engineering Challenge .................. 50 vii 5.2 Comparison of Two Variances ........................................................................... 54 5.3 Comparison of Three or More Population Means ............................................ 59 5.3.1 One-Factor Experiments ....................................................................... 60 5.3.1.1 Example of Biomedical Engineering Challenge ..................... 60 5.3.2 Two-Factor Experiments ....................................................................... 69 5.3.3 Tukey’s Multiple Comparison Procedure .............................................. 73 6. Linear Regression and Correlation Analysis ........................................................ 75 7. Power Analysis and Sample Size ......................................................................... 81 7.1 Power of a Test .................................................................................................. 82 7.2 Power Tests to Determine Sample Size ............................................................. 83 8. Just the Beginning ............................................................................................. 87 Bibliography .............................................................................................................. 91 Author Biography ...................................................................................................... 93