Biostatistics

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Biostatistics
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Statistics

• Sayings about statistics
• Statistics is a science about accurate work with
  inaccurate numbers.
• We know three kinds of lies intentional,
  unintentional and statistics

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Biostatistics what does it mean?

• It isnt separate field of science. Using this
  word we point out, that it is an application of
  statistical methods helping to resolve biological
  problems. and biological data are specific of
  their own

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And what is statistics indeed?

• (in laymen language) Ordered group of data
  statistics of shootings, statistics of car
  accidents in different regions
• (in scientific language) A science, what we are
  going to do with our data - (mathematical)
  statistics as a science
• Withing the scope of statistics a value
  calculated from numbers and synthesizing
  features of these numbers

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Anything can be proved with the help of
statistics

• especially by people, who dont understand
  statistics
• It is statistically proved, that widows live
  longer than their husbands.
• It is possible to put anything to diagrams and
  they look then very suggestive, especially when
  they are accompanied with right interpretation
  (data are fictitious, but according to reality)

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And much better with the help of diagrams
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Advice when somebody tells you, how many per
cents something got better, ask every time, which
base were the percents computed from.
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Goals of statistics

• (1) Descriptive statistics to sumarize data, to
  condensate information from many numbers to
  lesser number of parameters or to a diagram

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Compare
Average number of points was 74.5, whereas the
minimum value was 28 and the maximum value was
100.
Frequency diagram
No. of points
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The lower number of parameters I obtain

• the more transparent and more simple the result
  is
• the loss of information is bigger though (I am
  never able to find out from average or histogram
  how much points had František K., nor the value
  of all the numbers)
• - the art is to find the border, where the result
  is transparent but still having its predictive
  quality

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Thanks to the loss of information we are able to
say lies in statistics
According to the statistics, we all are flying.
Not so high in the clouds, but near the ground
and just slightly touching with the end of our
shoes the shit we are sitting in.
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The worst the patient is, the better the
medicine works.
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Argument for harmfulness of fluoridization (data
from USAs states)
Nicaragua should be here
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Storks bring babies
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Differentiate - correlation and causation

• The general scientific method

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Common scientific method on the example of
babies bringing storks 1. Observation finding
of pattern
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• 2. Interpretation Stork brings babies
• 3. Prediction if we remove storks, babies wont
  be born or their number would be decreased, if
  crows also do the job
• 4. Experiment In the half of regions (randomly
  selected!) we shoot out storks and watch changes
  in natality (in comparison with the changes in
  control regions)
• 5. (After statistical approach) we bring out
  there are no changes, so we can proclaim, that
  storks dont bring babies.

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Hypothetical-deductive approach (K. Popper)
good presumption can bring just good prediction,
bad presumption can bring both good and bad
prediction thanks to this we can never prove
the prediction (hypothesis), just reject it
Observation (pattern)
explanation
Hypothesis exclude each other, predictions differ
from each other
Hypothesis 1
Hypothesis 2
Hypothesis 3
Prediction 2
Prediction 3
Prediction 1
Result of the experiment compared with the reality
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Goals of statisticsPopulation and sample

• (2) Interferential statistics - Making an
  inference about (statistical) population from a
  sample
• Some (statistical) populations are too large or
  potentially infinite I am not able to check
  all the members
• What can I say about results of elections in the
  whole republic, when I ask just 1000 people?
• What can I say about amount of Cd in blood of
  wild geese in CZ, when I took blood just from 10
  specimens?

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Interferential statistic is common in biology

• I dont want to make conclusions about my 10
  laboratory rats, but on the base of these 10 rats
  I want to say something about all experiments
  done in the same way
• Should this be a science, the experiments have to
  be reproducible (comp. Journal of Irreproducible
  Research)

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Types of (not only biological) data

• Continuous and discrete data mathematical
  definition and reality of datas measuring in
  reality we always measure data with certain
  accuracy

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Types of (not only biological) data

• Ratio scale
• Interval scale
• Ordinal scale
• Nominal scale (categorical data)

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Circular scale
90
270
180
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Azimuth of the stem with lichen findings
degrees 5, 10, 5, 350, 350, 355 gt average
180 Time of doom-mongers ululating 2200,
2300, 2400, 100, 100, 200 gt average is
short after the midday
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Types of (not only biological) data

• Ratio scale
• Interval scale
• Ordinal scale
• Nominal scale (categorical data)

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Circular scale
90
270
180
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Population and Random sample

• Sampling Sampling design
• Random sample every individual has to have the
  same probability to be chosen, independent upon
  the fact that another individual was chosen
• Tabs and generators of (pseudo)random numbers

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Population sample and Random sample

• Almost philosophical question what it is
  random
• And what it is probability
• In statistics (that means in this course) we will
  use so-called a priori probability (also the
  Bayesian - posterior probability exists)

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To make a random sampling isnt usually trivial
in no case it is a sampling of typical
individuals it works reasonably well in
agricultural experiments
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Much more difficult it is in natural populations
even individual nearest to the random point
does not work here
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Basic statistical characteristics

• We usually mark N size of the population, n
  size of sample
• Characteristics of the population are usually
  marked with Greek alphabet and characteristics of
  sample with Roman characters
• Characteristics of location
• Means, median and modus
• Means are defined for quantitative data (i.e. on
  ratio and interval scale)

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Arithmetical mean
of population
of sample
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Geometrical mean

• n-root of the sum of n values (for a sample here)

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Harmonic mean

• Reciprocal of the mean of reciprocals.

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Median used for ordinal-scaled data also

• It is defined as one half of the values is under
  and the second one over the median (in endless
  populations is the probability, that random value
  is over as well as under the median 0.5). In
  populations with even number of terms is a value
  in the half of two middle values considered to be
  the median

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Upper and lower quartile

• Over the upper quartile is 1/4 observations,
  under the lower one is 1/4 of observations
  (similar with the endless populations)

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Make difference among meaning of mean and median
Example wages in two companies
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Modus the most common value in continuous data
in continuous data it is the peak in
frequency diagram we will define it as the
local maximum of the density-probabilities curve
later can be more than one
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mean
median
mean
median
mean
mean
median
median
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Characteristics of variability

• 1. Range is a difference between minimum and
  maximum
• 2. Interquartile range
• 3. Variance and standard deviation

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Variance average value of square deviation from
mean

• population -

estimation based on the sample
n-1 df degrees of freedom
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Standard deviation (sx, often also s.d. or
S.D.) is root from variance
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Compare variability in weight of elephant and ant

• Use either variance or standard deviation of data
  under logarithm, or coefficient of variation CV
• Both have its sense just for ratio-scaled data

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Standard error of mean

• Characteristic of sample means accuracy how
  big would be variability of means of this size
  from many random samples

variability in data
accuracy
We can higher accuracy thanks to larger sample.
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Graphic summarizations frequency diagram
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Box and whisker plot
Attention, nowadays is box whisker also used
for mean and standard deviation etc.
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