Today's Session starts with the differentiation between Chi Square Test and T-Test.............
Chi square test is used to analyze categorical data i.e. null hypothesis which means no relation between two informations provided where as T-test is used to analyze population and in different ways:
1. Single Sample
2. Independent Sample
3.Paired Sample
Chi square test is used to analyze categorical data i.e. null hypothesis which means no relation between two informations provided where as T-test is used to analyze population and in different ways:
1. Single Sample
2. Independent Sample
3.Paired Sample
SAMPLING:
A process used in statistical analysis in which a predetermined number of observations will be taken from a larger population. The methodology used to sample from a larger population will depend on the type of analysis being performed, but will include simple random sampling, systematic sampling and observational sampling.
We obtain a sample rather than a complete enumeration (a census ) of the population for many reasons few of which are a)Economy b)Timeliness c)the large size of many populations d)Inaccessibility of some of the population e)Destructiveness of the observation and f)accuracy
Reasons for Sampling:
1. The sample can save money.
2. The sample can save time.
3. For given resources, the sample can broaden the scope of the study.
4. Because the research process is sometime destructive, the sample can save product.
5. If accessing the population is impossible, the sample is the only option.
Category of Sampling:
1. Continuous Sampling
2. Discreet Sampling
Census - A census is the procedure of systematically acquiring and recording information about the members of a given population. It is a regularly occurring and official count of a particular population. The term is used mostly in connection with national population and housing censuses; other common censuses include agriculture, business, and traffic censuses.
Target Population - Target population is the entire set of units for which the survey data is to be used to make inferences. It can also be defined as the eligible population that is included in research work.
Sampling Frame - A set of information used to identify a sample population for statistical treatment. A sampling frame includes a numerical identifier for each individual, plus other identifying information about characteristics of the individuals, to aid in analysis and allow for division into further frames for more in-depth analysis.
Sample - A sample is a part of the population of interest, a sub-collection selected from a population.
Probability Sampling
In probability sampling, every item has a chance of being selected. For probability sampling, randomization is a feature of the selection process, rather than an assumption about the structure of the population.
1. Simple random
A simple random sample (SRS) of size n is produced by a scheme which ensures that each subgroup of the population of size n has an equal probability of being chosen as the sample.
2. Systematic Random
Systematic sampling is a statistical method involving the selection of elements from an ordered sampling frame.
The most common form of systematic sampling is an equal-probability method. In this approach, progression through the list is treated circularly, with a return to the top once the end of the list is passed. The sampling starts by selecting an element from the list at random and then every kth element in the frame is selected, where k, the sampling interval (sometimes known as the skip): this is calculated as:
k = N/n
where n is the sample size, and N is the population size.
3. Cluster Sampling
Cluster sampling is a sampling technique used when "natural" groupings are evident in a statistical population. It is often used in marketing research. In this technique, the total population is divided into these groups (or clusters) and a sample of the groups is selected. Then the required information is collected from the elements within each selected group.
4. Stratified sampling
Divide the population into "strata". There can be any number of these. Then choose a simple random sample from each stratum. Combine those into the overall sample. That is a stratified random sample. (Example: Church A has 600 women and 400 women as members. One way to get a stratified random sample of size 30 is to take a SRS of 18 women from the 600 women and another SRS of 12 men from the 400 men.)
Stratified random sampling gives more precise information than simple random sampling for a given sample size. So, if information on all members of the population is available that divides them into strata that seem relevant, stratified sampling will usually be used.
Benfords Law
Benford's Law (which was first mentioned in 1881 by the astronomer Simon Newcomb) states that if we randomly select a number from a table of physical constants or statistical data, the probability that the first digit will be a "1" is about 0.301, rather than 0.1 as we might expect if all digits were equally likely.
Non Probability samplingIn non-probability sampling, there is an assumption that there is an even distribution of characteristics within the population. This is what makes the researcher believe that any sample would be representative and because of that, results will be accurate. In non-probability sampling, since elements are chosen arbitrarily, there is no way to estimate the probability of any one element being included in the sample.
1. Convenience SamplingConvenience sampling is sometimes referred to as haphazard or accidental sampling. It is not normally representative of the target population because sample units are only selected if they can be accessed easily and conveniently.
There are times when the average person uses convenience sampling. A food critic, for example, may try several appetizers or entrees to judge the quality and variety of a menu.
Examples of convenience sampling include:
2. Judgement Sampling
In judgement sampling, the researcher or some other "expert" uses his/her judgement in selecting the units from the population for study based on the population’s parameters.
This type of sampling technique might be the most appropriate if the population to be studied is difficult to locate or if some members are thought to be better (more knowledgeable, more willing, etc.) than others to interview. This determination is often made on the advice and with the assistance of the client. For instance, if you wanted to interview incentive travel organizers within a specific industry to determine their needs or destination preferences, you might find that not only are there relatively few, they are also extremely busy and may well be reluctant to take time to talk to you. Relying on the judgement of some knowledgeable experts may be far more productive in identifying potential interviewees than trying to develop a list of the population in order to randomly select a small number.
3. Quota Sampling
In the quota sampling the selection of the sample is made by the interviewer, who has been given quotas to fill from specified sub-groups of the population.
For example,
An interviewer may be told to sample 50 females between the age of 45 and 60.
4. Snowball Sampling
A snowball sample is a non-probability technique that is appropriate to use in research when the members of a population are difficult to locate. A snowball sample is one in which the researcher collects data on the few members of the target population he or she can locate, then asks those individuals to provide information needed to locate other members of that population whom they know.
1. Simple random
A simple random sample (SRS) of size n is produced by a scheme which ensures that each subgroup of the population of size n has an equal probability of being chosen as the sample.
2. Systematic Random
Systematic sampling is a statistical method involving the selection of elements from an ordered sampling frame.
The most common form of systematic sampling is an equal-probability method. In this approach, progression through the list is treated circularly, with a return to the top once the end of the list is passed. The sampling starts by selecting an element from the list at random and then every kth element in the frame is selected, where k, the sampling interval (sometimes known as the skip): this is calculated as:
k = N/n
where n is the sample size, and N is the population size.
3. Cluster Sampling
Cluster sampling is a sampling technique used when "natural" groupings are evident in a statistical population. It is often used in marketing research. In this technique, the total population is divided into these groups (or clusters) and a sample of the groups is selected. Then the required information is collected from the elements within each selected group.
4. Stratified sampling
Divide the population into "strata". There can be any number of these. Then choose a simple random sample from each stratum. Combine those into the overall sample. That is a stratified random sample. (Example: Church A has 600 women and 400 women as members. One way to get a stratified random sample of size 30 is to take a SRS of 18 women from the 600 women and another SRS of 12 men from the 400 men.)
Stratified random sampling gives more precise information than simple random sampling for a given sample size. So, if information on all members of the population is available that divides them into strata that seem relevant, stratified sampling will usually be used.
Benfords Law
Benford's Law (which was first mentioned in 1881 by the astronomer Simon Newcomb) states that if we randomly select a number from a table of physical constants or statistical data, the probability that the first digit will be a "1" is about 0.301, rather than 0.1 as we might expect if all digits were equally likely.
Non Probability samplingIn non-probability sampling, there is an assumption that there is an even distribution of characteristics within the population. This is what makes the researcher believe that any sample would be representative and because of that, results will be accurate. In non-probability sampling, since elements are chosen arbitrarily, there is no way to estimate the probability of any one element being included in the sample.
1. Convenience SamplingConvenience sampling is sometimes referred to as haphazard or accidental sampling. It is not normally representative of the target population because sample units are only selected if they can be accessed easily and conveniently.
There are times when the average person uses convenience sampling. A food critic, for example, may try several appetizers or entrees to judge the quality and variety of a menu.
Examples of convenience sampling include:
- the female moviegoers sitting in the first row of a movie theatre
- the first 100 customers to enter a department store
- the first three callers in a radio contest.
2. Judgement Sampling
In judgement sampling, the researcher or some other "expert" uses his/her judgement in selecting the units from the population for study based on the population’s parameters.
This type of sampling technique might be the most appropriate if the population to be studied is difficult to locate or if some members are thought to be better (more knowledgeable, more willing, etc.) than others to interview. This determination is often made on the advice and with the assistance of the client. For instance, if you wanted to interview incentive travel organizers within a specific industry to determine their needs or destination preferences, you might find that not only are there relatively few, they are also extremely busy and may well be reluctant to take time to talk to you. Relying on the judgement of some knowledgeable experts may be far more productive in identifying potential interviewees than trying to develop a list of the population in order to randomly select a small number.
3. Quota Sampling
In the quota sampling the selection of the sample is made by the interviewer, who has been given quotas to fill from specified sub-groups of the population.
For example,
An interviewer may be told to sample 50 females between the age of 45 and 60.
4. Snowball Sampling
A snowball sample is a non-probability technique that is appropriate to use in research when the members of a population are difficult to locate. A snowball sample is one in which the researcher collects data on the few members of the target population he or she can locate, then asks those individuals to provide information needed to locate other members of that population whom they know.
Published by : Nitin Kumar Shukla
Group 8
Nitin Kumar Shukla
Praveen Iyer
Prerna Arora
Neeraj Ramadoss
Prakhar Swami
Nishant Agarwal
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