© 2003-09 The Catholic University of AmericaDept of Biomedical Engineering

ENGR 104: Lecture 2Statistical Analysis Using Matlab

Lecturers:

Dr. Binh Tran

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© 2003-09 The Catholic University of AmericaDept of Biomedical Engineering

Definitions

Statistics: Science that deals with collection, tabulation, analysis, and interpretation of data (qualitative or quantitative) in order to make objective decisions and solve problems.

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© 2003-09 The Catholic University of AmericaDept of Biomedical Engineering

Statistical Measures of Data

Average/(Arithmetic) Mean: The average value of all observations

Median: Middle observation Mode: Value where highest number of observations

occurs Range: Difference between max and min values (rough

measure of data dispersion) Standard Deviation: Special form of average

deviation from the Mean

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© 2003-09 The Catholic University of AmericaDept of Biomedical Engineering

Average/(Arithmetic) Mean

Mean: Mean:

Advantage:Advantage: Easy to Easy to computecompute

Disadvantage: Disadvantage: Distorted Distorted by extreme values by extreme values (outliers)(outliers)

n

XX

n

i 1

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© 2003-09 The Catholic University of AmericaDept of Biomedical Engineering

Median: Middle ObservationMedian: Middle Observation

Definition:Definition: Median value is Median value is middle itemmiddle item when items are when items are arranged according to sizearranged according to size

Advantage:Advantage: Not distorted by Not distorted by outliersoutliers

DisadvantageDisadvantage::Must be Must be rearranged according to sizerearranged according to size

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© 2003-09 The Catholic University of AmericaDept of Biomedical Engineering

Mode & RangeMode & Range ModeMode: : Most common value occurring in set of dataMost common value occurring in set of data

AdvantageAdvantage: : Most typicalMost typical value and independent of the value and independent of the extreme itemsextreme items

DisadvantageDisadvantage: : If values are not repeated and amount of If values are not repeated and amount of data is small, then the significance of the mode is limiteddata is small, then the significance of the mode is limited

RangeRange: : Difference between min/max values in seriesDifference between min/max values in series AdvantageAdvantage: : Easy to compute & simplest measure of Easy to compute & simplest measure of

dispersiondispersion DisadvantageDisadvantage: : No info regarding distribution of dataNo info regarding distribution of data

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© 2003-09 The Catholic University of AmericaDept of Biomedical Engineering

Standard Deviation

n

XXn

i 1

2

Definition: Definition:

Advantage: Advantage: Show the Show the degree of dispersion and degree of dispersion and variability variability

Disadvantage: Disadvantage: Not trivial Not trivial to computeto compute

2 = 95.5%

1 = 68.3%

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© 2003-09 The Catholic University of AmericaDept of Biomedical Engineering

Presentation of DataPresentation of Data

Frequency Plot: Histogram of # of occurrences. Curve Fitting: Polynomial fitting of experimental

data Time Series Analysis or Trend Plots::

– Analysis of trends in data

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© 2003-09 The Catholic University of AmericaDept of Biomedical Engineering

Data PresentationData Presentation::Frequency Plot or HistogramFrequency Plot or Histogram

Definition:Definition: Graphic Graphic representation of representation of frequency distributionfrequency distribution

AdvantageAdvantage: Quick : Quick visualization of datavisualization of data

Disadvantage:Disadvantage: Difficult to Difficult to analyze data, unless data is analyze data, unless data is grouped systematicallygrouped systematically

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© 2003-09 The Catholic University of AmericaDept of Biomedical Engineering

Data PresentationData Presentation:: Polynomial Curve Fitting

Best fit curve for dataBest fit curve for data Polynomial Equation:Polynomial Equation:

AdvantageAdvantage: Large set of data : Large set of data can be represented by a known can be represented by a known equationequation

DisadvantageDisadvantage: m>2, process : m>2, process becomes very laboriousbecomes very laborious

max

ma

mxamxay

1

110

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© 2003-09 The Catholic University of AmericaDept of Biomedical Engineering

Data PresentationData Presentation:: Ex:Polynomial Curve Fitting

21

12

0axaxay

Example: Example:

Where, Where,

4165.582

1411.21

0155.00

a

a

a

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© 2003-09 The Catholic University of AmericaDept of Biomedical Engineering

Data PresentationData Presentation:: Time Series (Trend) AnalysisTime Series (Trend) Analysis

Definition:Definition: Graphic Graphic representation consisting of representation consisting of description & measurement of description & measurement of various changes or movements of various changes or movements of data during a period of time.data during a period of time.

Types of trend measurementTypes of trend measurement• Semi-averageSemi-average• Moving averageMoving average

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© 2003-09 The Catholic University of AmericaDept of Biomedical Engineering

Data PresentationData Presentation:: Semi-AverageSemi-Average

Definition:Definition: Split data set Split data set into two equal parts; take into two equal parts; take average; draw average; draw straight linestraight line through two average pointsthrough two average points

Advantage:Advantage: Very simple to Very simple to calculatecalculate

Disadvantage: Disadvantage: Only gross Only gross representation of data trendsrepresentation of data trends

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© 2003-09 The Catholic University of AmericaDept of Biomedical Engineering

Data PresentationData Presentation:: Moving AverageMoving Average

Definition:Definition: A series of A series of successive group averages successive group averages

Advantage:Advantage: Simple to calculate; Simple to calculate; more accurate representation of more accurate representation of local changeslocal changes

Disadvantage:Disadvantage: Cannot be Cannot be brought up to datebrought up to date

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© 2003-09 The Catholic University of AmericaDept of Biomedical Engineering

Data PresentationData Presentation::Ex: Three-Item Moving AverageEx: Three-Item Moving Average

Values Total Moving Average

3

5 15 5.00

7 22 7.33

10 29 9.67

12 36 12.00

14 41 13.67

15 46 15.33

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Univ

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© 2003-09 The Catholic University of AmericaDept of Biomedical Engineering

Questions ?Questions ?

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Univ

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© 2003-09 The Catholic University of AmericaDept of Biomedical Engineering

Lab #2: Telemedicine Analysis

Lab Report Due: 9/29 Download Telemedicine data for 6

study subjects (txt files)– http://faculty.cua.edu/tran/engr104/Datafiles.htm

Using Matlab, statistically analyze the data and report your observations

See handout

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© 2003-09 The Catholic University of AmericaDept of Biomedical Engineering

LAB QUESTIONS: Is there a noticeable trend/pattern in the data? Across the

datasets? Is there a correlation between the blood glucose and high blood

pressure measure over time? Examine this using a time-series analysis (30-day epochs). Explain

your findings. Use curve fitting techniques to estimate the regression line best

fitting the data for each subject. 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?