1. © 2003-09 The Catholic University of America Dept of Biomedical Engineering ENGR 104: Lecture 2 Statistical Analysis Using Matlab Lecturers: Dr. Binh Tran

2. ENGR 104: Intro to Engineering Lab Dept of Biomedical Engineering, Catholic University © 2003-09 The Catholic University of America Dept of Biomedical Engineering Definitions n Statistics : Science that deals with collection, tabulation, analysis, and interpretation of data (qualitative or quantitative) in order to make objective decisions and solve problems.

3. ENGR 104: Intro to Engineering Lab Dept of Biomedical Engineering, Catholic University © 2003-09 The Catholic University of America Dept of Biomedical Engineering Statistical Measures of Data n Average/(Arithmetic) Mean : The average value of all observations n Median : Middle observation n Mode : Value where highest number of observations occurs n Range : Difference between max and min values (rough measure of data dispersion) n Standard Deviation : Special form of average deviation from the Mean

4. ENGR 104: Intro to Engineering Lab Dept of Biomedical Engineering, Catholic University © 2003-09 The Catholic University of America Dept of Biomedical Engineering Average/(Arithmetic) Mean n Mean: n Advantage: Easy to compute n Disadvantage: Distorted by extreme values (outliers)

5. ENGR 104: Intro to Engineering Lab Dept of Biomedical Engineering, Catholic University © 2003-09 The Catholic University of America Dept of Biomedical Engineering Median: Middle Observation n Definition: Median value is middle item when items are arranged according to size n Advantage: Not distorted by outliers n Disadvantage :Must be rearranged according to size

6. ENGR 104: Intro to Engineering Lab Dept of Biomedical Engineering, Catholic University © 2003-09 The Catholic University of America Dept of Biomedical Engineering Mode & Range n Mode : Most common value occurring in set of data n Advantage : Most typical value and independent of the extreme items n Disadvantage : If values are not repeated and amount of data is small, then the significance of the mode is limited n Range : Difference between min/max values in series n Advantage : Easy to compute & simplest measure of dispersion n Disadvantage : No info regarding distribution of data

7. ENGR 104: Intro to Engineering Lab Dept of Biomedical Engineering, Catholic University © 2003-09 The Catholic University of America Dept of Biomedical Engineering Standard Deviation n Definition: n Advantage: Show the degree of dispersion and variability n Disadvantage: Not trivial to compute 2  = 95.5% 1  = 68.3%

8. ENGR 104: Intro to Engineering Lab Dept of Biomedical Engineering, Catholic University © 2003-09 The Catholic University of America Dept of Biomedical Engineering Presentation of Data n Frequency Plot: Histogram of # of occurrences. n Curve Fitting: Polynomial fitting of experimental data n Time Series Analysis or Trend Plots:: – Analysis of trends in data

9. ENGR 104: Intro to Engineering Lab Dept of Biomedical Engineering, Catholic University © 2003-09 The Catholic University of America Dept of Biomedical Engineering Data Presentation: Frequency Plot or Histogram n Definition: Graphic representation of frequency distribution n Advantage : Quick visualization of data n Disadvantage: Difficult to analyze data, unless data is grouped systematically

10. ENGR 104: Intro to Engineering Lab Dept of Biomedical Engineering, Catholic University © 2003-09 The Catholic University of America Dept of Biomedical Engineering Data Presentation: Data Presentation: Polynomial Curve Fitting n Best fit curve for data n Polynomial Equation: n Advantage : Large set of data can be represented by a known equation n Disadvantage : m>2, process becomes very laborious

11. ENGR 104: Intro to Engineering Lab Dept of Biomedical Engineering, Catholic University © 2003-09 The Catholic University of America Dept of Biomedical Engineering Data Presentation: Data Presentation: Ex:Polynomial Curve Fitting n Example: n Where,

12. ENGR 104: Intro to Engineering Lab Dept of Biomedical Engineering, Catholic University © 2003-09 The Catholic University of America Dept of Biomedical Engineering Data Presentation: Time Series (Trend) Analysis n Definition: Graphic representation consisting of description & measurement of various changes or movements of data during a period of time. n Types of trend measurement Semi-averageSemi-average Moving averageMoving average

13. ENGR 104: Intro to Engineering Lab Dept of Biomedical Engineering, Catholic University © 2003-09 The Catholic University of America Dept of Biomedical Engineering Data Presentation: Semi-Average n Definition: Split data set into two equal parts; take average; draw straight line through two average points n Advantage: Very simple to calculate n Disadvantage: Only gross representation of data trends

14. ENGR 104: Intro to Engineering Lab Dept of Biomedical Engineering, Catholic University © 2003-09 The Catholic University of America Dept of Biomedical Engineering Data Presentation: Moving Average n Definition: A series of successive group averages n Advantage: Simple to calculate; more accurate representation of local changes n Disadvantage: Cannot be brought up to date

15. ENGR 104: Intro to Engineering Lab Dept of Biomedical Engineering, Catholic University © 2003-09 The Catholic University of America Dept of Biomedical Engineering Data Presentation: Ex: Three-Item Moving Average ValuesTotalMoving Average 3 5155.00 7227.33 10299.67 123612.00 144113.67 154615.33 17

16. ENGR 104: Intro to Engineering Lab Dept of Biomedical Engineering, Catholic University © 2003-09 The Catholic University of America Dept of Biomedical Engineering Questions ?

17. ENGR 104: Intro to Engineering Lab Dept of Biomedical Engineering, Catholic University © 2003-09 The Catholic University of America Dept of Biomedical Engineering Lab #2: Telemedicine Analysis n Lab Report Due: 9/29 n Download Telemedicine data for 6 study subjects (txt files) –http://faculty.cua.edu/tran/engr104/Datafiles.htm n Using Matlab, statistically analyze the data and report your observations n See handout

18. ENGR 104: Intro to Engineering Lab Dept of Biomedical Engineering, Catholic University © 2003-09 The Catholic University of America Dept of Biomedical Engineering LAB QUESTIONS: n Is there a noticeable trend/pattern in the data? Across the datasets? n Is there a correlation between the blood glucose and high blood pressure measure over time? n Examine this using a time-series analysis (30-day epochs). Explain your findings. n Use curve fitting techniques to estimate the regression line best fitting the data for each subject. n Is there a difference between the effects of tele-monitoring on diabetics vs. hypertensives (i.e. those with high blood pressure)? Explain. –Is there any useful information in the histogram?