We all know ‘Sample’ means a small part or quantity intended to show what the whole is like. Similarly, the ‘Random Sampling’ is a way of selecting a portion chosen from the population in order to make inferences about the whole population. For example, pre-polls or exit polls results obtained from random voters aims to predict the likely results of an election.
Sample and population:
The term ‘sample’, is also called statistic. Sample is not from the population but probable from the sample. The term ‘population’ does not mean that it relates to people; it may be any items that are to be studied. The portrayal of population is called parameter. Thus, a statistic is a characteristic of a sample; a parameter is a characteristic of a population. Typically, statisticians use lower case Roman letters to denote sample statistics and Greek or Capital letters to denote population parameters. We can describe samples and populations by using measures such as mean, median, mode and standard deviation.
The following are four main types of random sampling.
Simple Random Sampling:
A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. So, Simple Random Sampling refers to an unbiased representation of a group. The names of 50 students being chosen out of 500 students of a school is an example of Simple Random Sampling.
Systematic sampling method is a probability sampling method where the elements are chosen from a target population by selecting a random starting point and selecting other members after a fixed ‘sampling interval’. Sampling interval is calculated by dividing the entire population size by the desired sample size.
In Stratified Sampling, the population is divided into subgroups and random sample is taken in proportion to the size of each subgroup. The members in each of the division formed have similar attributes and characteristics.
The researcher divides the population in to cluster (a group of similar things or people positioned or occurring closely together separate groups, called clusters) and then conducts his analysis on data from the sampled clusters.
Data Analysis: “Data analysis is the process by which sense and meaning is made of the data gathered in qualitative research. These data taken for analysis also includes records of group discussions and interviews.
Sampling distribution: A sampling distribution is the probability distribution of a given random-sample-based statistic.
Sample distribution of the mean: The probability distribution of all the possible means of samples is known as the sample distribution of the mean. In a normally distributed population, the sampling distribution of the mean and it has a mean equal to the mean. Further, sample distribution of the mean has a standard deviation equal to the population standard deviation divided by the square root of the sample size. Note that the spread of the sampling distribution of the mean decreases as the sample size increases.
Standard error: The standard deviation of the sampling distribution of the mean is called the standard error of the mean.
What are Null hypothesis and alternative hypothesis?