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Medical StatisticsMedical Statistics

Tao YuchunTao Yuchun

Practice 1Practice 1

http://cc.jlu.edu.cn/ms.html

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Review Review

1.1. Population and Sample

•Randomization

2.2. Probability and Frequency

I.I. Basic conceptsBasic concepts

3.3. Parameter and Statistic

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II. Types of dataII. Types of data

1.1. Numerical Variable (Measurement Data)

•quantitatively

2.2. Categorical Variable (Enumeration Data)

•qualitatively •Nominal Variable •Count Data

3.3. Ordinal variable ( Rank data )

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III. The Basic Steps of Statistical WorkIII. The Basic Steps of Statistical Work

1.1. Design of study Design of study

2.2. Collection of data Collection of data

3.3. Data SortingData Sorting

4.4. Data Analysis Data Analysis

• Descriptive statistics

• Inferential statistics

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IV. Statistical Description for MeasurementIV. Statistical Description for Measurement

DataData

1.1 1.1 Frequency Distribution

(1)(1) Steps of establishing a frequency tableSteps of establishing a frequency table

((2)2) Frequency plot ---histogram Frequency plot ---histogram

((3)3) The use of frequency table The use of frequency table

• central tendency

• measure of dispersion

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1.2 1.2 Measures for Average ★

(1)(1) Arithmetic Mean (Arithmetic Mean (meanmean))

μ X

n

X

n

X

n

XXXX

n

ii

n

121 ...

•Suitable to symmetric distribution.

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(2)(2) Geometric Mean (Geometric Mean (GG))

)lg

(lg)lg...lglg

(lg 1211

21

n

X

n

XXXG

XXXG

n

nn

•lg-1 =10x

•Suitable to positive skew distribution,

like geometric progression.

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(3)(3) Median (Median (MM))

a. For raw data

•Ranking the data, finding the middle value.

For odd number, it is; for even number, it is

mean of two middle values.

b. For frequency table

)2

( LM

fn

f

iLM

•Suitable to all kinds of data, but usually to

positive skew distribution.

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Add:Add: PercentilePercentile --- Px

P Li

fn x f

x

x

L ( % )

•Symmetric •Positive skew

1.3 1.3 Measures for variability ★

(1)(1) Range (Range (RR))

R = Maximum - Minimum

•Suitable to all kinds of data, but no useful.

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(2)(2) InterQuartile Range (InterQuartile Range (IQRIQR))

257513 PPQQIQR

•Suitable to all kinds of data, but usually skew

distribution.

(3)(3) Variance Variance andand Standard Deviation ( Standard Deviation (SS2 2 and and SS))

1

)( 22

n

XXS

1

/)(

1

)( 222

n

nXX

n

XXS

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•Suitable to symmetric distribution.

(4)(4) Coefficient of Variation (Coefficient of Variation (CVCV))

CVS

X 100%

• Comparison of the variation of two variables

with different dimensions oror bigger difference

of means .

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Calculative tools Calculative tools

I.I. Scientific calculatorScientific calculator

• The scientific calculator with statistical

function. (like CASIO fx-3600PV or CASIO fx-82TL)

• Calculative method is often:

Input all raw data, press the special

button under statistical mode, you will

get the result (like , S) directly. X

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II. Excel II. Excel ★

• Many statistical function.

• The macro of statistical analysis tool.

• Using any expression directly.

• Many statistical graphs.

•See the example (stat1(English).xls)

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III. Statistical softwareIII. Statistical software

• Professional statistical analysis tool.

• The special data management and

statistical analysis procedure.

• The special executive commands.

• Include almost all statistical methods.

• SAS, SPSSSPSS, Stata, BDMP, …

• If you want use it, you should have tolearn another lesson.

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Practice in class Practice in class Exercise 1Exercise 1: the blood-glucose(mmol/L) values from

12 randomly selected patients.

5.31, 6.12, 6.53, 6.53, 6.65, 6.66, 6.71, 6.93, 7.05,

7.15, 7.21, 7.35

Please calculate the arithmetic mean, geometric

mean and median; range, quartile range and standard

deviation.

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Exercise 2Exercise 2: the frequency table of latent period (day)

from 110 certain infectious disease patients.

(1) (2)

2~ 26 26 23.644~ 48 74 67.276~ 25 99 90.008~ 6 105 95.45

10~ 3 108 98.1812~14 2 110 100.00

total 110 － －

(4)=(3)/n

tab2 the frequency table of latent period (day) from some infectious disease patients

latentperiod

CumulativeFrequency(∑ f )frequency(f )

CumulativeFrequency(%)

(3)

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1) Please calculate the arithmetic mean, geometric mean and

median, which one better reflects the average level ?

2) Please calculate the range, quartile range and standard

deviation, which one better reflects the variation ?

Answer Answer

•See the Excel file (practice1key.xls)

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HomeworkHomework There are raw data of temperature （℃） for 102 female

students from certain college(see below).

37.05 36.90 37.20 37.10 37.00 36.85 36.85 37.40 37.05 36.8537.20 37.00 37.00 36.90 36.85 37.15 37.10 36.80 37.40 37.4037.30 37.40 37.25 37.10 37.10 36.85 36.80 37.05 37.00 36.9037.35 37.25 36.95 37.05 36.80 37.15 37.05 37.15 37.15 37.2537.50 37.00 37.35 37.05 37.10 37.00 37.05 37.35 37.10 37.1037.25 37.20 36.95 37.00 37.10 37.00 36.90 37.05 37.00 36.9036.55 36.80 37.05 36.60 37.05 37.20 36.70 37.20 36.90 37.3036.85 36.70 37.15 37.10 37.05 36.95 37.25 36.90 37.05 36.7536.90 36.85 36.70 36.95 37.15 36.90 37.05 36.90 37.35 37.0537.05 37.00 37.35 37.10 37.20 36.65 36.65 36.90 36.95 36.9036.70 36.80

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CC

1) Please work out a frequency table and a histogram.

2) Please calculate the arithmetic mean, median, quartile

range, standard deviation and coefficient of variation.

(http://en.wikipedia.org/wiki/Great_Wall_of_China)

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CASIO

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CASIO fx-82TL

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