11.1-11.6 of Sampling by Steven Thompson, 3rd edition. A sample is a smaller, manageable version of a larger group. ?̶��sg�\$7y� Auditor, generally Certified Public Accountant (CPA), use this formula at large for vouching and verification. It is important to note that the variance of estimates under post-stratification is different from under stratification. Stratified sampling with proportional allocation, we use the same algorithms as the sampling and simple random, systematic without replacement. There is no reason that the classes are more homogeneous in weight, and therefore there is no reason why this stratified random sampling is any better than a simple random sampling. In a survey of human population, stratification may be based on socioeconomic factors or geographic regions. As a result, stratified random sampling is more advantageous when the population varies widely since it helps to better organize the samples for study. <> Can you think of a couple of additional examples where stratified sampling would make sense? &= 0.007\\ The question is, given a total sample size of n, how do we allocate these among L strata? It is quite difficult to talk to one million people and take their opinion; rather, its quite easy and time-saving to create various groups, select a few amongst them, and take opinions from them as these data segregation would be representative of the entire population. Looking back at the data, if we had used simple random sampling, would our CI have been tighter or looser? \hat{V}ar(\text{post}-\text{stratified }\bar{y}) & \approx \dfrac{1}{n}\left(\dfrac{N_1}{N}s^2_1+\dfrac{N_2}{N}s^2_2\right)+\dfrac{1}{n^2}\left[\left(1-\dfrac{N_1}{N}\right) s^2_1 + \left(1-\dfrac{N_2}{N}\right) s^2_2 \right]\\ Thus we will choose $$n_1=12, n_2=14$$ and $$n_3=14$$. Stratified sampling with proportional allocation Description of the algorithms we use the same algorithms as the sampling and simple random systematic without replacement. Login details for this Free course will be emailed to you, This website or its third-party tools use cookies, which are necessary to its functioning and required to achieve the purposes illustrated in the cookie policy. Stratified random sampling is a method of sampling that involves the division of a population into smaller groups known as strata. An advertising firm, interested in determining how much to emphasize television advertising in a certain county decides to conduct a sample survey to estimate the average number of hours each week that households within that county watch television. $$\bar{y}_{st}$$ under the proportional allocation: $$nN_h/N$$ and a term that shows the amount of increase one expects from the post- rather than the pre-stratification. \end{array}, $$\hat{\tau}_{st} \pm t\sqrt{\hat{V}ar(\hat{\tau}_{st})}$$ Although stratified random allocation was used to allocate participants to treatment groups, there was no guarantee that each group would have equal numbers because the sample size was small. Refer to the example we have presented in class. You can see that this turns out pretty easy to remember, and one can easily obtain the estimates for the population mean. $$N_3=93, \sigma_3=10$$, $$n_1=\dfrac{40 \times 155 \times 5}{155 \times 5+62 \times 15+93 \times 10}=11.7647$$, $$n_2=\dfrac{40 \times 62 \times 15}{155 \times 5+62 \times 15+93 \times 10}=14.1176$$, $$n_3=\dfrac{40 \times 93 \times 10}{155 \times 5+62 \times 15+93 \times 10}=14.1177$$. determine the optimal allocation of sample sizes. = 13. We use the same principles for calculating total and proportions to finish on statistical evaluation of the results. A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups, which may be related in certain features. Out of the 4,000 participants, the breakdown of majors is as follows: The researchers have their five strata from the stratified random sampling process. The simple random sample is often used when there is very little information available about the data population, when the data population has far too many differences to divide into various subsets, or when there is only one distinct characteristic among the data population. R code:  Chapter6_TVhour.R.txt. Calculate the stratified estimator $$\bar{y}_{st}$$ and the variance of $$\bar{y}_{st}$$. Also estimate the total and the variance of the estimator of total for this example.. This video shows how to allocate proportionally for stratified random sampling. Let’s assume a research team is doing a survey for an FMCG company about the taste and preferences of people in food choices. &= 0.6\\ Compute the estimated variance of the strartified proportion. A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups, which may be related in certain features. The special case where from each stratum a simple random sample is drawn is called a stratified random sample. But, the formula mentioned below is used widely. Assume the team researches the demographics of college students in the U.S and finds the percentage of what students major in: 12% major in English, 28% major in science, 24% major in computer science, 21% major in engineering, and 15% major in mathematics.