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Biostatistics
M. Gayathri, M.Sc, M.Phil.
Assistant Professor
Department of Mathematics
Sri Sarada Niketan college of Science for women , Karur-5
Data
Data:
■ The numerical value or information recorded in experiment is called data
■ Data obtained from the primary source or the secondary source
Primary Data:
● The data which are collected from the field under the control and supervision of an
investigator
● Primary data means original data that has been collected specially for the purpose in
mind This type of data are generally afresh and collected for the first time
● It is useful for current studies as well as for future studies
Primary Research Methods
● Observations
● Interviews
● Questionnaire
● Experiments
Merits of Primary data
● It is original and fresh.
● They are more accurate.
● They are reliable.
● They are the latest information at hand.
Demerits of Primary Data:
● Collection of primary data is a time consuming affair.
● It may be expensive too.
● It is difficult to find sincere and honest interviewers or enumerators.
● In the case of questionnaire method, the researcher might face the problem of non-
response.
● The respondents may not be prepared for an interview when the enumerator approaches
them with the schedule.
Secondary Data
Data gathered and recorded by someone else prior to and
for a purpose other than the current project. Secondary data
is data that has been collected for another purpose. It
involves less cost, time and effort .Secondary data is data
that is being reused. Usually in a different context
Sources of Secondary Data:
● books
● records
● journals
● dissertations
● Government Orders
Merits of Secondary Data:
● It is easy to use information already gathered by someone.
● It will not be expensive.
● Collection of secondary data is not a time consuming affair.
● The researcher need not depend on anyone for the necessary information.
● There is no need for a questionnaire or schedule.
Demerits of Secondary Data:
● It is difficult to find data that would be just relevant for the study.
● There is no guarantee that the available information will be reliable in most cases.
● Analysis carried out on inaccurate data will render the study useless.
● The market trend, consumer behaviour etc., are not static. A study in marketing
pertaining to these would not, therefore, warrant the use of secondary data.
● The researcher, in certain cases, may not find access to certain records.
Sampling and Sampling Design
Sample :
Subset of the population that is selected for a study.
Sampling :
The process of choosing a representative portion of the entire population.
– an integral part of research methodology.
– involves selecting a group of people, events, behaviors or other elements with which to
conduct a study.
Essentials of sampling
● A sample should be representative of the universe from which it is drawn.
● The size of the sample should be adequate.
● The number of samples should be such that the variation between them
could lie between explainable limits.
Merits of Sampling
Economical:
It is economical, because we have not to collect all data. Instead of getting data
from 5000 farmers, we get it from 50-100 only.
Less Time Consuming:
As number of units is only a fraction of the total universe, time consumed is
also a fraction of total time. Number of units is considerably small, hence the
time.
Reliable:
If sample is taken judiciously, the results are very reliable and accurate.
Organisational Convenience:
As samples are taken and the number of units is smaller, the better (Trained)
enumerators can be employed by the organisation.
More Scientific:
Samples are chosen by the researcher more scientifically. Hence error can be
minimised.
Demerits of Sampling
Absence of Being Representative:
Methods, such as purposive sampling may not provide a sample, that is representative.
Wrong Conclusion:
If the sample is not representative, the results will not be correct. These will lead to the
wrong conclusions.
Small Universe:
Sometimes universe is so small that proper samples cannot be taken not of it. Number of
units are so less.
Specialised Knowledge:
It is a scientific method. Therefore, to get a good and representative sample, one should
have special knowledge to get good sample and to perform proper analysis so that reliable
result may be achieved.
Personal Bias:
As in many cases the investigator, chooses samples, such as
convenience method, chances of personal bias creep in.
Probability Sampling:
In probability sampling, every element of the population has an
equal chance of being selected. Probability sampling gives us the
best chance to create a sample that is truly representative of the
population.
Non-Probability Sampling:
In non-probability sampling, all elements do not have an equal
chance of being selected. Consequently, there is a significant risk of
ending up with a non-representative sample which does not
produce generalizable results
Types of sampling
Probability Sampling Methods:
Simple Random Sampling
This is a type of sampling technique you must have come across at
some point. Here, every individual is chosen entirely by chance and
each member of the population has an equal chance of being
selected.
Systematic Sampling
In this type of sampling, the first individual is selected randomly
and others are selected using a fixed ‘sampling interval’. Let’s take
a simple example to understand this.
Say our population size is x and we have to select a sample size of n.
Then, the next individual that we will select would be x/nth
intervals away from the first individual. We can select the rest in
the same way.
Stratified Sampling
In this type of sampling, we divide the population into subgroups
(called strata) based on different traits like gender, category, etc.
And then we select the sample(s) from these subgroups.
Cluster Sampling
In a clustered sample, we use the subgroups of the population as
the sampling unit rather than individuals. The population is divided
into subgroups, known as clusters, and a whole cluster is randomly
selected to be included in the study
Multi-Stage Sampling:
Population is divided into multiple clusters and then these
clusters are further divided and grouped into various sub groups
(strata) based on similarity. One or more clusters can be
randomly selected from each stratum. This process continues
until the cluster can’t be divided anymore. For example country
can be divided into states, cities, urban and rural and all the areas
with similar characteristics can be merged together to form a
strata.
Non-Probability Sampling Methods:
Convenience Sampling
This is perhaps the easiest method of sampling because individuals
are selected based on their availability and willingness to take part.
Convenience sampling is prone to significant bias, because the
sample may not be the representation of the specific
characteristics such as religion or, say the gender, of the
population.
Quota Sampling
In this type of sampling, we choose items based on predetermined
characteristics of the population.In quota sampling, the chosen
sample might not be the best representation of the characteristics
of the population that weren’t considered.
Judgment Sampling
It is also known as selective sampling. It depends on the judgment
of the investigator when choosing whom to ask to participate.
Snowball Sampling
Existing people are asked to nominate further people known to
them so that the sample increases in size like a rolling snowball.
This method of sampling is effective when a sampling frame is
difficult to identify.
CLASSIFICATION
CLASSIFICATION:
The grouping of related facts/data into different classes according
to certain common characteristic
Types of Classification:
1. Geographical i.e. area wise
• Total Population of Orissa by districts
• No. of death due to malaria by districts.
• Infant deaths in Orissa by districts
2. Chronological or Temporal • i.e. on the basis of time
(years,months,weeks,days,hours and so on)
Table: 2 Death by lightning
YEAR NUMBERS
1941 10
1951 5
1961 6
1971 4
1981 5
TOTAL 30
3. Qualitative i.e. on the basis of some attributes
Example: People by place of residence, sex and literacy
4. Quantitative: On the basis of quantitative class intervals
For example age, income production , price , profits, height weight
and so on
Weight (in kg) Numbers
50-60 28
60-70 25
70-80 10
total 63
OBJECTIVES OF CLASSIFICATION
● Helps in condensing the mass of data such that similarities and
dissimilarities can be readily distinguished.
● Facilitate comparison
● Most significant features of the data can be pin pointed at a
glance
● Enables statistical treatment of the collected data
● Averages can be computed
● Variations can be revealed
● Association can be studied
● Model for prediction / forecasting can be built
● Hypothesis can be formulated and tested etc.
Principles of Classification
There is no hard and fast rules for deciding the class interval,
however it depends upon:
● Knowledge of the data
● Lowest and highest value of the set of observations
● Utility of the class intervals for meaningful comparison and
interpretation
● The classes should be collectively exhaustive and non-
overlapping i.e. mutually exclusive.
● The number of classes should not be too large other wise the
purpose of class i.e. summarization of data will not be served.
● The number of classes should not be too small either, for this
also may obscure the true nature of the distribution.
● The class should preferable of equal width. Other wise the class
frequency would not be comparable, and the computation of
statistical measures will be laborious.
Tabulation
What is a Table?
Table involves the orderly and systematic presentation of
numerical data in a form designed to elucidate the problem under
consideration.
MEANING:
Table is systematic organization and presentation of data in the
form of rows and columns. Whereas rows are horizontal
arrangements and columns are vertical arrangements.
Objectives of Tabulation
● To carry out investigation
● To do comparison
● To locate omissions and errors in the data.
● To use space economically
● To simplify data
● To use it as future reference
Difference between classification and tabulation
BASIS FOR COMPARISON CLASSIFICATION TABULATION
Meaning Classification is the process of
grouping data into different
categories, on the basis of
nature, behavior, or common
characteristics.
Tabulation is a process
of summarizing data
and presenting it in a
compact form, by
putting data into
statistical table.
Order
After data collection
After classification
Arrangement Attributes and variables Columns and rows
Purpose To analyse data To present data
Bifurcates data into Categories and sub-categories Headings and sub-
headings
Parts of a Table :
● Table number
● Title of the table
● Caption
● Stubs
● Body
● Head note
● Footnote
● source note
BIOSTATISTICS - Data, Types of Data, and collection of data
Table number:
A table should be always be numbered for identification and reference in the
future.
Title of the table:
The title is the main heading written in capitals shown at the top of the table. It
must explain the contents of the table and throw light on the table, as whole
different parts of the heading can be separated by commas. There are no full
stops in the little.
Captions:
The vertical heading and subheading of the column are called columns captions.
The spaces where these column headings are written is called the box head. Only
the first letter of the box head is in capital letters and the remaining words must
be written in lowercase.
Stubs :
The horizontal headings and sub heading of the row are called row captions and
the space where these rows headings are written is called the stub.
Body :
This is the main part of the table which contains the numerical information
classified with respect to row and column captions.
Head note
A statement given below the title and enclosed in brackets usually describes the
units of measurement and is called the prefatory notes.
Footnote
These appear immediately below the body of the table providing additional
explanation.
source note
The source notes are given at the end of the table indicating the source the
information has been taken from. It includes the information about compiling
agency, publication, etc.
Rules for Tabulation
● A good table must contain all the essential parts, such as, Table number, Title,
Head note, Caption, Stub, Body, Foot note and source note.
● A good table should be simple to understand. It should also be compact,
complete and self-explanatory.
● A good table should be of proper size. There should be proper space for rows
and columns. One table should not be overloaded with details. Sometimes it
is difficult to present entire data in a single table. In that case, data are to be
divided into more number of tables.
● A good table must have an attractive get up. It should be prepared in such a
manner that a scholar can understand the problem without any strain.
● Rows and columns of a table must be numbered.
● In all tables the captions and stubs should be arranged in some systematic
manner. The manner of presentation may be alphabetically, or chronologically
depending upon the requirement.
● The unit of measurement should be mentioned in the head note.
● The figures should be rounded off to the nearest hundred, or thousand or
lakh. It helps in avoiding unnecessary details.
● Percentages and ratios should be computed. Percentage of the value for item
to the total must be given in parenthesis just below the value.
● In case of non-availability of information, one should write N.A. or indicate it
by dash (-).
● Ditto marks should be avoided in a table. Similarly the expression ‘etc’ should
not be used in a table.

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BIOSTATISTICS - Data, Types of Data, and collection of data

  • 1. Biostatistics M. Gayathri, M.Sc, M.Phil. Assistant Professor Department of Mathematics Sri Sarada Niketan college of Science for women , Karur-5
  • 2. Data Data: ■ The numerical value or information recorded in experiment is called data ■ Data obtained from the primary source or the secondary source Primary Data: ● The data which are collected from the field under the control and supervision of an investigator ● Primary data means original data that has been collected specially for the purpose in mind This type of data are generally afresh and collected for the first time ● It is useful for current studies as well as for future studies
  • 3. Primary Research Methods ● Observations ● Interviews ● Questionnaire ● Experiments Merits of Primary data ● It is original and fresh. ● They are more accurate. ● They are reliable. ● They are the latest information at hand.
  • 4. Demerits of Primary Data: ● Collection of primary data is a time consuming affair. ● It may be expensive too. ● It is difficult to find sincere and honest interviewers or enumerators. ● In the case of questionnaire method, the researcher might face the problem of non- response. ● The respondents may not be prepared for an interview when the enumerator approaches them with the schedule.
  • 5. Secondary Data Data gathered and recorded by someone else prior to and for a purpose other than the current project. Secondary data is data that has been collected for another purpose. It involves less cost, time and effort .Secondary data is data that is being reused. Usually in a different context
  • 6. Sources of Secondary Data: ● books ● records ● journals ● dissertations ● Government Orders Merits of Secondary Data: ● It is easy to use information already gathered by someone. ● It will not be expensive. ● Collection of secondary data is not a time consuming affair. ● The researcher need not depend on anyone for the necessary information. ● There is no need for a questionnaire or schedule.
  • 7. Demerits of Secondary Data: ● It is difficult to find data that would be just relevant for the study. ● There is no guarantee that the available information will be reliable in most cases. ● Analysis carried out on inaccurate data will render the study useless. ● The market trend, consumer behaviour etc., are not static. A study in marketing pertaining to these would not, therefore, warrant the use of secondary data. ● The researcher, in certain cases, may not find access to certain records.
  • 8. Sampling and Sampling Design Sample : Subset of the population that is selected for a study. Sampling : The process of choosing a representative portion of the entire population. – an integral part of research methodology. – involves selecting a group of people, events, behaviors or other elements with which to conduct a study.
  • 9. Essentials of sampling ● A sample should be representative of the universe from which it is drawn. ● The size of the sample should be adequate. ● The number of samples should be such that the variation between them could lie between explainable limits.
  • 10. Merits of Sampling Economical: It is economical, because we have not to collect all data. Instead of getting data from 5000 farmers, we get it from 50-100 only. Less Time Consuming: As number of units is only a fraction of the total universe, time consumed is also a fraction of total time. Number of units is considerably small, hence the time.
  • 11. Reliable: If sample is taken judiciously, the results are very reliable and accurate. Organisational Convenience: As samples are taken and the number of units is smaller, the better (Trained) enumerators can be employed by the organisation. More Scientific: Samples are chosen by the researcher more scientifically. Hence error can be minimised.
  • 12. Demerits of Sampling Absence of Being Representative: Methods, such as purposive sampling may not provide a sample, that is representative. Wrong Conclusion: If the sample is not representative, the results will not be correct. These will lead to the wrong conclusions.
  • 13. Small Universe: Sometimes universe is so small that proper samples cannot be taken not of it. Number of units are so less. Specialised Knowledge: It is a scientific method. Therefore, to get a good and representative sample, one should have special knowledge to get good sample and to perform proper analysis so that reliable result may be achieved.
  • 14. Personal Bias: As in many cases the investigator, chooses samples, such as convenience method, chances of personal bias creep in.
  • 15. Probability Sampling: In probability sampling, every element of the population has an equal chance of being selected. Probability sampling gives us the best chance to create a sample that is truly representative of the population. Non-Probability Sampling: In non-probability sampling, all elements do not have an equal chance of being selected. Consequently, there is a significant risk of ending up with a non-representative sample which does not produce generalizable results Types of sampling
  • 16. Probability Sampling Methods: Simple Random Sampling This is a type of sampling technique you must have come across at some point. Here, every individual is chosen entirely by chance and each member of the population has an equal chance of being selected.
  • 17. Systematic Sampling In this type of sampling, the first individual is selected randomly and others are selected using a fixed ‘sampling interval’. Let’s take a simple example to understand this. Say our population size is x and we have to select a sample size of n. Then, the next individual that we will select would be x/nth intervals away from the first individual. We can select the rest in the same way.
  • 18. Stratified Sampling In this type of sampling, we divide the population into subgroups (called strata) based on different traits like gender, category, etc. And then we select the sample(s) from these subgroups. Cluster Sampling In a clustered sample, we use the subgroups of the population as the sampling unit rather than individuals. The population is divided into subgroups, known as clusters, and a whole cluster is randomly selected to be included in the study
  • 19. Multi-Stage Sampling: Population is divided into multiple clusters and then these clusters are further divided and grouped into various sub groups (strata) based on similarity. One or more clusters can be randomly selected from each stratum. This process continues until the cluster can’t be divided anymore. For example country can be divided into states, cities, urban and rural and all the areas with similar characteristics can be merged together to form a strata.
  • 20. Non-Probability Sampling Methods: Convenience Sampling This is perhaps the easiest method of sampling because individuals are selected based on their availability and willingness to take part. Convenience sampling is prone to significant bias, because the sample may not be the representation of the specific characteristics such as religion or, say the gender, of the population.
  • 21. Quota Sampling In this type of sampling, we choose items based on predetermined characteristics of the population.In quota sampling, the chosen sample might not be the best representation of the characteristics of the population that weren’t considered.
  • 22. Judgment Sampling It is also known as selective sampling. It depends on the judgment of the investigator when choosing whom to ask to participate. Snowball Sampling Existing people are asked to nominate further people known to them so that the sample increases in size like a rolling snowball. This method of sampling is effective when a sampling frame is difficult to identify.
  • 23. CLASSIFICATION CLASSIFICATION: The grouping of related facts/data into different classes according to certain common characteristic Types of Classification: 1. Geographical i.e. area wise • Total Population of Orissa by districts • No. of death due to malaria by districts. • Infant deaths in Orissa by districts
  • 24. 2. Chronological or Temporal • i.e. on the basis of time (years,months,weeks,days,hours and so on) Table: 2 Death by lightning YEAR NUMBERS 1941 10 1951 5 1961 6 1971 4 1981 5 TOTAL 30
  • 25. 3. Qualitative i.e. on the basis of some attributes Example: People by place of residence, sex and literacy 4. Quantitative: On the basis of quantitative class intervals For example age, income production , price , profits, height weight and so on Weight (in kg) Numbers 50-60 28 60-70 25 70-80 10 total 63
  • 26. OBJECTIVES OF CLASSIFICATION ● Helps in condensing the mass of data such that similarities and dissimilarities can be readily distinguished. ● Facilitate comparison ● Most significant features of the data can be pin pointed at a glance ● Enables statistical treatment of the collected data ● Averages can be computed ● Variations can be revealed ● Association can be studied ● Model for prediction / forecasting can be built ● Hypothesis can be formulated and tested etc.
  • 27. Principles of Classification There is no hard and fast rules for deciding the class interval, however it depends upon: ● Knowledge of the data ● Lowest and highest value of the set of observations ● Utility of the class intervals for meaningful comparison and interpretation ● The classes should be collectively exhaustive and non- overlapping i.e. mutually exclusive. ● The number of classes should not be too large other wise the purpose of class i.e. summarization of data will not be served.
  • 28. ● The number of classes should not be too small either, for this also may obscure the true nature of the distribution. ● The class should preferable of equal width. Other wise the class frequency would not be comparable, and the computation of statistical measures will be laborious.
  • 29. Tabulation What is a Table? Table involves the orderly and systematic presentation of numerical data in a form designed to elucidate the problem under consideration. MEANING: Table is systematic organization and presentation of data in the form of rows and columns. Whereas rows are horizontal arrangements and columns are vertical arrangements.
  • 30. Objectives of Tabulation ● To carry out investigation ● To do comparison ● To locate omissions and errors in the data. ● To use space economically ● To simplify data ● To use it as future reference
  • 31. Difference between classification and tabulation BASIS FOR COMPARISON CLASSIFICATION TABULATION Meaning Classification is the process of grouping data into different categories, on the basis of nature, behavior, or common characteristics. Tabulation is a process of summarizing data and presenting it in a compact form, by putting data into statistical table. Order After data collection After classification Arrangement Attributes and variables Columns and rows Purpose To analyse data To present data Bifurcates data into Categories and sub-categories Headings and sub- headings
  • 32. Parts of a Table : ● Table number ● Title of the table ● Caption ● Stubs ● Body ● Head note ● Footnote ● source note
  • 34. Table number: A table should be always be numbered for identification and reference in the future. Title of the table: The title is the main heading written in capitals shown at the top of the table. It must explain the contents of the table and throw light on the table, as whole different parts of the heading can be separated by commas. There are no full stops in the little.
  • 35. Captions: The vertical heading and subheading of the column are called columns captions. The spaces where these column headings are written is called the box head. Only the first letter of the box head is in capital letters and the remaining words must be written in lowercase. Stubs : The horizontal headings and sub heading of the row are called row captions and the space where these rows headings are written is called the stub. Body : This is the main part of the table which contains the numerical information classified with respect to row and column captions.
  • 36. Head note A statement given below the title and enclosed in brackets usually describes the units of measurement and is called the prefatory notes. Footnote These appear immediately below the body of the table providing additional explanation. source note The source notes are given at the end of the table indicating the source the information has been taken from. It includes the information about compiling agency, publication, etc.
  • 37. Rules for Tabulation ● A good table must contain all the essential parts, such as, Table number, Title, Head note, Caption, Stub, Body, Foot note and source note. ● A good table should be simple to understand. It should also be compact, complete and self-explanatory. ● A good table should be of proper size. There should be proper space for rows and columns. One table should not be overloaded with details. Sometimes it is difficult to present entire data in a single table. In that case, data are to be divided into more number of tables.
  • 38. ● A good table must have an attractive get up. It should be prepared in such a manner that a scholar can understand the problem without any strain. ● Rows and columns of a table must be numbered. ● In all tables the captions and stubs should be arranged in some systematic manner. The manner of presentation may be alphabetically, or chronologically depending upon the requirement. ● The unit of measurement should be mentioned in the head note.
  • 39. ● The figures should be rounded off to the nearest hundred, or thousand or lakh. It helps in avoiding unnecessary details. ● Percentages and ratios should be computed. Percentage of the value for item to the total must be given in parenthesis just below the value. ● In case of non-availability of information, one should write N.A. or indicate it by dash (-). ● Ditto marks should be avoided in a table. Similarly the expression ‘etc’ should not be used in a table.