Instructor:Yves ChabalBME 101 Head TA:Mehmet KayaBME 118 Lecture in B-120 (Eng.) Labs:Weeks 1, 2, 3, 4, 10,12,13: BME 104 Week 5, 6, 7: Engineering Weeks 8, 9, 11: Engineering A209 Welcome to 125:315 Measurements and Analysis Laboratory

315: Measurements and Analysis Laboratory Monday Tuesday Wednesday Thursday Friday Lecture Lab #5 Lab #1 Lab #2 Lab #3 Lab #4

Purpose of the course 1.Consolidation of experimental methodology  Mandatory lab report for each lab (55% of grade) 2. Exposure to BME topics and faculty members  Mandatory attendance of lectures (15% of grade) Final exam will test knowledge and experimental methodology (30% of grade) learned over the whole semester

Week 1 (9/6/05)IntroductionY. Chabal Week 2 (9/13/05)ECGJ. Semmlow Week 3 (9/20/05)Evoked PotentialsJ. Semmlow Week 4 (9/27/05)Respiratory PhysiologyJ. Semmlow Week 5 (10/4/05)Biomechanical TestingN. Langrana Week 6 (10/11/05)Biomedical FractureA. Mann Week 7 (10/18/05)Soft Tissue MechanicsD. Shreiber Week 8 (10/25/05)Protein AnalysisC. Roth Week 9 (11/1/05)Cell Growth and ImagingP. Moghe Week 10 (11/8/05)Renal PhysiologyT. Shinbrot Week 11 (11/15/05)Gene TransferC. Roth Week 12 (11/29/05)Cardiac PhysiologyS. Dunn Week 13 (12/6/05)Neuro PhysiologyW. Craelius Exam (12/21/05)Y. Chabal Schedule

Expectations Prior to new lecture/lab (i.e. before Tuesday morning): Download from website ( ): Background material on the particular lecture Lecture notes Lab write up Read background material and lab write up Copy lecture notes and lab write up (to take to lecture and lab) Be ready for a short quiz at beginning of each lab Perform lab completely (consider extra credit at least one time) Write lab report independently following the required format (turn within one week of your lab period)

Lab report Note: important that each lab report represents 100% personal effort (wording, description, analysis). Each students must go through complete exercise, even when working in pairs. Critical thinking and creativity will be rewarded. The mandatory format of the report is: Introduction: Motivate lab in your own words (personal assessment of topic importance); Give justification for use of method used in the lab Description of measurements: Describe experimental protocol Method and care taken to perform lab Results: Data (Objective summary of results) Focus on organization of data Analysis Significance of results, how statistical analysis can help? What conclusions can or cannot be derived and why? Summary & conclusions References (quote all sources used, including web sources, no plagiarism)

Exam The final exam will include: Questions on big picture and associated basic knowledge (back of the envelope calculations, quantities and units, ….) Questions drawn from first two slides of each lectures Topical questions from main points of each lecture To test knowledge of subject matter in more detail Lab questions to test understanding of measurements e.g. why and how measurements are done, derivation of cause-effect, possibly some details on analysis Test of analytical skills Give set of data (observations), derive meaningful conclusions Design of experiment (extra credit) Pose problem and ask to design an experiment to solve it

Lab #1: Measurements and Error Analysis Experimental measurements only have a meaning with an error bar to test a theory (e.g. light deflection by sun) to answer a practical question (e.g. materials problem) Types of errors: random errors unpredictable statistical fluctuations (temp., voltage, etc) equally likely to be positive or negative can be made smaller by taking more data points ************* precision: small random errror ***************** systematic errors always present during measurements, with a definite sign due to something different from what is assumed (e.g. slow timer) cannot be made smaller by increasing the number of data points ************* accuracy: small systematic error *****************

Statistical treatment of data Given a set of measurements x 1, x 2, x 3, ….., x N the mean (average) is: To estimate the error in the mean, we need to introduce the idea of a distribution, or histogram: # readings in interval 0.02

Distribution function Definition: Curve that would be obtained for a very large (infinite) number of measurements (interval is very small) The distribution function, f(x), is such that: f(x) dx is the fraction of N readings that lie in the interval x to x+dx i.e., f(x) is the probability that a single measurement taken at random will lie in the interval x to x+dx By definition, And the mean (the average over all measurements) is: X 

Error The error in a measurement with value x is: x - or x - X And the standard deviation of the distribution is s where: or for a finite set of measurements: The root-mean-square, or standard deviation is therefore:

Standard error in the mean The standard deviation of a distribution of the means pf sets of measurements, each set containing the same number N o single measurements is: Where S represents the error in a single measurement and S m the error in the mean of N measurements.

The Gaussian Distribution For a number of reasons, the function has most of properties of a distribution of measurements with random errors: 1.It is symmetric about X 2.It has its maximum value at X 3.It tends rapidly to zero as  x- X  becomes large compare with . Note: it is normalized, i.e. its integral = 1 its standard deviation is  the points of inflexion occur at x=  . Probability: 1  (68%), 2  (95%)

Propagation of Errors Important to estimate the error in a quantity that is a function of one or several measurable quantities, each with some error or uncertainty Example A.Volume of Cylinder measure r, h V =  r 2 h V +  V =  (r +  r) 2 (h +  h) All terms with  2 are small, so…. V +  V =  r 2 h + 2  rh  r +  r 2  h + …  V = 2  rh  r +  2  h  V = + where and

Propagation of errors In general, for independent random errors: if q = x +… +Z – (u+…+w ), then  q = if then and if q = x n, then For a function of a single variable, q=q(x) then

Laboratory this week: Measurement and uncertainty Measure your reaction time to a stimulus (set of data) Plot a histogram Produce a distribution Analyze using a Gaussian distribution approximation Derive meaningful conclusions about the measurements and the ability to distinguish reaction times

References: “Practical Physics”, G.L. Squires, Cambridge University Press (1968, 4 th edition, 2001) “An introduction to Error Analysis”, John R. Taylor, University Science Books (1982, 2 nd edition 1997)