Direct method of standardization of indices

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Direct method of standardization of indices
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Average Values

• Mean ? the average of the data ? sensitive
  to outlying data
• Median ? the middle of the data ? not
  sensitive to outlying data
• Mode ? most commonly occurring value
• Range ? the difference between the largest
  observation and
• the smallest
• Interquartile range ? the spread of the data
  ? commonly used for skewed data
• Standard deviation ? a single number which
  measures how much the observations vary
  around the mean
• Symmetrical data ? data that follows normal
  distribution ? (meanmedianmode)
  ? report mean standard deviation n
• Skewed data ? not normally distributed
  ? (mean?median?mode)
  ? report median IQ Range

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Average Values

• Limit is it is the meaning of edge variant in a
  variation row
• lim Vmin Vmax

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Average Values

• Amplitude is the difference of edge variant of
  variation row
• Am Vmax - Vmin

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Average Values

• Average quadratic deviation characterizes
  dispersion of the variants around an ordinary
  value (inside structure of totalities).

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Average quadratic deviation
s
simple arithmetical method
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Average quadratic deviation
d V - M
genuine declination of variants from the true
middle arithmetic
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Average quadratic deviation
s i
method of moments
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Average quadratic deviation
is needed for 1. Estimations of typicalness of
the middle arithmetic (? is typical for this row,
if s is less than 1/3 of average) value. 2.
Getting the error of average value. 3.
Determination of average norm of the phenomenon,
which is studied (?1s), sub norm (?2s) and edge
deviations (?3s). 4. For construction of sigmal
net at the estimation of physical development of
an individual.
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Average quadratic deviation
This dispersion a variant around of average
characterizes an average quadratic deviation ( ?
)
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• Coefficient of variation is the relative measure
  of variety it is a percent correlation of
  standard deviation and arithmetic average.

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Correlation coefficient
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Correlation coefficient
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Correlation coefficient
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Types of correlation

• There are the following types of correlation
  (relation) between the phenomena and signs in
  nature
• ?) the reason-result connection is the connection
  between factors and phenomena, between factor and
  result signs.
• ?) the dependence of parallel changes of a few
  signs on some third size.

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Quantitative types of connection

• functional one is the connection, at which the
  strictly defined value of the second sign answers
  to any value of one of the signs (for example,
  the certain area of the circle answers to the
  radius of the circle)

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Quantitative types of connection

• correlation - connection at which a few values of
  one sign answer to the value of every average
  size of another sign associated with the first
  one (for example, it is known that the height
  and mass of mans body are linked between each
  other in the group of persons with identical
  height there are different valuations of mass of
  body, however, these valuations of body mass
  varies in certain sizes round their average
  size).

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Correlative connection

• Correlative connection foresees the dependence
  between the phenomena, which do not have clear
  functional character.
• Correlative connection is showed up only in the
  mass of supervisions that is in totality. The
  establishment of correlative connection foresees
  the exposure of the causal connection, which will
  confirm the dependence of one phenomenon on the
  other one.

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Correlative connection

• Correlative connection by the direction (the
  character) of connection can be direct and
  reverse. The coefficient of correlation, that
  characterizes the direct communication, is marked
  by the sign plus (), and the coefficient of
  correlation, that characterizes the reverse one,
  is marked by the sign minus (-).
• By the force the correlative connection can be
  strong, middle, weak, it can be full and it can
  be absent.

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Estimation of correlation by coefficient of
correlation
Force of connection Line () Reverse (-)
Complete 1
Strong From 1 to 0,7 From -1 to -0,7
Average from 0,7 to 0,3 from 0,7 to 0,3
Weak from 0,3 to 0 from 0,3 to 0
No connection 0 0
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Types of correlative connection

• By direction
• direct () with the increasing of one sign
  increases the middle value of another one
• reverse (-) with the increasing of one sign
  decreases the middle value of another one

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Types of correlative connection

• By character
• rectilinear - relatively even changes of middle
  values of one sign are accompanied by the equal
  changes of the other (arterial pressure minimal
  and maximal)
• curvilinear at the even change of one sing
  there can be the increasing or decreasing middle
  values of the other sign.

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Terms Used To Describe The Quality Of Measurements

• Reliability is variability between subjects
  divided by inter-subject variability plus
  measurement error.
• Validity refers to the extent to which a test or
  surrogate is measuring what we think it is
  measuring.

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Measures Of Diagnostic Test Accuracy

• Sensitivity is defined as the ability of the test
  to identify correctly those who have the disease.
• Specificity is defined as the ability of the test
  to identify correctly those who do not have the
  disease.
• Predictive values are important for assessing how
  useful a test will be in the clinical setting at
  the individual patient level. The positive
  predictive value is the probability of disease in
  a patient with a positive test. Conversely, the
  negative predictive value is the probability that
  the patient does not have disease if he has a
  negative test result.
• Likelihood ratio indicates how much a given
  diagnostic test result will raise or lower the
  odds of having a disease relative to the prior
  probability of disease.

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Measures Of Diagnostic Test Accuracy
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Expressions Used When Making Inferences About Data

• Confidence Intervals
• The results of any study sample are an estimate
  of the true value in the entire population. The
  true value may actually be greater or less than
  what is observed.
• Type I error (alpha) is the probability of
  incorrectly concluding there is a statistically
  significant difference in the population when
  none exists.
• Type II error (beta) is the probability of
  incorrectly concluding that there is no
  statistically significant difference in a
  population when one exists.
• Power is a measure of the ability of a study to
  detect a true difference.

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Multivariable Regression Methods

• Multiple linear regression is used when the
  outcome data is a continuous variable such as
  weight. For example, one could estimate the
  effect of a diet on weight after adjusting for
  the effect of confounders such as smoking status.
• Logistic regression is used when the outcome data
  is binary such as cure or no cure. Logistic
  regression can be used to estimate the effect of
  an exposure on a binary outcome after adjusting
  for confounders.

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Survival Analysis

• Kaplan-Meier analysis measures the ratio of
  surviving subjects (or those without an event)
  divided by the total number of subjects at risk
  for the event. Every time a subject has an event,
  the ratio is recalculated. These ratios are then
  used to generate a curve to graphically depict
  the probability of survival.
• Cox proportional hazards analysis is similar to
  the logistic regression method described above
  with the added advantage that it accounts for
  time to a binary event in the outcome variable.
  Thus, one can account for variation in follow-up
  time among subjects.

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Kaplan-Meier Survival Curves