Biostatistics

Dr. Arshad Sabir A.P2009

Session-I

04/08/23 1

Biostatistics

Statistics: Science of figure. Science concerned with techniques or methods of collection, classification, summarization, interpretation of data, drawing inference , testing of hypotheses and making recommendations etc.

Biostatistics: when tools of statistics are applied to data derived from biological sciences as medicine is known as biostatistics .

Health statistics--Medical Statistics--Vital statistics

04/08/23 2

3

Types of Biostatistics

1. Descriptive Statistics: /deductive statistics merely describe, organize or summarize data. It refers to actual data available. Blood pressure pattern of class students , disease prevalence in the community, a case report .

2. Inferential statistics: Involves deriving inference beyond the actual data….correlation of B.P with weights of the students, if any. Involves inductive reasoning like estimating whole class B.P by assessing B.P of a sample.

04/08/23

4

CHARACTISTICS OF STATISTICS

1. Statistics are aggregate facts 2. Statistics are affected by multiple factors/ variable.3. Statistics deals with facts which are numerically

measurable and expressible4. Statistics are measurable with a degree of accuracy5. Statistics are comparable and are capable of further

mathematical manipulation. 6. Statistics are collected with some objectives. 7. Statistical results are true only on the average or in long run not in strict sense (sample based estimate).8. Statistics provides only a tool for analysis and can not change actuality or true values.

04/08/23

5

Why we need statistics?

• Any science needs demands precision for its development, so does medical science.

• Clarity of judgment, right assessments and correct decision making

• For precision facts, observations or measurements have to be expressed in figures.

• When you can measure what you are speaking about and express it in numbers you know some thing other wise your knowledge is meager and of unsatisfactory kind. LORD KELVEIN

04/08/23

6

Why Biostatistics?• Every thing in medicine; be research,

Diagnosis ,treatment or public health depends upon counting and measurements. Testing hypothesis, spleen enlargement , High & low B.P, efficacy of a treatment or mortality pattern of a population.

• In nature Heights & weights of people, action of drugs etc vary. Extent of this variability in an attribute whether it is natural/ normal or not ( due to play of an external factor)is learnt by studying statistics as a science.

04/08/23

Variability Biological data (Quant. Or Quali.) is highly

variable. Ht. Wt. Hb. IQ. Behavior & effect of same drug in diff. pts etc. ………..Variability is a normal character.

Types or variability:1. Biological variability2. Real variability 3. Experimental Variability

04/08/23 7

8

How to measure? VARIABLE: A measurable quantity which varies from one

individual or object to another is called variable.• It is the characteristic or property of a person, object or

phenomenon which can take more than one value. • It is characteristic that takes on different values in

different persons , places or things.• A quantity that varies within limits

CONSTANT: a quantity that do not vary like “ g = 9.8” , “ π = 3.14“ etc. They do not require any statistical studies.

For a give distribution its summary values , mean, median, Mode, Range, MD, SD and SE, Correlation Coefficient

are also constant. 04/08/23

9

Uses of Biostatistics in medical sciences

1. To define limits of normality e.g. Weight, B.P, Gender, Pulse rate.

2. To compare certain attributes of the two different populations…..is the difference is normal / natural or by chance, or is due to play of some external factor.

3. To find difference b/w efficacy of two drugs or vaccine (is by chance or otherwise).

4. To study cause & effect relationship in disease causation. (obesity & CHD)

5. To establish sign symptoms of the diseases ( fever not cough, is significantly asso. with typhoid fever)

04/08/23

10

Biostatistics as science of figure (Public health)

1. What are leading causes of deaths2. What are common health problems 3. Whether a particular disease is decreasing or

increasing4. How is severity of a diseases.5. How a disease affects other persons6. Who are high risk groups, Conditions & Locations.7. What is productive power of a certain population8. What could be health needs of a certain community 9. How is health seeking attitude of a population10. How successful a health program is?

04/08/23

11

Basic Biostatical concepts & terms DATA: • A Collection of facts and figures• A set of values recorded on one or

more observational units• Any information as a fact or figure.• Numerical facts relating to any field

of study. • Data is a medium for expression of a

variable 04/08/23

12

Data types• Raw Data: First hand as such collected data

with out any treatment. A haphazard mass of accumulated facts.

• Processed data: Data after some mathematical or statistical treatment given to it. other types… NOIR

Qualitative / Categorical Quantitative / Numeric 04/08/23

13

Important concepts

Observation: An event and its measurement like Height (event) and its measurement (5.6 Feet), Gender-M/F

Observational unit: Source that gives the observations such as persons, Hospitals, patients.

Population: It is an entire group of people or the study elements – persons, things or measurements for which we have an interest at a particular time like all women of reproductive age, Serum cholesterol levels, Hb% etc. (Parameter)

Sample: It is subset of the population which comes under study. (statistic)

04/08/23

How to describe a Distribution!

• Measure of Central TendencyMeanMedian

Mode• Modes of Dispersion

Range Variance (Mean deviation) Standard DeviationCoefficient of Variation (CV)

04/08/23 14

MeanSum of all values () divided by total number of observations. It is denoted by x. (µ)

• Advantages– Easy to calculate – Contains more information– Amenable to most statistical treatments

• Disadvantages Influenced by extreme valuesMay not convey proper sense e.g. Mean No. of

children may turn out to be 5.7704/08/23 15

Calculation of MeanAverage income college office staff

1. 10,0002. 20,0003. 15,0004. 11,000 = Ʃ Xi-n / N

5. 16,000 158,000 / 10 = 15,800

6. 17,000 Mean = 15,800 7. 23,000 x = 15,8008. 24,0009. 13,00010. 9,000SUM= 158,00004/08/23 16

Effect of Extreme Values on Mean 1 10,000 10,0002 10,000 10,000 3 10,000 10,0004 10,000 10,0005 10,000 10,0006 15,000 15,0007 15,000 15,0008 16,000 16,0009 16,000 16,00010 20,000 600,00011 20,000 500,000Mean= ∑167,000/N ∑1,212,000 / N167,000/11 = 15,182 1,212,000/11 =

110,182

04/08/23 17

Median (positional average)

When the data is arranged in ascending or

descending order, the median is the value that

divides the data in two equal parts.

• Advantages

It is not influenced by extreme values

• Disadvantages

Not very precise measure

Not amenable to further statistical

evaluation

04/08/23 18

Calculation of Median

1. Arrange all values in Ascending or Descending order.

2. Add 1 to the number of observations. (n + 1 )

3. Divide by 2. ( n+1 / 2 )

4. The answer will be the number (serial number) of observation, which constitutes Median.

04/08/23 19

Effect of Extreme Values on Median 1 10,000 10,0002 10,000 10,000 3 10,000 10,0004 10,000 10,0005 10,000 10,0006 15,000 15,0007 15,000 15,0008 16,000 16,0009 16,000 16,00010 20,000 600,00011 20,000 500,000

Median = n+1/2 Median = n+1/2

11 + 1 /2 = 6th Value 11 + 1 /2 = 6th Value 6th Value = 15,000 6th Value =

15,000 04/08/23 20

MODE• It is most frequently occurring value in the

distribution. Example No. of T.B Pts seen in one month at private clinics in RWP.

• Data: (5 – 45 Pts in various clinics) • Pts f (clinics)

• 5-15 50 ( it is recorded 50 times)• 16-25 35• 26-35 28• 36-45 10 Mode is 50 ( frequently 5 to 15 pts of T.B are seen at private

clinic in Rawalpindi)

04/08/23 21

Mean is not sufficientSame Mean for 2 different populations

Group – 130 – 34 Years 0

35 – 39 Years 10

40 – 44 Years 20

45 – 49 Years 40

50 – 54 Years 20

55 – 59 Years 10

≥ 60 Years 0

Mean Age 45

Group – 230 – 34 Years 40

35 – 39 Years 10

40 – 44 Years 0

45 – 49 Years 0

50 – 54 Years 0

55 – 59 Years 10

≥ 60 Years40

Mean Age 45

04/08/23 22

Measures of Dispersions 1. Range: Difference b/w highest and lowest figures in

the given distribution. It consider only extreme value and not the values in between

2. Mean deviation: Average of all deviations from the arithmetic mean. (Variance, S2)

∑ (xi-n – x )2

= ---------------

n

It is actually average of all squared deviations and is of no practical use.

3. Standard Deviation. 4. Co efficient of Variation (CV) = SD/Mean x 100

04/08/23 23

Standard Deviation

• It is a measure, which describes how much individual measurements differ on average, from the mean.

• It expresses in quantitative terms the scatter of data around the mean.

• It is the most important measure of dispersion around the mean and forms the basis of most statistical analysis.

• It is denoted by (population) or SD (sample)

04/08/23 24

Calculation of Standard DeviationCalculate mean of the given distribution( Xi-n )Find difference of each individual observation from

the Mean (Deviation Score)

(xi-n – x )Square all the differences (deviations) (xi-n – x )2

Take sum of all squared differences ∑ (xi-n – x )2

Divide sum by total number of observation (n).to find average deviation

∑ (xi-n – x )2 / nTake square root of whole

√ ∑ (xi-n – x)2 / n-1 = SD04/08/23 25

Mean of Systolic Blood Pressure in 5 individuals

Observed Value(mm Hg)

Mean (mm Hg)

X

Deviation from mean (d)

Square of deviation(d)2

110 124 -14 196

116 124 -8 64

120 124 -4 16

130 124 +6 36

144 124 +20 Ʃ= 00 or 52 400

∑ ( d )2 = 712

S.D. = √ ∑ ( d )2 √ 712 , √ 178 = 13.3

n – 1 5-1

04/08/23 26

Standard Deviation

1. Most important tool in statistical analysis 2. SD helps to describe “Normal Curve”3. It gives an idea whether the observed diff. of

an individual value from the mean is by chance , normal or is significant.

4. Helps in calculation of “Standard error”.5. Helps in calculating “Sample size”.

04/08/23 27

Normal Distribution/Gaussian Distribution Theoretical, mathematical model to best describe many

biological characteristics like Ht., Wt., B.P, Hb.& cholesterol. Main features• Devised by Gauss (Germany), Lapless (France)• Graphic presentation of freq. dist. table of Qunti. Continuous

variable based on a large random sample.• Symmetrical about its mean• Smooth Bell shaped curve• This dist. provides foundation to “Central limit theorem” upon

which most statistical calculations are based. • It can be arithmetically expressed in terms of its mean and

Standard deviation.

04/08/23 28

Normal Distribution

1. Mean±1SD include 68.27%. (2/3rd) of observations. Reaming 32% (1/3rd) lie outside the range mean±1SD

2. Mean±2SDinclude 95.45% of the observations while 4.55% will lie outside the this limit. Mean±1.96SDlimits include 95% of the observations.

3. Mean± 3SDlimits include 99.73% of the observations. Mean± 2.58SD observations include 99% of the values.

4. It means values higher or lower than mean±3SD are very rare (only 0.27%) and their chances of being normal are 0.27times in 100.

Such high values are not normal or unusual and may even be pathological.

04/08/23 29

STANDARD NORML CURVE. • Mathematically designed curve• Perfectly bell shaped symmetrical curve. • Mean, Mode & Median coincide• Mean is zero• SD is 1

Mean ± 1 SD = 68.2 % 68 % of obs.

Mean ± 2 SD = 95.4 % 95 % “Mean ± 3 SD = 99.7 % 99 % “

04/08/23 30

Standard Normal Curve

Mathematical Formula of Standard Normal Curve

n c – x2 / 2 σ2

Y = __________________

σ √ 2 π

04/08/23 31

04/08/23 32

Ht. in cm f- in each gp 1SD±Mean 1SD±Mean 1SD±Mean

144 1

146 5 5

148 18 18

150 22 22 22

152 39 39 39

154 74 74 74

156 107 107 107 107

158 155 155 155 155

160 157 Mean ±1 SD Mean ±2SD Mean ±3SD

162 154 154 154 154

164 107 107 107 107

166 74 =680 (68%) 74 74

168 38 38 38

170 23 23 23

172 19 =950 19

174 5 (95%) 5

176 2 =1000 997 (99.7%)

04/08/23 33

http://en.wikipedia.org/wiki/File:Standard_deviation_diagram.svg

http://en.wikipedia.org/wiki/File:Standard_deviation_diagram.svg