Bio Statistics.pptx by Dr.REVATHI SIVAKUMAR

Statistics is the scientific discipline that provides methods to help us make decisions and draw conclusions in
the presence of variability. That is, statistics is an art as well as science of decision making in the face of
uncertainty.
By uncertainty, we mean that successive observations of a system or phenomenon do not produce exactly the
same result.
We all encounter these type of variability in our everyday lives, and statistical thinking can give us a useful
way to incorporate this variability into our decision-making processes.
Because statistical methods are used to organize, summarize, and draw conclusions from data, a familiarity
with statistical techniques and statistical literacy is vital in today’s society.

We encounter data in every field of our life and natural phenomenon.
The field of statistics deals with the collection, presentation, analysis, and use of data to make decisions,
solve problems, and design products and processes.
We may define statistics as a field of study concerned with
(1) collection, organization, summarization, and analysis of data; and
(2) drawing of inferences about a body of data when only a part of the data is observed.

The person who performs these statistical activities must be prepared to interpret and to communicate the
results to someone else as the situation demands. Simply put, we may say that data are numbers, numbers
contain information, and the purpose of statistics is to investigate and evaluate the nature and meaning of this
information. The tools of statistics are employed in many fields—industry, business, education, psychology,
agriculture, economics, and so on.
Bio statistics:
When the data analyzed are derived from the biological sciences and medicine, we use the term biostatistics to
distinguish this particular application of statistical tools and concepts.

Statistics has traditionally been used with two purposes in mind.
(1) to organize and summarize data, and
(2) to reach decisions about a large body of data by examining only a small part of it.
The concepts and methods necessary for achieving the first objective are presented under the heading of
descriptive statistics, and the second objective is reached through the study of what is called inferential
statistics.

Statistical investigation is a comprehensive and requires systematic collection of data about some group of
people or objects, describing and organizing the data, analyzing the data with the help of different statistical
method, summarizing the analysis and using these results for making judgements, decisions and predictions.
The validity and accuracy of final judgement is most crucial and depends heavily on how well the data was
collected in the first place. The quality of data will greatly affect the conditions and hence at most importance
must be given to this process and every possible precautions should be taken to ensure accuracy while
collecting the data.

Collection of Data
The statistical data may be already available or may have to be collected by an investigator or an agency.
Data collected for a specific purpose are called ‘Primary data’ .
For example, data collected by a particular person or organisation from the primary source for his own use,
collection of data about the population by censuses and surveys, etc.
Data collected and published by one organisation and subsequently used by other organisations are called
‘Secondary data’.
The various sources of collection for secondary data are: newspapers and periodicals; publications of trade
associations; research papers official publications governments and other organisations etc.
The collection expenses of primary data are more than secondary data. Secondary data should be used with care.

Following are the two principal methods of data collection-census method and sample survey.
1.Census method-By this method we mean complete enumeration of each and every element of the source.
Data obtained by taking relevant measurement or observation of each and every of the source constitute
census data.
2.Sample survey-When only some selected elements of the source are taken and measurements or
observations of these selected elements are recorded the data is called sample data. It may be noted that
elements are selected according to some valid procedure.

The various methods of collection of primary data are:
(i) Direct personal investigation (interview/observation)
(ii) Indirect oral investigation
(iii) Data from local agents and correspondents
(iv) Mailed questionnaires
(v) Questionnaires to be filled in by enumerators
(vi) Results of experiments, etc.
Data collected in this manner are called ‘raw data’.

Presentation of data:
The data collected needs be organised and presented in meaningful and readily comprehensible form inorder
to facilitate further statistical analysis.
Usually we present the data in the following ways:
1.Textual presentation-data is presented along with the text.
2.Tabular presentation-data are arranged in a systematic way in rows and columns.
3.Graphic or diagrammatic presentation-for quick and ready comprehension, the data is presented either as a
graph or diagram.

CLASSIFICATION OF DATA
The process of arranging data in groups or classes according to their resemblances and affinities and gives
expression to the unity of attributes that may subsist amongst a diversity of individuals is known as classification
of data.
Classification condenses the data by dropping out unnecessary details. It facilitates comparison between
different sets of data clearly showing the different points of agreement and disagreement.
The bases of classification are:
Arranging data according to geographical region-Geographical classification
Arranging data according to the order of time-Chronological classification
Arranging data according to its numerical magnitude-Quantitative classification

Variables:
As we observe a characteristic, we find that it takes on different values in different persons, places, or things
and so we label the characteristic a variable.
Some examples of variables include diastolic blood pressure, heart rate, heights, weights of preschool
children, ages of patients visted in an OP etc.
A quantitative variable is one that can be measured in the usual sense. We can, for example, obtain
measurements on the heights of adult males, the weights of preschool children, and the ages of patients seen
in a dental clinic. These are examples of quantitative variables. Measurements made on quantitative variables
convey information regarding amount.

Some characteristics are not capable of being measured in the sense that height, weight, and age are
measured. In such cases measuring consists of categorizing. We refer to variables of this kind as qualitative
variables. Measurements made on qualitative variables convey information regarding attribute.
Many characteristics can be categorized only, as, for example, colour, gender, etc.
Measurement :
This may be defined as the assignment of numbers to objects or events according to a set of rules. The
various measurement scales result from the fact that measurement may be carried out under different sets
of rules.

Nominal Scale: A nominal scale of measurement deals with variables that are non-numeric or where the
numbers have no value. A nominal scale, as the name implies, is simply some placing of data into categories,
without any order or structure.
The practice of using numbers to distinguish among the various medical diagnoses constitutes measurement
on a nominal scale. male–female, child–adult, married–not married are some examples of nominal scale
measurement.
An example of a nominal scale is the terms we use for colours.
In research activities a YES/NO scale is nominal.

Ordinal Scale: The ordinal type allows for rank order (1st, 2nd, 3rd, etc.) by which data can be sorted, but
still does not allow for relative degree of difference between them.
Whenever observations are not only different from category to category but can be ranked according to
some criterion, they are said to be measured on an ordinal scale.
Education level, income level, disease stage are some examples of ordinal scale.
Note that an ordinal scale of measurement looks at variables where the order matters but the differences
do not matter.
Note:In the case of letter grades, we don't really know how much better an A is than a D. We know that A
is better than B, which is better than C, and so on. But is A four times better than D? Is it two times better?
In this case, the order is important but not the differences.

Interval Scale:
Interval scales are numeric scales in which we know not only the order, but also the exact differences
between the values. The interval scale is a more sophisticated scale than the nominal or ordinal in that with
this scale not only it is possible to order measurements, but also the distance between any two
measurements is known. Note that in Interval scale the same difference at two places on the scale has the
same meaning.
Interval Scale is defined as a numerical scale where the order of the variables is known as well as the
difference between these variables. It may be noted that for interval scale there is no pre-decided starting
point or a true zero value.
Example: Time, Temperature

Note: We know that the difference between a measurement of 20 and a measurement of 30 is equal to the
difference between measurements of 30 and 40. The ability to do this implies the use of a unit distance and
a zero point, both of which are arbitrary. The selected zero point is not necessarily a true zero in that it does
not have to indicate a total absence of the quantity being measured.
Perhaps the best example of an interval scale is provided by the way in which temperature is usually
measured (degrees Fahrenheit or Celsius).
The unit of measurement is the degree, and the point of comparison is the arbitrarily chosen “zero degrees,”
which does not indicate a lack of heat. The interval scale unlike the nominal and ordinal scales is a truly
quantitative scale.

Ratio Scale: It is an interval scale with the additional property that its zero position indicates the absence of
the quantity being measured. You can think of a ratio scale as the three earlier scales rolled up in one. Like a
nominal scale, it provides a name or category for each object (the numbers serve as labels). Like an ordinal
scale, the objects are ordered (in terms of the ordering of the numbers). Like an interval scale, the same
difference at two places on the scale has the same meaning. And in addition, the same ratio at two places on
the scale also carries the same meaning.

Ratio Scale is defined as a variable measurement scale that not only produces the order of variables but
also makes the difference between variables known along with information on the value of true zero. It is
calculated by assuming that the variables have an option for zero, the difference between the two
variables is the same and there is a specific order between the options.
The highest level of measurement is the Ratio Scale.Fundamental to the ratio scale is a true zero point.
The measurement of height, weight, length etc. makes use of the ratio scale.

Bio Statistics.pptx by Dr.REVATHI SIVAKUMAR

Quantitative variables take numerical values and these variables are often further classified as either:
•Discrete, when the variable takes on a countable number of values.
Most often these variables indeed represent some kind of count such as the number of prescriptions an
individual takes daily.
•Continuous, when the variable can take on any value in some range of values.
Common examples would be height (inches), weight (pounds), or time to recovery (days).

Raw data: Measurements that have not been organized, summarized, or otherwise manipulated are
called raw data.
Unless the number of observations is extremely small, it will be unlikely that these raw data will impart
much information until they have been put into some kind of order.
There are several techniques for organizing and summarizing data so that we may more easily determine
what information they contain.
The ultimate in summarization of data is the calculation of a single number that in some way conveys
important information about the data from which it was calculated.
Such single numbers that are used to describe data are called descriptive measures.

A first step in organizing data is the preparation of an ordered array.
An ordered array is a listing of the values of a collection in order of magnitude from the smallest value to
the largest value.
An ordered array enables one to determine quickly the value of the smallest measurement, the value of
the largest measurement, and other facts about the arrayed data that might be needed for quick
understanding of the data.

Consider a set of data on age of 189 patients who visited an OP department of a hospital .

To group the above set of observations, we select a set of contiguous, nonoverlapping intervals such that
each value in the set of observations can be placed in one, and only one, of the intervals.
These intervals are usually referred to as class intervals.
One of the first considerations when data are to be grouped is how many intervals to include. Too few
intervals are undesirable because of the resulting loss of information. On the other hand, if too many
intervals are used, the objective of summarization will not be met.
The best guide to this, as well as to other decisions to be made in grouping data, is your knowledge of the
data. A commonly followed rule of thumb states that there should be no fewer than five intervals and no
more than 15.

More specific guidance in the matter of deciding how many class intervals to employ is available by using
Sturges’s formula.
This formula gives k=1+3.332 log n
where k stands for the number of class intervals and n is the number of values in the data set under
consideration.
Class intervals generally should be of the same width, although this is sometimes impossible to
accomplish. The width may be determined by dividing the range by k, the number of class intervals.
Symbolically, the class interval width is given by w=R/k where R (the range) is the difference between
the smallest and the largest observation in the data set, and k is defined as above.

When we group data, we count the number of observations falling in the various intervals and
such number is called frequency.
The resulted grouped data is exhibited in the form of a table.
Such table shows the way in which the values of the variable are distributed among the specified
class intervals and we can determine the frequency of occurrence of values within any one of the
class intervals shown. Such table is called frequency distribution.

Relative Frequencies: In many of the situations it may be useful to know the proportion, rather than the
number, of values falling within a particular class interval.
We obtain relative frequencies by dividing the number of values in the particular class interval by the
total number of values.
We may refer to the proportion of values falling within a class interval as the relative frequency of
occurrence of values in that interval.

The level of precision observed in reported data that are measured on a continuous scale indicates some
order of rounding. When a frequency distribution is constructed from the data, the class interval limits
usually reflect the degree of precision of the raw data.

Histogram:
We may display a frequency distribution (or a relative frequency distribution) graphically in the form of
a histogram, which is a special type of bar graph.
When we construct a histogram the values of the variable under consideration are represented by the
horizontal axis, while the vertical axis has as its scale the frequency (or relative frequency) of
occurrence.

Bio Statistics.pptx by Dr.REVATHI SIVAKUMAR

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