Well, sort of. The Chi-square distribution is the sampling distribution of the variance. It is derived based on a random sample. A perfect random sample is where any value in the sample has any relationship to any other value. I would say that if the Chi-square distribution is used, then every effort should be made to make the sample as random as possible. I would also say that if the Chi-square distribution is used and the sample is clearly not a random sample, then improper conclusions may be reached.
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The main difference is that the way of selecting a sample Random sample purely on randomly selected sample,in random sample every objective has a an equal chance to get into sample but it may follow heterogeneous,to over come this problem we can use stratified Random Sample Here the difference is that random sample may follow heterogeneity and Stratified follows homogeneity
Stratified random sampling is a sampling scheme which is used when the population comprises a number of strata, or subsets, which are similar within the strata but differ from one stratum to another. One example is school children stratified according to classes, or salaries stratified by departments.A simple random sample may not have enough representatives from each stratum and the solution is to use stratified random sampling. Under this scheme, the overall sampling proportion (sample size/population size) is determined and a sample is drawn from each stratum which represents the same proportion.
There are two equivalent ways of defining a simple random sample from a larger population. One definition is that every member of the population has the same probability of being included in the sample. The second is that, if you generate all possible samples of the given size from the population, then each such sample has the same probability of being selected for use.
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A simple random sample or a probability sample.