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Biostatistics?
Topics Covered in the Presentation
Measurement of Central Tendencies
• Mean
What is Biostatistics?
Biostatistics is the branch of statistics responsible for the proper
interpretation of scientific data generated in the biology, public health and
other health sciences (i.e., the biomedical sciences). In these sciences,
subjects (patients, mice, cells, etc.) exhibit considerable variation in their
response to stimuli. This variation may be due to different treatments or it
may be due to chance, measurement error, or other characteristics of
the individual subjects. Biostatistics is particularly concerned with
disentangling these different sources of variation. It seeks to distinguish
between correlation and causation, and to make valid inferences from
known samples about the populations from which they were drawn. (For
example, do the results of treating patients with two therapies justify the
conclusion that one treatment is better than the other.
Biostatistics is a branch of applied statistics and it must be taught
with the focus being on its various applications in biomedical
research. Biostatistics is a broad discipline encompassing the
application of statistical theory to real-world problems, the
practice of designing and conducting biomedical experiments
and clinical trials (experiments with human subjects), the study of
related computational algorithms and display of data, and the
development of mathematical statistical theory. Biostatistics is
integral to the advance of knowledge in biology, health policy,
clinical medicine, public health policy, health economics,
proteomics, genomics, and other disciplines.
Applications of Biostatistics
• Public health, including epidemiology, health services research, nutrition,
environmental health and healthcare policy & management.
• Design and analysis of clinical trials in medicine
• Assessment of severity state of a patient with prognosis of outcome of a
disease.
• Population genetics, and statistical genetics in order to link variation in
genotype with a variation in phenotype. This has been used in agriculture
to improve crops and farm animals (animal breeding). In biomedical
research, this work can assist in finding candidates for gene alleles that
can cause or influence predisposition to disease in human genetics
• Analysis of genomics data, for example from microarray or proteomics
experiments. Often concerning diseases or disease stages.
• Ecology, ecological forecasting
• Biological sequence analysis
• Systems biology for gene network inference or pathways analysis
Central Tendency
In statistics, a central tendency (or measure of central tendency) is a
central or typical value for a probability distribution. It may also be
called a center or location of the distribution. Colloquially, measures
of central tendency are often called averages. The term central
tendency dates from the late 1920s.
The most common measures of central tendency are the arithmetic
mean, the median and the mode. A central tendency can be
calculated for either a finite set of values or for a theoretical
distribution, such as the normal distribution. Occasionally authors use
central tendency to denote "the tendency of quantitative data to
cluster around some central value. Measures of central tendency are
numbers that tell us where the majority of values
in the distribution are located.
Measures of central tendency
The following may be applied to one-dimensional data. Depending on the
circumstances, it may be appropriate to transform the data before calculating a
central tendency.
• Arithmetic mean (or simply, mean) – the sum of all measurements divided by the
number of observations in the data set.
• Median – the middle value that separates the higher half from the lower half of the
data set. The median and the mode are the only measures of central tendency that
can be used for ordinal data,
in which
valuestendency
are ranked relative to each other but
Measures
of central
are not measured absolutely.
• Mode – the most frequent value in the data set. This is the only central tendency
measure that can be used with nominal data, which have purely qualitative category
assignments.
• Geometric mean – the nth root of the product of the data values, where there are n
of these. This measure is valid only for data that are measured absolutely on a strictly
positive scale.
• Harmonic mean – the reciprocal of the arithmetic mean of the reciprocals of the data
values. This measure too is valid only for data that are measured absolutely on a
strictly positive scale.
Mean (Arithmetic)
The mean (or average) is the most popular and well known measure of
central tendency. It can be used with both discrete and continuous
data, although its use is most often with continuous data. The mean is
equal to the sum of all the values in the data set divided by the
number of values in the data set. So, if we have n values in a data set
and they have values x1, x2, ..., xn, the sample mean, usually denoted
by (pronounced x bar), is:
This formula is usually written in a slightly different manner using the
Greek capitol letter, , pronounced "sigma", which means "sum of...":
Question-Find the average height.
• Statisticians generally use the arithmetic mean as a measure
of central tendency for numbers that are from a ratio scale
(e.g., many biological values, height, blood sugar,
cholesterol), from an interval scale (e.g., Fahrenheit
temperature or personality measures such as depression), or
from an ordinal scale (high, medium, low).
• The values may be either discrete or continuous; for
example, ranking on an attitude scale (discrete values) or
blood cholesterol measurements (continuous).
References
https://medschool.vanderbilt.edu/biostatistics/content/what-biostatistics