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In which direction is it biased?

Would you say that this sampling method (asking people to simply circle 10 representative words) is biased? . In which direction is it biased? Explain how you can tell this from the dot plot of the sample averages . Suggest some reasons why this sampling method turns out to be biased.

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In which direction is it biased?

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  1. Would you say that this sampling method (asking people to simply circle 10 representative words) is biased? In which direction is it biased? Explain how you can tell this from the dot plot of the sample averages. Suggest some reasons why this sampling method turns out to be biased.

  2. Consider a different sampling method: Close your eyes and point to the text of the Gettysburg Address 10 times to select the words for your sample. Explain why this method would also be biased toward overestimating. Would using this sampling method with a larger sample (say, 20 or 30 words) eliminate the sampling bias? Explain. Suggest how you might employ a different sampling method that would be unbiased.

  3. One way to avoid a biased sampling method is to select items from the population in such a way that gives every item an equal chance of being chosen for the sample. Moreover, the selection method should ensure that every possible sample of items (of the desired sample size) has an equal chance of being the sample ultimately selected. Such a sampling design is called Simple Random Sampling.

  4. Simple Random Sampling(SRS) is easier said than done! • One method for attempting to implement SRS is physical mixing: • write each word from the Gettysburg Address on an individual piece of paper • put the papers into a hat • mix them thoroughly • draw them out one at a time (without looking) until the sample is complete This method often remains fraught with potential for hidden bias: e.g., different sizes of paper, insufficient mixing, etc A better alternative for selecting a SRS is to use computer-generated random digits or random sampling simulations.

  5. Random Digit Table

  6. Sampling Frame for the Gettysburg Address

  7. A statistic is said to provide unbiased estimates of the population parameter if values of the statistic calculated from different samples tend to cluster symmetrically around the actual parameter value (i.e., tend to be centered around the parameter with roughly equal frequency). Does random sampling appear to have produced unbiased estimates of the average word length in the population, which is 4.29 letters?

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