MAKING INFERENCES

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MAKING INFERENCES
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Inferring

• Guessing or concluding or assuming something.

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Sample

• typical or representative of the population.
• A sample can be assumed to be representative only
  of the population which is available to be
  sampled.

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Population

• Definition (statistics) whatever is defined it
  to be.
• Target population the greater, inaccessible
  population (all women in the world)
• Study population a group of individuals who are
  actually available and from whom the sample could
  actually be taken (patients of Samra clinic)

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Population parameter

• The feature or characteristic of a population
  whose value you want to determine.
• The mean of some variable in a population, or the
  median, or the standard deviation, are all
  population parameters.
• Their values define that population

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Sample Statistic

• The value that you get from your sample (on which
  you are going to base your estimate of the
  population value),
• This is why we are so interested in the summary
  descriptive measures (such as the sample mean,
  the sample median, and so on).
• These are the sample statistics on which you will
  base your inferences.
• You can use the sample mean to estimate the
  population mean, the sample median to estimate
  the population median, and so on.

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Summary

• Statistical inference is the process of using a
  value obtained from the sample, known as the
  sample statistic, to estimate the value of the
  corresponding population parameter.

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Schematic of the process of statistical inference
The population parameter whose value we wish to
estimate, i.e. the of women in the USA with
genital chlamydia
We assume that the sample statistic is about the
same as the population parameter and infer that
this therefore is also approx 2.6.
A representative sample from this population
gives a value for the corresponding sample
statistic, the with genital chlamydia, equal
to 2.6.
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Inference from Hypothesis testing

• Making an (informed) assumption about the value
  of some population parameter
• Then use the appropriate sample statistic to see
  whether its value supports your assumption.

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Probability, Risk, and Odds
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Probability

• A measure of the chance of getting some
  particular outcome, when you perform some
  experiment.
• For example, rolling a dice (with six possible
  outcomes, 1 to 6), taking a biopsy (two possible
  outcomes, benign or malignant), determining an
  Apgar score for an infant (11 possible outcomes,
  from 0 to 10), and so on.
• The probability, p, of an event X, written as
  p(X), can vary from 0 to 1. 0 p(X) 1
• Risk" is synonymous with "probability

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Event

• Event is defined as some particular outcome, or
  combination of outcomes.
• For example, the event "rolling an even number
  when throwing a dice" is a combination of the
  outcomes, rolling a 2 or rolling a 4 or rolling a
  6.

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Calculating Probability

• Probability of an event The number of outcomes
  which favor that event divided by the total
  number of possible outcomes

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Probability and the Normal Distribution

• If data is normally distributed then 95 of the
  values will lie no further than two standard
  deviations from the mean.
• In probability terms, there is an equivalent
  probability of 0.95 that a single value chosen at
  random from the set of values will lie no further
  than two standard deviations from the mean.

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Risk

• Risk of an event Number of favorable outcomes
  divided by the total number of outcomes
• Absolute risk the risk for a single group
• Relative risk the risk for one group compared
  to the risk for some other group

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Odds

• Odds for an event The number of outcomes
  favorable to the event divided by the number of
  outcomes not favorable to the event.
• When the odds for an event are less than 1, the
  odds are unfavorable the event is less likely to
  happen than it is to happen.
• When the odds equal 1, the event is as likely to
  happen as not. (reference value)
• When the odds are greater than 1, the odds are
  favorable the event is more likely to happen
  than not.

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The Link between Probability and odds

• Risk or probability odds/(l odds)
• Odds probability / (1 - probability)
• PE/T, TEX, E/EXE/X//EX/XO/1O
• OE/X, XT-E,
• E/T-EE/T//T-E/TP/1-P

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The Risk Ratio

• Dividing the risk for one group (usually the
  group exposed to the risk factor) by the risk for
  the second, non-exposed group.

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Risk Ratio

a/ac
a(bd)
b/bd
b(ac)
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The Odds Ratio

• Dividing the odds that those with a disease will
  have been exposed to the risk factor by the odds
  that those who dont have the disease will have
  been exposed.

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Odds ratio
Odds Ratio

a/c
ad
b/d
bc
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Numbers Needed to Treat (NNT)

• the effectiveness of a clinical procedure which
  is related to risk, more precisely to absolute
  risk-this is the numbers needed to treat, or NNT.
• It is the number of patients who would need to
  be treated with the active procedure rather than
  a placebo (or alternative procedure) in order to
  reduce by one the number of patients experiencing
  the condition.
• Absolute risk reduction (ARR) is the difference
  in these two absolute risks. It's the reduction
  in risk gained by weighing more than 18lb at one
  year rather than weighing 18lb or less. In this
  case
• ARR absolute risks of exposed group AR of non
  exposed group.
• Now NNT is defined as follows
• NNT l/ARR
• This means that if you had some treatment
  (infant-care advice for vulnerable parents, for
  example), which would cause infants who would
  otherwise have weighed less than 18lb at one year
  to weigh 18lb or more, then you would need to
  "treat" eight infants (or their parents) to
  ensure that one patient did not have coronary
  heart disease.
• NNT is often used to give a familiar and
  practical meaning to outcomes from clinical
  trials, and systematic reviews, where measures of
  risk and risk ratios may be difficult to
  translate into the potential benefit to patients.

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