Survey Design and Analysis - Assignment Example

Survey Design and Analysis (6BUS0281) Assignment Three This assignment is worth 35% of the marks for this module. This assignment should be completedindividually and not in collaboration with any of your fellow group members. The text you enter will be checked using the TurnItIn website. Please enter your name and student number in the box below.       Part One In the box below, explain why the accuracy of a confidence interval calculated from survey data increases as the survey’s sample size increases. (10 marks) Marks will be awarded according to the following criteria. (i) Correctness of arguments used in explanations. (75%) (ii) Clarity of arguments used in explanations. (25%) The accuracy of confidence interval calculated from survey data increases as the surveys sample size increases because the standard error involved in survey data is inversely proportional to the sample size and as the sample size increases, standard error decreases and hence the accuracy of confidence interval increases so that the sample mean approaches more close to the population mean in probability (ie. consistency improves to great extent). For example if the confidence interval is wider enough ie.99% there is a high confidence of the population mean falling into the confidence interval rather than 95% confidence interval. Here the Sample Mean plus or minus 2 times the Standard Error is the confidence interval and it leads to prediction of population mean with 95% confidence where it is called as 2sigmal limits. Whenever the confidence interval is widening as much as possible, it has high probability of including the population mean. This section reserved for feedback from tutor Mark: [XX] out of 10 Comment: Part Two In the box below, give recommendations as to when stratified sampling can be useful when conducting a survey. (10 marks) Marks will be awarded according to the following criteria. (i) Correctness of arguments used in recommendations. (75%) (ii) Clarity of arguments used in recommendations. (25%) Stratified sampling should be used when more heterogenity of data values are present. For eg. in conudcting economic survey the whole region should be identified as slum area, posh locality, middle class area, lower middle class, Government Colony etc.. When stratification is done the within sample variance will decrease and the accuracy improves to a considerable extent. The stratification can be according to geographic constraint, economic consideration, educational consideration and the stratification reduces the sample variance. The stratification can be accompanied by cost or without cost. When it is done proportional to the population size, it is called Neyman allocation. When the cost constraint is involved, the cost per stratum should be proportional to the inverse of the variance. The cost per stratum is ch and the stratum variance is Sh. Within each stratum we have to adopt to sampling (simple random sampling) and compute the stratum mean or variance. Stratification leads to reduction in the population variance when compared to other sampling methods viz. systematic sampling and simple random sampling. This section reserved for feedback from tutor Mark: [XX] out of 10 Comment: Part Three In the box below, give recommendations as to when cluster sampling can be useful when conducting a survey. (10 marks) Marks will be awarded according to the following criteria. (i) Correctness of arguments used in recommendations. (75%) (ii) Clarity of arguments used in recommendations. (25%) Cluster sampling can be useful when the sample size is equal among different sampling methods. It is widely used in marketing research where a huge population is divided into groups (clusters) and a sample of the groups is selected. After selecting groups, subsamples from each group forms the sample for this type of sampling. For a given stipulated expenses, it gives large sample size. Cluster sampling can be one stage cluster sampling, two stage cluster sampling or multi stage cluster sampling. For example consider sampling of youth in a college. We can take simple random sampling. But it may not be representative of the whole population. Sampling bias is more in simple random sampling. Rather than if we select cluster sampling which consists of some selected sections and then draw sample within each cluster, collect all such subsamples to make a single sample, the precsion would be more better when compared to simple random sampling where the bias is more compared to any other sampling methods viz. systematic sampling, stratified random sampling and cluster sampling. This section reserved for feedback from tutor Mark: [XX] out of 10 Comment: Part Four If you were to repeat your group’s survey for a larger population, spread over the whole of the United Kingdom, state in the box below what clusters (i.e. geographical areas) would you recommend if cluster sampling were to be used. In your answer, give justifications for your recommendations. (10 marks) Marks will be awarded according to the following criteria. (i) Correctness of arguments used in recommendations/justifications. (75%) (ii) Clarity of arguments used in recommendations/justifications. (25%) Out of the nine goegraphical regions spread over England which is having a large population, three popular regions can be taken into consideration viz. London, North West England and South West England. Then we can take sub samples from it, collect altogether and make it as a single sample. Within this geographical regions, we can conveniently select administrative sub divisions as sub samples and select the individual units within it. Here the regions form primary sampling units or clusters. The area within the regions are the secondary sampling units. Often the secondary sampling units are elements of the population. Cluster sampling thus helps us in framing the observation units in a simpler way, least expensive and comfortable.  This section reserved for feedback from tutor Mark: [XX] out of 10 Comment: Part Five In the context of your answer to Part Four, what would you estimate the value of the intra-class correlation coefficient to be? Give justifications for your estimate. (10 marks) Marks will be awarded according to the following criteria. (i) Correctness of arguments used in justifications. (75%) (ii) Clarity of arguments used in justifications. (25%) The intra class correlation coefficient explains the similarity of elements in the same cluster. It depicts the homogenity within clusters.If clusters are perfectly homogeneous then the intra class correlation coefficient is 1. It can also be called as the common correlation among pairs of observations from the same cluster. It is calculated 1 - M/(M-1) SSW/SST where SSW denotes Sum of Squares within the M clusters and SST is the total variance. The variance in cluster sampling is greater than the variance due to stratification yet it provides more information about the clusters. This section reserved for feedback from tutor Mark: [XX] out of 10 Comment: Part Six Imagine that you are conducting a new survey. From one particular question in your survey you wish to estimate a percentage and require a 95% confidence interval for this percentage to be no wider than a certain value. In the box below, determine the sample size required if simple random sampling is to be used in the survey. You will have to invent an estimated percentage and required width which you must state clearly in the box below along with the sample size. You MUST show your workings. As details of the population are not available, you may assume it is large enough and thus YOU CAN IGNORE THE FPC. (10 marks) Marks will be awarded according to the following criteria. (i) Appropriateness of statistical method used. (25%) (ii) Accuracy of workings shown. (75%) The finite population correction (fpc) canbe ignored provided that the sample size is well within 10% of the population size ie.n Read More