In: Statistics and Probability
Determine the sampling method used in the following scenarios and state whether it is generally biased, or generally unbiased. If a method is generally biased give a reason why it may be biased. a. A factory uses three machines to make a product and the output follows a pattern of Machine 1, Machine 2, Machine 3, Machine 1, … To collect a sample one of the first three products in the line is selected and then every 10th product is selected. b. In order to complete an assignment in a statistics class, a student surveys 15 of their friends. c. A sports talk show posts a poll on their website on the topic they are discussing that day. d. In a clinical trial an independent company is hired to administer a drug trial. 100 people are selected to participate in the trial and split into two groups of 50. One group of 50 is given the medication, and the other 50 are given sugar pills (placebo). The participants and the person administering the “medication” do not know if they are in the test group, or the placebo group.
a) The method of choosing the products gives a biased sample. If the first product is selected (which is the one that came from Machine 1), the next product selected are the 11th, 21st, 31st and so on. Hence, the machines whose products are selected in this case are Machine 1, Machine 2, Machine 3, Machine 1, and so on.. Hence once the first product selected is known, the next ones can be calculated as (first product machine code + 10)%3, (first product machine code + 20)%3, first product machine code, (first product machine code + 10)%3, and so on. Similar sequence generation pattern can be worked out if the first product chosen came from Machine 2 or 3.
b) Surveying students in the same class can give a biased sample, as the students will generally be of similar age group/background/way of thinking, etc.
c) Sports show posting a poll on the topic they're discussing that day is expected to result in an unbiased sample, as the visitors to the site might come from different places/background, and can be expected to result in a varied, unbiased set of opinions.
d) The clinical trial is expected to give unbiased sample as neither the administering agent nor the participants are aware of which particular pill is given to which person. Hence, the distribution of the 2 types of pills among the participant is random, doing away with any possible biases in sampling.