Assignment 3:

 1. Generalization in Sampling:

                                      Generalization refers, to the process of drawing a general conclusion from specific observations. Instead of doing research on the whole population researcher may take few samples and than applying the result to the whole population. The result taken from the sample can be applicable or generalize to the group. 

2. Population and Sample are two important terms in the subject ‘Statistics’. In simple terms, population is the largest collection of items that we are interested to study, and the sample is a subset of a population.

Sample

   A sample may consist of two or more items that have been selected out of the population. The lowest possible size for a sample is two and highest would equals to the size of population.

Population

         Any collection of entities, which are interesting to investigate is simply defined as ‘population.’ Population is the base for samples. Any set of objects in the universe can be a population, based on the declaration of study. Generally, a population should be comparatively large in size and hard to infer some characteristics by considering its items individually.

sample vs Population

           The interesting relationship between the sample and the population is that the population can exist without a sample, but, sample may not exist without population. This argument further proves that a sample depends on a population, but interestingly, most of the population inferences depend on the sample. The main purpose of a sample is to estimate or infer some measurements of a population as accurate as possible. A higher accuracy can be inferred from the overall result obtained from several samples of the same population rather than from one sample. Another important thing to know is, when selecting more than one sample from a population one item can also be included in another sample. This case is known as ‘samples with replacements’. Further more, investing the relevant measurements of the population from a sample and obtaining almost similar output is a golden opportunity to save the cost and time value.

          It is crucial to know that, when the sample size increases, the accuracy of the estimate for the population parameter also increases. Logically, in order to have better estimates for the population, sample size should not be too small. Further, random samples also should be considered to have better estimates. Therefore, it is crucial to pay attention on the size and randomness of the sample to be representative to get best estimates for the population.

3.   A subset of a statistical population that accurately reflects the members of the entire population. A representative sample should be an unbiased indication of what the population is like. In a classroom of 30 students in which half the students are male and half are female, a representative sample might include six students: three males and three females.

4. Target population means the whole population like population of the India, if we want to study the intelligence of all students of India age group (12-20) then it is known as

target population.

     Accessible population means a part of target population. It quite difficult to study the whole at a short time that's why use the term accessible means we can take a part of whole population, it helps us to study the matter easily.

5.  Randomization:

         To make random in arrangement, especially in order to control the variables in an experiment.

         In other words randomization is a deliberately haphazard arrangement of observations so as to simulate chance

Random selection:

           Random selection is how you draw the sample of people for your study from a population.

 Random assignment:

         Random assignment is how you assign the sample that you draw to different groups or treatments in your study.

It is possible to have both random selection and assignment in a study. Let's say you drew a random sample of 100 clients from a population list of 1000 current clients of your organization. That is random selection. Now, let's say you randomly assign 50 of these clients to get some new additional treatment and the other 50 to be controls. That's random assignment.

6.

Simple random sampling 

In a simple random sample (SRS) of a given size, all such subsets of the frame are given an equal probability. Each element of the frame thus has an equal probability of selection: the frame is not subdivided or partitioned. Furthermore, any given pair of elements has the same chance of selection as any other such pair (and similarly for triples, and so on). This minimises bias and simplifies analysis of results. In particular, the variance between individual results within the sample is a good indicator of variance in the overall population, which makes it relatively easy to estimate the accuracy of results

Stratified sampling

Where the population embraces a number of distinct categories, the frame can be organized by these categories into separate "strata." Each stratum is then sampled as an independent sub-population, out of which individual elements can be randomly selected.

Cluster sampling

it is a variation of the simple random sample that is particularly appropriate when the population o interest is infinite, when a list of the members of the population of interest is infinite, when a list of the members of the population does not exist, or when the geographic distribution of the individuals is widely scattered.

 9.         A table of numbers generated in an unpredictable, haphazard sequence. Tables of random numbers are used to create a random samples. A random number table is 10.   External validity is the validity of generalized (causal) inferences in scientific studies, usually based on experiments as experimental validity ,In other words, it is the extent to which the results of a study can be generalized to other situations and to other people.

therefore also called a random sample table. A random number table is a list of numbers, composed of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Numbers in the list are arranged so that each digit has no predictable relationship to the digits that preceded it or to the digits that followed it.

11.     Population Generalizability- The extent to which the results obtained from a sample are generalizable to a larger group.

    

      Ecological Generalizability- The degree to which results can be generalized to environments and conditions outside the research setting.

12.  Sampling Size- The sample size of a statistical sample is the number of observations that constitute it. The sample size is typically denoted by n and it is always a positive integer. No exact sample size can be mentioned here and it can vary in different research settings. However, all else being equal, large sized sample leads to increased precision in estimates of various properties of the population.

13.  When a sample is not representative, the result is known as a sampling error. Using the classroom example again, a sample that included six students, all of whom were male, would not be a representative sample. Whatever conclusions were drawn from studying the six male students would not be likely to translate to the entire group since no female students were studied.