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Introduction To

Biostatistics

Text Book : Basic Concepts andMethodology for the Health

Sciences 1


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Introduction To

Biostatistics


Sciences 2


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Key words :

Statistics , data , Biostatistics,

Variable ,Population ,Sample


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Statistics is a field of study concernedwith1-collection, organization,

summarization and analysis of data.2- drawing of inferences about a body ofdata when only a part of the data isobserved.Statisticians try to interpret andcommunicate the results to others.


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The tools of statistics are employed inmany fields:business, education, psychology,agriculture, economics, etc.When the data analyzed are derived fromthe biological science and medicine,we use the term biostatistics to

distinguish this particular application ofstatistical tools and concepts.


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The raw material of Statistics is data. We may define data as figures. Figuresresult from the process of counting orfrom taking a measurement. For example: - When a hospital administrator countsthe number of patients (counting). - When a nurse weighs a patient

(measurement)


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We search for suitable data to serve as theraw material for our investigation.Such data are available from one or moreof the following sources:1-Routinely kept records.For example:- Hospital medical records containimmense amounts of information onpatients.- Hospital accounting records contain awealth of data on the facilitys business- activities.


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* Sources of Data:


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2- External sources.The data needed to answer a question may alreadyexist in the form ofpublished reports, commercially available databanks, or the research literature, i.e. someone elsehas already asked the same question.


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3- Surveys:The source may be a survey, if the data needed isabout answering certain questions.For example:If the administrator of a clinic wishes to obtaininformation regarding the mode of transportation

used by patients to visit the clinic,then a survey may be conducted amongpatients to obtain this information.


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4- Experiments.Frequently the data needed to answera question are available only as theresult of an experiment.For example:

If a nurse wishes to know which of severalstrategies is best for maximizing patientcompliance,she might conduct an experiment in whichthe different strategies of motivatingcompliance

are tried with different patients.Text Book : Basic Concepts and

Methodology for the HealthSciences 10


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It is a characteristic that takes on differentvalues in different persons, places, orthings.For example:- heart rate,- the heights of adult males,- the weights of preschool children,- the ages of patients seen in a dental

clinic.

Text Book : Basic Concepts and



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s o var antitativeQualitati

Quantitative VariablesIt can be measuredin the usual sense.For example:- the heights ofadult males,- the weights ofpreschool children,- the ages ofpatients seen in a- dental clinic.



Qualitative VariablesMany characteristics arenot capable of beingmeasured. Some of themcan be ordered orranked.For example:

- classification of people intosocio-economic groups,- social classes based onincome, education, etc.


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uan a veiscreteContinuoA discrete variableis characterized bygaps or interruptionsin the values that itcan assume.For example:- The number of dailyadmissions to ageneral hospital,- The number ofdecayed, missing orfilled teeth per child- in an- elementary- school. Text Book : Basic Concepts andMethodology for the HealthSciences 13

A continuous variablecan assume any value within aspecified relevant interval ofvalues assumed by the variable.For example:- Height,

- weight,- skull circumference.No matter how close together the

observed heights of twopeople, we can find anotherperson whose height fallssomewhere in between.


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It is the largest collection of values of arandom variable for which we have aninterest at a particular time.For example:The weights of all the children enrolled ina certain elementary school.Populations may be finite or infinite.




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* A sample:It is a part of a population.For example:The weights of only a fraction ofthese children.




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Question (6) Page 17 Question (7) Page 17

Situation A , Situation B




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Strategies for understanding the meanings ofData


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Key words

frequency table, bar chart ,range

width of interval ,mid-intervalHistogram , Polygon




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Example:Suppose that we take asample of size 16 fromchildren in a primary school

and get the following dataabout the number of theirdecayed teeth,

3,5,2,4,0,1,3,5,2,3,2,3,3,2,4,1

To construct a frequency

table:1- Orderthe values from thesmallest to the largest.

0,1,1,2,2,2,2,3,3,3,3,3,4,4,5,5

2- Count how many

numbers are the same.

Relative

FrequencyFrequencyNo. of

decayed

teeth

0.0625

0.125

0.25

0.31250.125

0.125

1

2

4

52

2

0

1

2

34

5

116Total


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Number of decayed teeth

5.004.003.002.001.00.00

6

5

4

3

2

1

0

22

5

4

2

1

Text Book : Basic Concepts andMethodology for the Health Sciences 20

We can representthe above simplefrequency tableusing the bar

chart.


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Forlarge samples, we cant use the simple frequency table

to represent the data.We need to divide the data into groups orintervals or

classes.

So, we need to determine:

1- The number of intervals (k).Too few intervals are not good because information will be

lost.

Too many intervals are not helpful to summarize the data.

A commonly followed rule is that 6 k 15,or the following formula may be used,

k = 1 + 3.322 (log n)




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2- The range (R).It is the difference between the largest and thesmallest observation in the data set.

3- The Width of the interval (w).Classintervals generally should be of the samewidth. Thus, if we want k intervals, then w is

chosen such thatw R / k.




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Example:Assume that the number of observationsequal 100, thenk = 1+3.322(log 100)= 1 + 3.3222 (2) = 7.6 8.Assume that the smallest value = 5 and the largestone of the data = 61, thenR = 61 5 = 56 andw = 56 / 8 = 7.To make the summarization more

comprehensible, the class width may be5 or 10 or the multiples of 10.




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We wish to know how many class interval to have in

the frequency distribution of the data in Table1.4.1 Page 9-10 of ages of 189 subjects whoParticipated in a study on smoking cessation

Solution : Since the number of observations

equal 189, then k = 1+3.322(log 169) = 1 + 3.3222 (2.276) 9, R = 82 30 = 52 and w = 52 / 9 = 5.778 It is better to let w = 10, then the intervals will be in the form:




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FrequencyClass interval

1130 39

4640 49

7050 59

4560 69

1670 79

180 89189Total


Sum of frequency

=sample size=n

The C m lati e F eq enc


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The Cumulative Frequency:

It can be computed by adding successivefrequencies.

The Cumulative Relative Frequency:

It can be computed by adding successive relativefrequencies.

TheMid-interval:It can be computed by adding the lower bound ofthe interval plus the upper bound of it and then

divide over 2.


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Cumulative

Relative

Frequency

Relative

Frequency

R.f

Cumulative

Frequency

Frequency

Freq (f)

Mid

interval

Class

interval

0.05820.0582111134.530 39

-0.2434574644.540 49

0.6720-127-54.550 59

0.91010.2381-45-60 690.99480.08471881674.570 79

10.0053189184.580 89

1189Total Text Book : Basic Concepts andMethodology for the Health Sciences 27

R.f= freq/n


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From the above frequency table, complete the tablethen answer the following questions:

1-The number of objects with age less than 50years ?

2-The number of objects with age between 40-69years ?

3-Relative frequency of objects with age between70-79 years ?

4-Relative frequency of objects with age more than

69 years ? 5-The percentage of objects with age between 40-

49 years ?




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6-The percentage of objects with age less than 60years ?

7-The Range (R) ?

8- Number of intervals (K)?

9- The width of the interval ( W) ?




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To draw the histogram, the true classes limits should be used. Theycan be computed by subtracting 0.5 from the lower limit and adding0.5 to the upper limit for each interval.

FrequencyTrue class limits

1129.5


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0

10

20

30

40

50

60

70

80

34.5 44.5 54.5 64.5 74.5 84.5




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Pages : 31 34 Questions: 2.3.2(a) , 2.3.5 (a)

H.W. : 2.3.6 , 2.3.7(a)




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key words:

Descriptive Statistic, measure of centraltendency ,statistic, parameter, mean (),median, mode.




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A Statistic:It is a descriptive measure computed from the dataof a sample.A Parameter:It is aa descriptive measure computed from the dataof a population.Since it is difficult to measure a parameter fromthe population, a sample is drawn of size n,

whose values are 1 , 2 , , n. From this data,we measure the statistic.Text Book : Basic Concepts and



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A measure of central tendency is a measure whichindicates where the middle of the data is.The three most commonly used measures ofcentral tendency are:The Mean, the Median, and the Mode.The Mean:It is the average of the data.



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The Population Mean: = which is usually unknown, then we use thesample mean to estimate or approximate it.The Sample Mean:

=

Example:Here is a random sample of size 10 of ages, where 1 = 42, 2 = 28, 3 = 28, 4 = 61, 5 = 31, 6 = 23, 7 = 50, 8 = 34, 9 = 32, 10 = 37.

= (42 + 28 + + 37) / 10 = 36.6x

x


1

N

i

i

N

X

1

n

i

i

n

x


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Properties of the Mean: Uniqueness.For a given set of data there isone and only one mean. Simplicity. It is easy to understand and tocompute. Affected by extreme values. Since allvalues enter into the computation.Example: Assume the values are 115, 110, 119, 117, 121and 126. The mean = 118.But assume that the values are 75, 75, 80, 80 and 280. Themean = 118, a value that is not representative of the set

of data as a whole.Text Book : Basic Concepts and



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The Median:When ordering the data, it is the observation that dividethe set of observations into two equal parts such that half

of the data are before it and the other are after it.* If n is odd, the median will be the middle of observations.It will be the (n+1)/2 th ordered observation.When n = 11, then the median is the 6th observation.* If n is even, there are two middle observations. Themedian will be the mean of these two middleobservations. It will be the (Xn/2+ X(n/2+1) )/2orderedobservation.When n = 12, then the median is the 6.5th observation,

which is an observation halfway between the 6th and 7thordered observation.




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Example:For the same random sample, the orderedobservations will be as:23, 28, 28, 31, 32, 34, 37, 42, 50, 61.Since n = 10, then the median is the 5.5thobservation, i.e. = (32+34)/2 = 33.Properties of the Median: Uniqueness.For a given set of data there isone and only one median. Simplicity. It is easy to calculate. It is not affected by extreme values asis the mean.




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The Mode:It is the value which occurs most frequently.If all values are different there is no mode.Sometimes, there are more than one mode.Example:For the same random sample, the value 28 is

repeated two times, so it is the mode.Properties of the Mode: Sometimes, it is not unique. It may be used for describing qualitative data.




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key words:

Descriptive Statistic, measure ofdispersion , range ,variance, coefficient ofvariation.




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A measure of dispersion conveys informationregarding the amount of variability present in aset of data.

Note:

1. If all the values are the same There is no dispersion .

2. If all the values are different

There is a dispersion:

3.If the values close to each other

The amount of Dispersionsmall.

b) If the values are widely scattered

The Dispersion is greater.Text Book : Basic Concepts and



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** Measures of Dispersion are :1.Range (R).

2. Variance.

3. Standard deviation.

4.Coefficient of variation (C.V).




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Range =Largest value- Smallest value =

Note: Range concern only onto two values

Example 2.5.1 Page 40: Refer to Ex 2.4.2.Page 37 Data: 43,66,61,64,65,38,59,57,57,50.

Find Range? Range=66-38=28



SLxx


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It measure dispersion relative to the scatter of thevalues a bout there mean.

a) Sample Variance ( ) : ,where is sample mean Example 2.5.2 Page 40: Refer to Ex 2.4.2.Page 37 Find Sample Variance of ages , = 56 Solution: S2= [(43-56) 2 +(66-43) 2+..+(50-56) 2 ]/ 10

= 900/10 = 90

x

x


2S

1

)(1

2

2

n

xx

S

n

i

i


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b)PopulationVariance( ) : where , is Population mean3.The Standard Deviation: is the square root of variance=a) Sample Standard Deviation = S =

b)Population Standard Deviation = =



2

N

x

N

i

i

1

2

2

)(

Varince

2S

2


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Is a measure use to compare the dispersion intwo sets of data which is independent of theunit of the measurement .

where S: Sample standard

deviation. : Sample mean.



)100(.X

SVC

X


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Suppose two samples of human males yield thefollowing data:

Sampe1 Sample2

Age 25-year-olds 11year-oldsMean weight 145 pound 80 pound

Standard deviation 10 pound 10 pound




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We wish to know which is more variable. Solution:

c.v (Sample1)= (10/145)*100= 6.9

c.v (Sample2)= (10/80)*100= 12.5

Then age of 11-years old(sample2) is morevariation




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Pages : 52 53

Questions: 2.5.1 , 2.5.2 ,2.5.3

H.W. : 2.5.4 , 2.5.5, 2.5.6, 2.5.14

* Also you can solve in the review questionspage 57:

Q: 12,13,14,15,16, 19


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