# Block design a block design is the experimental

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Block Design A block design is the experimental counterpart to a stratified sample. A block design recognizes inherent differences in groups of experimental units. The random assignment of experimental units is carried out separately for each block. Matched Pairs Design A matched pairs design begins with pairs of experimental units that are matched to be as similar within a pair as possible. The members of each pair are then randomly assigned to one or the other of two treatments. The matched pairs design is essentially a two treatment block design with each pair being a block. Statistical Inference Statistical inference is concerned with extending the results of a survey or an experiment to the population. Since sample results and experimental results typically have inherent variation, the population level conclusions will be open to question. The particular observed outcomes may be an artifact of the sample or experiment. In statistics, we claim that an effect is statistically significant if it is an effect that is so large that it would rarely occur just by chance. On the other hand, the lack of ‘design’ associated with anecdotal evidence provides no basis for drawing conclusions. The observed patterns may be the result of biased samples, inadequate coverage, o r poorly designed experiments. With anecdotal evidence, you just don’t know. Sampling Distributions This introduction to sampling distributions uses a simulation to reveal the main elements of a sampling distribution. It is intended as a preview to the material that will come later in the course. In Chapter 4, the mathematical tools of probability will be developed. These tools will be used to provide an alternative development of sampling distributions that are not dependent on simulations. Consider the fo llowing ‘thought experiment’. A sample of ‘n’ observations provides a single value for a statistic. In class, the statistic represented the proportion of the people in the survey that supported getting rid of the long gun registration. Figure 1 displays the result of the first 10
respondents in a single simulated survey. The statistic, the proportion of 100 respondents that are not in favour of maintaining the long gun registry, has a value of 0.39 or 39%. This statistic can be used as an estimate of the proportion of the population that support getting rid of the long gun registration. This represents one large area of statistics, statistical estimation. A sample is taken from a population. A statistic is calculated from the sample. The value of the statistic is used to estimate a parameter of the population. The estimate will depend on the size, n, of the sample, and it is expected to be different (ie vary) if the survey or sample is repeated (with a new random sample from the population.) This variation between one sample and other possible samples is referred to as sampling variability. Part of the statistical design such as blocking or stratifying reduces the variability within a block or strata. Larger sample sizes also tend to reduce the sampling variability of the computed statistics.