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# Statistics Presentation

Sampling methods and Frequency distribution
by

## Shiruy Daver

on 26 September 2014

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#### Transcript of Statistics Presentation

Step1:
Identify largest value ....... [3.7]
Identify smallest value ....... [1.2]
Determine their difference D ....... [2.5]

Step2:
Count the total number of observations N ...... [14]
Determine the total number of classes T, using the Sturge's Rule
T=1+3.322 log N ....... [5]
(the values of T are rounded off)

Step3:
Determine the width of the class W, using the formula
W=D/T ....... [0.5]

Step4:
List the data according to the width interval

Step5
: Depending on the occurrence of the data in a particular interval, the frequency of each class is determined.
Attempts to obtain a sample of convenient elements.
1. Convenience Sampling Method
A form of convenience sampling. Populations are selected based on the judgement of the researcher and pre-determined criteria.
2.Judgemental Sampling Method
As with stratified samples, the population is broken down into different categories.
3.Quota Sampling Method
An initial group of respondents are selected randomly, subsequent respondents are then selected on the referral or information provided by the initial respondents.
4.Snowball Sampling Method
It is basically the difference between collected values (sample) as compared to the actual values (population).
Sampling Errors
Sampling
Methods

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RANDOM
SAMPLING

Also called probablity sampling.
What is it?
A sampling method in which each member of a population, or sampling frame, has the same probability of being chosen regardless of any other information
1. Simple Random Method
A sampling method in which a population is split into groups or strata either through geographic location, age, sex etc
2.Stratified Sampling Method
Is a form of probability sample where respondents are drawn from a random sample of mutually exclusive groups called "Clusters" (usually geographic areas) within a total population.
3.Cluster Sampling Method
Sample is chosen from the population according to a fixed rule.
4.Systematic Sampling Method
Example
NON
RANDOM
SAMPLING

There are 4 methods of generating a random sample.
A sampling method in which all members of a group (population or universe) have an equal and independent chance of being selected.
Lottery Method
Tippet's Method
The sample will be free from Bias.
High representativeness.
Difficult to construct sampling frame.
More Sampling Errors.
eg.
Ramdomly picking up roll numbers from a class of 40 students for a certain task.
After the segmentation of a population into strata, Simple random sampling would be used to collect the sample.
Homogenity within the Stratum.
Hetrogenity between Strata
eg.
A class is 1st divided on basis of gender i.e. one stratum of girls and another of boys.
Then from the each stratum ramdomly 5 students are choosen.
Focuses on important subpopulations
Improves the accuracy/efficiency of estimation
High representativeness
Not useful when there are no homogeneous subgroups
Can be expensive to implement
Hetrogenity within the Cluster
Homogenity between Clusters
Less expensive
Less time consuming
Can show "regional" variations
Not a genuine random sample
Likely to yield a biased result (especially if only a few clusters are sampled)
eg.
There are 10 streets in Andheri.
All houses on street number 5 are selected to conduct an opinion poll regarding sewage treatment.
This method should yield a more representative sample than the random sample
eg.
Every 500th registrant for Mumbai MUN was given a free T-Shirt.
Easy implementation
Can eliminate sources of biases
Can introduce bias where the pattern used for the samples coincides with a pattern in the population
Not always representative of population
Also called non-probablity sampling.
What is it?
There are 4 methods of generating a non random sample.
Probability sampling, or random sampling, is a sampling technique in which the probability of getting any particular sample may be calculated. Nonprobability sampling does not meet this criterion and should be used with caution.
The selection of sampling units is left to the interviewer.
Respondents are selected as they are in the right place at the right time.
eg.
First five names from the list of patients coming in the doctor's clinic
Measurable and co-operative
Least expensive
Doesn't accurately represent population
Can have many biases involved
The researcher uses judgement or expertise chooses elements to be included in the sample because they believe it is representative of the population of interest.
eg.
A school teacher chooses monitors from each row in a class.
Doesn't allow for generalizations of population
It's inexpensive, convenient
Can be subjective and inaccurate dependent on researcher
However, the size of the sample of each category does not reflect the population as a whole.
eg.
Interviewing more children than adults for a survey on computer games.
Lower Cost
Greater Convenience
No assurance of representation
Selection bias
eg.
If a researcher wishes to interview undocumented immigrants from Mexico, he or she might interview a few undocumented individuals that he or she knows or can locate and would then rely on those subjects to help locate more undocumented individuals.
Relatively low cost
Find rare characteristics easily
Time Consuming
Vague Overall Sampling Size
Arise due to:
1.Biased: Arise due to biased opinions of the enumerators
2.Unbiased:arise due to approximation
Can be considered to be Systematic errors
POPULATION
Simple Random
Stratified
Cluster
Systematic
Frequency Distribution
Classes
Steps to make a Frequency Table
A frequency distribution shows us a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in a class.
It is a way of showing unorganized data e.g. to show results of an election, income of people for a certain region, sales of a product within a certain period, student loan amounts of graduates, etc.
Frequency distributions are used for both qualitative and quantitative data.
Exclusive:
Upper limit of 1st class forms the lower limit of the next class.
Inclusive:
Upper limit of one class is included in that class itself.
THANK YOU
DATA
1.2; 1.4; 1.6; 2; 1.5; 1.7; 2.5; 2.2
2.4; 2.7; 3; 3.3; 3.4; 2.2; 3.7
Class Frequency
1.2-1.7 5
1.8-2.3 3
2.4-2.9 2
3-3.5 3
3.6-4.1 1
TOTAL 14
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