Biostatistics course Part 4 Probability

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Biostatistics coursePart 4Probability

• Dr. C. Nicolas Padilla Raygoza
• Department of Nursing and Obstetrics
• Division of Health Sciences and Engioneering
• Campus Celaya Salvatierra
• University of Guanajuato

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Biosketch

• Medical Doctor by University Autonomous of
  Guadalajara.
• Pediatrician by the Mexican Council of
  Certification on Pediatrics.
• Postgraduate Diploma on Epidemiology, London
  School of Hygine and Tropical Medicine,
  University of London.
• Master Sciences with aim in Epidemiology,
  Atlantic International University.
• Doctorate Sciences with aim in Epidemiology,
  Atlantic International University.
• Professor Titular A, Full Time, University of
  Guanajuato.
• Level 1 National Researcher System
• padillawarm_at_gmail.com raygosan_at_ugto.mx

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Competencies

• The reader will define what is probability.
• He (she) will know and describe additive law.
• He (she) will know and describe multiplicative
  law.

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Definitions

• Probability is the possibility that an event
  occur.
• If we repeat many times an experiment, when
  obtained expected result, it is divided between
  number of experiments to know the probability.
• If a result is sure that occur the probability
  will be 1 (100).
• If a event is sure that does not occur the
  probability will be 0.

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Examples

• If we throw a coin in the air once, the
  probability to obtain face is ½, because only we
  can obtain face or cross.
• If we throw a dice once, the probability to
  obtain a 4 is 4/16, because there are 6 sides in
  the dice.
• If we have a box with 100 balls 5 blue, 5 green,
  10 orange, 10 yellow, 20 red, 20 white and 30
  brown, the higher probability is to obtain a
  brown ball, 30/100 0.3 30.

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Probability

• Frequentist (objective)
• Probability that an event will occur, is the
  probability of times that the result will be
  observe if we repeat the experiment many times.
• Bayesian (subjective)
• It permit the explicit use of external judgment
  and believes in the analysis and interpretation
  of data.

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Probability

• An experiment is a process planed to obtain data.
• An opposite event of the interest is called
  complementary event and its probability is
  obtained subtracting of 1 the probability of
  interest event.
• Probability to have amebiasis is 59/200 0.295
  29.5
• Probability of does not have amebiasis es
  151/200 0.705 70.5 or 1 - 0.0.2950.705
  70.5

Results for E. histolytic n ()
Positive 59 (29.5)
Negative 151 (70.5)
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Probability

• If I throw a dice, the probability to obtain 6
  is 1/6 if throw the dice 20 times will be
  difficult to obtain a 6 in three of 20 times that
  I throw the dice but if I throw it 1000 times,
  obtained a 6 is more near at 16.7.
• Proportion that vary up or down of 16.7 is a
  consequence of chance.

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Probability rules

• Mutually excluded events
• Two events are mutually excluded if the
  occurrence of an event avoid the occurrence of
  the other.
• For example
• If a baby is male, cannot be female.
• If a child had positivity for E. histolytic, can
  not had negativity.
• The probability of occurrence of two mutually
  excluded events, is the probability of occurrence
  of an event or another, and we can obtain the
  probability, add the individual probabilities of
  each event.

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Probability rules

• Example
• 100 new born in a maternity of Celaya
• 55 were females and 45 males
• Probability to be female 55/100 0.55
• Probability to be male 45/1000.45
• Probability to be anyone 0.55 0.45 1.00

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Probability rules

• Example
• 200 children with a test for E. histolytic
• 59 had positive result.
• 151 had negative result
• Probability of positivity for E. histolytic was
  59/200 0.295
• Probability of negativity for E. histolytic was
  51/200 0.705
• Probability for positive or negative result was
  0.295 0.705 1.00

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Probability rules

• Independent events
• Two events are independents if the occurrence of
  a event does not affect the occurrence of the
  second event.
• Example
• If the first new born is male, does not affect
  that the next be female.
• Probability of two independent events is obtained
  multiplying individual probabilities of each
  event.
• This is the multiplicative law of probability.

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Probability rules

• Example
• In a blood bank, they determined blood groups

Group n
0 45 45
A 29 29
B 21 21
AB 5 5
Total 100 100
What is the probability of next two persons will
be 0 group? Is it mutually excluded or
independent?
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Probability rules

• If the next person has 0 group does not interfere
  with that the second next person has 0 group,
  because of this are independent events.
• Their individual probabilities, are multiplied
• 0.45 x 0.45 0.2025 20.25

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Probability rules

• Example
• 100 new born in a maternity in Celaya
• 55 were females and 45 males
• Probability of to be women was 55/100 0.55
• Probability to be boy was 45/100 0.45

What is the probability of the next three
deliveries are females?
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Probability rules

• Example
• They are excluded mutually events, and their
  individual probabilities are multiplied.
• 0.55 x 0.55 x 0.55 0.1664 16.64

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Bibliografía

• 1.- Last JM. A Dictionary of epidemiology. New
  York, 4ª ed. Oxford University Press, 2001173.
• 2.- Kirkwood BR. Essentials of medical
  stastistics. Oxford, Blackwell Science, 1988
  1-4.
• 3.- Altman DG. Practical statistics for medical
  research. Boca Ratón, Chapman Hall/ CRC 1991
  1-9.