Lec. biostatistics

Public Health Methodologies

Biostatistics

[email protected]

Dr. Riaz A. Bhutto 2

Data• Data is a collection of facts, such as values or

measurements.OR

• Data is information that has been translated into a form that is more convenient to move or process.

OR• Data are any facts, numbers, or text that can be

processed by a computer.3/3/2012


Statistics

Statistics is the study of the collection, summarizing, organization, analysis, and interpretation of data.

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Vital statistics

Vital statistics is collecting, summarizing, organizing, analysis, presentation, and interpretation of data related to vital events of life as births, deaths,

marriages, divorces, health & diseases.

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Biostatistics

Biostatistics is the application of statistical techniques to scientific research in health-related fields, including medicine, biology, and public health.

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Descriptive Statistics

The term descriptive statistics refers to statistics that are used to describe. When using descriptive statistics, every member of a group or population is measured. A good example of descriptive statistics is the Census, in which all members of a population are counted.

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Inferential or Analytical Statistics

Inferential statistics are used to draw conclusions and make predictions based on the analysis of numeric data.

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Primary & Secondary Data

• Raw or Primary data: when data collected having lot of unnecessary, irrelevant & un wanted information

• Treated or Secondary data: when we treat & remove this unnecessary, irrelevant & un wanted information

• Cooked data: when data collected not genuinely and is false and fictitious

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Ungrouped & Grouped Data

• Ungrouped data: when data presented or observed individually. For example if we observed no. of children in 6 families

2, 4, 6, 4, 6, 4

• Grouped data: when we grouped the identical data by frequency. For example above data of children in 6 families can be grouped as:

No. of children Families 2 1

4 3 6 2

or alternatively we can make classes:

No. of children Frequency 2 - 4 4

5 - 7 2 3/3/2012


Variable

A variable is something that can be changed, such as a characteristic or value. For example age, height, weight, blood pressure etc

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Types of Variable Independent variable: is typically the

variable representing the value being manipulated or changed. For example smoking

Dependent variable: is the observed result of the independent variable being manipulated. For example ca of lung

Confounding variable: is associated with both exposure and disease. For example age is factor for many events

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Categories of DATA

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Quantitative or Numerical data

This data is used to describe a type of information that can be counted or expressed numerically (numbers)

2, 4 , 6, 8.5, 10.5

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Quantitative or Numerical data (cont.) This data is of two types1. Discrete Data: it is in whole numbers or values and

has no fraction. For example Number of children in a family = 4 Number of patients in hospital = 320 2. Continuous Data (Infinite Number): measured on a

continuous scale. It can be in fraction. For example Height of a person = 5 feet 6 inches 5”.6’ Temperature = 92.3 °F

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Qualitative or Categorical dataThis is non numerical data as Male/Female, Short/TallThis is of two types1. Nominal Data: it has series of unordered categories ( one can not √ more than one at a time) For example

Sex = Male/Female Blood group = O/A/B/AB 2. Ordinal or Ranked Data: that has distinct ordered/ranked categories.

For example

Measurement of height can be = Short / Medium / Tall Degree of pain can be = None / Mild /Moderate / Severe

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Dr. Riaz A. Bhutto 169/3/2012

Measures of Central Tendency & Variation (Dispersion)


Measures of Central Tendency

are quantitative indices that describe the center of a distribution of data. These are

• Mean • Median (Three M M M)• Mode

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Mean Mean or arithmetic mean is also called AVERAGE and

only calculated for numerical data. For example• What average age of children in years? Children 1 2 3 4 5 6 7 Age 6 4 4 3 2 4 6

--

Formula X = ∑ X ___

n

Mean = 6 4 4 3 2 4 5 = 28 = 4 years 7 79/3/2012


Median

• It is central most value. For example what is central value in 2, 3, 4, 4, 4, 5, 6 data?

• If we divide data in two equal groups 2, 3, 4, 4, 4, 5, 6 hence 4 is the central most value

• Formula to calculate central value is: Median = n + 1 (here n is the total no. of value)

2 Median = (n + 1)/2 = 7 + 1 = 8/2 = 4

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Mode

• is the most frequently (repeated) occurring value in set of observations. Example

• No mode Raw data: 10.3 4.9 8.9 11.7 6.3 7.7 • One mode Raw data: 2 3 4 4 4 5 6• More than 1 mode Raw data: 21 28 28 41 43 43

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Measures of Dispersion

quantitative indices that describe the spread of a data set. These are

• Range• Mean deviation• Variance• Standard deviation• Coefficient of variation• Percentile

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Range

It is difference between highest and lowest values in a data series. For example:

the ages (in Years) of 10 children are 2, 6, 8, 10, 11, 14, 1, 6, 9, 15 here the range of age will be 15 – 1 = 14 years

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Mean Deviation This is average deviation of all observation

from the mean -

Mean Deviation = ∑ І X – X І _______ _ n here X = Value, X = Mean n = Total no. of value

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Mean Deviation ExampleA student took 5 exams in a class and had scores of 92, 75, 95, 90, and 98. Find the mean deviation for her test

scores.

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• First step find the mean.

_ x = ∑ x ___

n = 92+75+95+90+98

5

= 450 5 = 90


Values = X ˉ Mean = X

Deviation from ˉ Mean = X - X

Absolute value ofDeviationIgnoring + signs

92 90 2 2

75 90 -15 15

95 90 5 5

90 90 0 0

98 90 8 8

Total = 450

n = 5 Mean Deviation = _ ∑І X – X І _______ = 30/5 n

--∑ X - X = 30

= 6

Average deviation from mean is 6

• 2nd step find mean deviation


Variance

• It is measure of variability which takes into account the difference between each observation and mean.

• The variance is the sum of the squared deviations from the mean divided by the number of values in the series minus 1.

• Sample variance is s² and population variance

is σ²9/3/2012


Variance (cont.)

• The Variance is defined as:• The average of the squared differences from the

Mean.• To calculate the variance follow these steps:• Work out the Mean (the simple average of the

numbers)• Then for each number: subtract the Mean and square

the result (the squared difference)• Then work out the average of those squared

differences. 9/3/2012

http://www.mathsisfun.com/mean.html


Step 1

Step 2 Step 3

Step 4

Values = X ˉ Mean = XDeviation from ˉ Mean = X - X

ˉ ( X – X)²

2 4 -2 45 4 1 14 4 0 06 4 2 43 4 -1 1

Step 6 s² _ ∑ ( X – X )² = _______ = 10/5 n

∑ = 10 Step 5

= 2 S²= 2 persons²

Example: House hold size of 5 families was recorded as following: 2, 5, 4, 6, 3 Calculate variance for above data.


Standard Deviation

• The Standard Deviation is a measure of how spread out numbers are.

• Its symbol is σ (the greek letter sigma)• The formula is easy: it is the square root of

the Variance.i-e s = √ s²• SD is most useful measure of dispersion s = √ (x - x²) n (if n > 30)

s = √ (x - x²) n-1 (if n < 30)

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ExampleYou and your friends have just measured the heights of your

dogs (in millimeters):

• The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm.

• Find out the Mean, the Variance, and the Standard Deviation.9/3/2012

:


Your first step is to find the Mean:Answer:

Mean = 600 + 470 + 170 + 430 + 300 = 1970 = 394 5 5

so the mean (average) height is 394 mm. Let's plot this on the chart:

329/3/2012 So, the Variance is 21,704.Dr. Riaz A. Bhutto

Now, we calculate each dogs difference from the Mean:

To calculate the Variance, take each difference, square it, and then average the result:


And the Standard Deviation is just the square root of Variance, so:Standard Deviation: σ = √21,704 = 147.32... = 147 (to the nearest mm)

And the good thing about the Standard Deviation is that it is useful. Now we can

show which heights are within one Standard Deviation (147mm) of the Mean:

• So, using the Standard Deviation we have a "standard" way of knowing what is normal, and what is extra large or extra small.

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Lec. biostatistics

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