7-3F Unbiased and Biased Samples

Unbiased and Biased Samples The manager of a television station want to conduct a survey to determine which sport people consider their favorite to watch.

Unbiased and Biased Samples 1. Suppose she decides to survey a group of 100 people at a basketball game. Should you assume the results would represent all of the people in the viewing area? Explain?

Unbiased and Biased Samples 2. Suppose she decides to survey 100 students at your middle school. Should you assume the results would represent all of the people in the viewing area? Explain.

Unbiased and Biased Samples 3. Suppose she decides to call every 100th household in the telephone book. Should you assume the results would represent all of the people in the viewing area? Explain. * To get valid results, a sample must be chosen very carefully. An unbiased sample is selected so that it accurately represents the entire population.

Vocabulary In a biased sample, one or more parts of the population are favored over others.

Sampling Methods A farmer has just cleared a field for corn that can be divided into 100 smaller plots. The land has a river running down one side of it. The farmer isn’t sure whether harvesting the entire field is worth the expense. So he decides to harvest 10 plots an use this information to estimate the total yield. Based on this information he will decide whether to harvest the remaining plots.

Method 1: Convenience Sample The farmer begins by choosing 10 plots that are most convenient to him to harvest without any other considerations.

Method 1: Convenience Sample BIASED A convenience sample consists of members of a population that are easily accessed. Example: To represent all students attending a school, the principal surveys the students in one math class

Second Thoughts The farmer has second thoughts about the selection and has decided to come to you with all your statistical wisdom to help him determine the approximate yield of the field. You are still using 10 plots to harvest early. Your job is to use one of following methods and decide which one is the best to use.

Method 2: Simple Random Sample Choose 10 plots at random. 95, 91, 15, 52, 41, 74, 5, 34, 100, 21

Method 2: Simple Random Sample UNBIASED Each item or person in the population is as likely to be chosen as any other. Example: Each student’s name is written on a piece of paper. Their names are placed in a bowl, and names are picked without looking.

Method 3: Stratified (by column) Random Sample Think of the field as grouped in 10 vertical columns. Randomly select one plot from each vertical column. 1, 7, 8, 7, 6, 10, 10, 3, 6, 10

Method 3: Stratified (by row) Random Sample Think of the field as grouped in 10 horizontal rows. Randomly select one plot from each horizontal row. 9, 3, 8, 10, 5, 4, 10, 8, 9, 1

Method 3: Stratified Random Sample UNBIASED The population is divided into similar, non- overlapping groups. A simple random sample is then selected from each group. Example: Students are picked at random from each grade level at school.

A Year Has Passed A year has passed and the crop of corn is up. Below is a grid showing the yield per plot. REMEMBER, you would never have such information. You would only know this for the plots you planted and gathered. But for this exercise, this information is provided.

Sampling Methods 5 16 21 37 44 54 68 77 82 96 8 13 22 33 42 57 64 72 80 93 2 26 30 51 52 63 86 98 15 24 66 73 89 92 4 14 27 32 45 53 65 75 83 94 17 28 31 47 60 74 87 99 6 18 36 50 59 76 90 9 38 41 62 29 39 78 81 91 7 19 23 48 84 Sampling Method Total Yield Average yield per plot Estimate of field’s yield Convenience Sample 62 6.2 620 Simple Random Sample 331 33.1 3310 Stratified by Column 502 50.2 5020 Stratified by Row 607 60.7 6070 Is there a good reason to choose one method over another (without having the benefit of the charts above)? What was the actual yield of the farmer’s field? Which method came closest to that figure? Why?

Method 4: Systematic Random Sample UNBIASED The items or people are selected according to a specific time or item. Example: Every 20th person is chosen from an alphabetical list of all students attending a school.

Method 5: Voluntary Response Sample BIASED Involves only those who want to participate in the sampling. Example: Students at a school who wish to express their opinions complete an online survey.

Determine Validity of Conclusions Determine whether each conclusion is valid. Justify your answers. Every tenth person who walks into a department store is surveyed to determine his or her music preference. Our of 150 customer, 70 stated they prefer rock music. The manager concludes that about half of all customers prefer rock music. Since the population is every tenth customer of a department store, the sample is an unbiased, systematic random sample. The conclusion is valid.

Determine Validity of Conclusions Determine whether each conclusion is valid. Justify your answers. 2. The customers of a music store are surveyed to determine their favorite leisure time activity. Of these, 85% said that they like to listen to music, so the store manager concludes that most people prefer to listen to music in their leisure time. The customers of a music store probably like to listen to music in their leisure time. This sample is a biased, convenience sample since all of the people surveyed are in one specific location. The conclusion is not valid.

Check Your Progress a. A radio station asks listeners to indicate their preference for one of two candidates in an upcoming election. Seventy-two percent of the listeners who responded preferred candidate A, so the radio station announced that candidate A would win the election. Is the conclusion valid? Justify your answer.

Check Your Progress b. An instructor at a swimming pool asked her students if they would be interested in an advanced swimming course, and 60% stated that they would. Are the results valid? If so, suppose there are 870 pool members. How many people can the instructor expect to take the course?