Medical Statisitcs

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A brief introduction to medical statistics

• Dr. Naglaa Arafa
• Lecturer of Public Health

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Objectives

• By the end of this lecture, the student should be
  able to
• Calculate the measures of central tendency
• List the advantages and disadvantages of each
• Understand the measures of dispersion
• Appreciate the uses of statistics in medicine

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Definition

• Statistics is the science of data
• collection
• summarization
• analysis
• presentation
• interpretation
• I.e. it is used to obtain FACTS from FIGURES

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Measures of central tendency

• Also called measures of location
• Gives one number which is representative of all
  the data
• They are the mean, median and mode

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Mean

• Also called the average
• Calculated as the sum of all values divided by
  the number of values
• E.g. Hb level of 5 pregnant women
• 12 12.5 11 13 12.5
• 12.2 g

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Mean

• E.g. Hb level of 6 pregnant women
• 12 12.5 11 13 12.5 8
• 11.5 g

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Mean

• Advantages
• Simple and easy
• Most widely used
• Can be used for further statistical tests
• All values are included
• Does not need arrangement of data

• Disadvantages
• Affected by extreme values
• Sometimes looks ridiculous e.g. average number of
  children 2.7

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Median

• Value which divides the data into two equal parts
  after arrangement of data into ascending or
  descending order

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Median

• For odd number of variables
• Hb level of 5 pregnant women
• 12 , 12.5, 11, 13, 12.5
• 11, 12, 12.5, 12.5, 13
• Median 12.5

• For even number of variables
• Hb level of 6 pregnant women
• 12, 12.5, 11, 13, 12.5, 8
• 8, 11, 12, 12.5, 12.5, 13
• Median (12 12.5)/2
• 12.25

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Median

• Advantages
• Not affected by extreme values
• Used for growth curves and income
• Can be determined graphically

• Disadvantages
• Needs arrangement of data
• Difficult to calculate from large amounts of data
• Not all values are represented

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Mode

• Most common occurring value (fashionable value)
• Hb level of 5 pregnant women
• 12, 12.5, 11, 13, 12.5 Mode 12.5
• Hb level of 6 pregnant women
• 12, 12.5, 11, 13, 12.5, 8 Mode 12.5
• More than one mode may occur (bimodal, trimodal)
• Sometimes there is no mode

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Mode

• Advantages
• Not affected by extreme values

• Disadvantages
• Not all values are represented

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Measure of dispersion

• Also called measures of spread or dispersion
• They show the variability of data and how
  scattered it is
• They are the range, variance and
• standard deviation

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Range
Difference between highest and lowest value

• E.g Hb level of 5 pregnant women
• 12, 12.5, 11, 13, 12.5
• Range 13-11 2

• E.g. Hb level of 6 pregnant women
• 12, 12.5, 11, 13, 12.5, 8
• Range 13-8 5

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Range

• It is affected by extreme values
• It does not provide information about other
  values and how dispersed they are

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Standard Deviation

• Average deviation of values around the mean

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Standard deviation
HB Mean Deviation from mean (x - mean) (x - mean) 2
12 12.5 11 13 12.5 8 11.5 11.5 11.5 11.5 11.5 11.5 - 0.5 - 1 0.5 - 1.5 - 1 3.5 0.25 1 0.25 2.25 1 12.25
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Standard deviation

• variance 17/(6-1) 3.4
• SD v variance
• v 3.4 1.84
• Hb level of 6 pregnant women
• 12, 12.5, 11, 13, 12.5, 8
• Mean 11.5, SD 1.84

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Standard deviation

• If mean HB of 10 women is 11.5 and SD is 3, what
  does this tell you about the dispersion of these
  values around the mean as compared to the
  previous example?

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E.g. Systolic blood pressure

• Smoking males
• 120 130 120 150
• 130 170 180 160
• 170 150
• Mean SBP 148
• Range 180-120
• SD 22

• Non-smoking males
• 110 130 120 140
• 130 150 160 130
• 130 150
• Mean SBP 135
• Range 160-110
• SD 15.1

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Uses of Statistics

• Data presentation
• Simplifies large numbers of figures and reduces
  volume of data
• Enables comparisons across different groups
• Helps us to form and test hypotheses
• Helps in prediction, planning and administration
• Helps form suitable policies
• Helps measure standard of health

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Thank you