Lesson Video: Biased versus Unbiased Samples | Nagwa Lesson Video: Biased versus Unbiased Samples | Nagwa

Lesson Video: Biased versus Unbiased Samples Mathematics • Third Year of Preparatory School

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In this video, we will learn how to determine whether a sample is biased or unbiased.

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Video Transcript

In this video, we will learn how to determine whether a sample is biased or unbiased. We will begin by defining these two terms.

A biased sample is one in which some members of the population have a higher or lower sampling probability than others. This includes sampling or selecting based on age, gender, or interests. An unbiased or fair sample must, therefore, be representative of the overall population being studied. Time and resources often mean that we can’t ask every single member of the population. In order to ensure that our sample is a fair reflection, we must ensure it is unbiased. Every member of the population must have an equal chance of being selected. When talking about population, we don’t necessarily mean every person in a country or in the world. We could be talking about the population of a school or a sports club.

For our sample to be unbiased, each of these people has to have an equal chance of being chosen. We will now look at some questions involving biased and unbiased sampling. In each case, we need to ask ourselves the question, does each person in the population have an equal chance of being chosen? If the answer is yes, our sample is unbiased. However, if the answer is no, we’re dealing with a biased sample.

Jennifer is doing a research project on whether or not students in her school eat healthy food. She decides to interview her friends who do gymnastics with her. Is her sample biased?

In order to work out if any sample is biased, we need to ask ourselves one question. The question is this: does every member of the population have an equal chance of being selected? In this question, the students in Jennifer’s school are the population. She’s researching whether they eat healthy food or not. In Jennifer’s sample, she’s only selecting friends from gymnastics. This means that any students in the school who do not do gymnastics cannot be selected.

The answer to the question “Does every member of the population have an equal chance of being selected?” is therefore no. If this is the case, we know that the sample is biased or unfair. The correct overall answer is, therefore, yes, Jennifer’s sample is biased. This is because the only students that can be selected in her sample are those that do gymnastics. It is also quite possible — although not certain — that many of the students who do gymnastics eat healthy food. This means that the sample that she has chosen could skew the results of her research project. They could potentially give a more positive outlook on those students who eat healthy food.

In our next question, we need to select the unbiased sample.

A school principal wants to find out what the students think about the teaching quality in the school. Which of these samples is unbiased? Is it (A) All ninth-grade students are interviewed? (B) A list of female students to interview is randomly generated. (C) A list of male students to interview is randomly generated. (D) A list of students to interview is randomly generated. Or (E) a questionnaire is available at the library for anyone who wants to take part in the survey.

In order to decide whether a sample is biased or unbiased, we need to ask ourselves one question, does every member of the population have an equal chance of being selected? In this question, the students in the school are the population. If each of these has an equal chance of being selected, we can say, yes, the sample is unbiased. If the answer to the question is no, then the sample is biased. A biased sample would mean that some students have a greater chance of being selected than others. Let’s now look at our five options.

In option (A), all ninth-grade students are being interviewed. This means that no students in any other year will be interviewed. This means that this form of sampling is biased, as every member of the population does not have an equal chance of being selected. Options (B), (C), and (D) all talk about randomly generated lists. This suggests that they could be unbiased as each student could have an equal chance of being selected. However, option (B) is just a list of female students. As no male students can be selected in this sample, this is a biased sample. The same is true of option (C). This time, we’re selecting only male students. So, this too is biased.

Option (D), on the other hand, is an unbiased sample. A list of the students is being randomly generated from the whole population. This could be done using a random number generator or a raffle. As long as the list is randomly generated, the sample is unbiased. Option (E) involves leaving a questionnaire at the library for anyone who wants to take part. The fact that anyone can take part suggests it could be unbiased. However, as it is left in the library, not every student will have an equal chance of being in the sample. There is also an element of choice here, which also indicates that the sample is biased. The correct answer is option (D). A list of students to interview is randomly generated will create an unbiased sample for the principal.

Our third question, we’ll look at what we mean by a representative sample.

A student wants to research the amount of pocket money students in his middle school receive. Which of the following would be the best way to get a representative sample of the population? Option (A) asking all the students in the library on a Monday lunchtime how much pocket money they receive. (B) Asking a random sample of 50 students from his grade how much pocket money they receive. (C) Asking the teachers of each class how much pocket money they think the students in their class receive. Or (D) asking a random sample of 20 students from each grade how much pocket money they receive.

As we’re trying to get a representative sample, we want our sample to be unbiased. In order to do this, we ask ourselves a question, does each member of the population have an equal chance of being selected? If our answer to this question is yes, the sample is unbiased. In this question, the population are the students in the middle school. Each of these students needs to have an equal chance of being selected for the sample to be unbiased. The one that is the best representative sample is the one that is closest to this.

In option (A), all the students in the library on a Monday lunchtime are being asked. This is not very representative of the whole school, as the students will have to be in the library on Monday lunchtime. If they’re not there at this time, they will not be in the sample. So, we can rule out option (A). Option (B) talks about a random sample which suggests that it could be representative of the whole population. However, these students are only selected from the student’s grades. This means that any student in a different grade will not be selected. We can, therefore, say that the sample is biased and will therefore not be a good a representation of the population.

It is pretty obvious that option (C) will not get a good representative sample as we’re not asking the students but the teachers. They are also being asked for their opinion as opposed to the actual money that the students receive. An opinion can be skewed by people’s perceptions and is, therefore, biased. Option (D), like option (B), talks about a random sample. The key here is that we are selecting students from each grade. This means that it will give a good representation of the whole population. Students in each grade will have an equal chance of being selected. Therefore, this is the best way to get a representative sample of the students.

We’ll now look at two further questions in different scenarios.

Which of the following is a representative sample? Is it (A) to find out how students travel to school, student representatives from each grade ask a random sample of 20 students from across the grade. (B) A hospital wants to investigate the reasons why people go to the emergency room, so questionnaires are handed out to a random sample of people waiting in the emergency room on a Monday morning. (C) A market research company wants to find out how much waste people recycle, so they survey 100 people at the city recycling drop-off location. (D) A student wants to find out how much students at their school enjoy math classes, so they give a questionnaire to everyone at the math club.

A representative sample is a subset of the population that seeks to accurately reflect the characteristics of the larger group. This means that, where possible, it needs to be unbiased, such that each member of the population has an equal chance of being selected. In option (A), the population is the students in the school. As they are selecting a random sample of 20 students from each grade, this will represent the whole school. Option (A) is, therefore, a representative sample of the whole school as students are not selected based on gender, age, or interest.

In option (B), the population is the people visiting the hospital’s emergency room. Whilst they are asking people in the emergency room, they’re only asking on Monday mornings. This means that the sample is not representative, as people visiting the emergency room at any other time cannot be selected. In option (C), the market research company wants to look at the whole population to see how much they recycle. As they are only serving people at the city recycling drop-off location, the survey is biased. The results would be skewed as these people are more likely to recycle more waste than the general public. This means that option (C) is not a representative sample.

In option (D), the population is the students in the school. As they are only asking students at math club, the questionnaire will be biased. Once again, this is not a representative sample, as those students at math club are more likely to enjoy math classes. Once again, this will skew the results. The correct answer is option (A).

A doctor wants to find out about some possible side effects of a common drug they have prescribed. Which of these samples is unbiased? Is it (A) sending a survey to a select group of patients? (B) Interviewing patients who suffer from side effects of the drug. (C) Interviewing all the patients who come for an appointment on a Saturday. (D) Interviewing patients who come for an appointment during the week at random. Or (E) generating a list of patients to interview by phone randomly from the patient registry.

In order to identify whether a sample is unbiased or biased, we need to ask ourselves a question, does each member of the population have an equal chance of being selected? If the answer to this question is yes, then our sample is unbiased. In this question, the population are the patients that have been prescribed the drug. We want each of these patients to have an equal chance of being selected. Option (A) does not satisfy this criteria, as only a select group of patients have been surveyed. Option (B) is also incorrect, as this time we’re interviewing patients who have suffered from side effects of a drug. This means that our results will be skewed. Each member of the population, those who have and those who haven’t suffered side effects, must be able to be selected.

Options (C) and (D) are incorrect as we’re not asking the correct members of the population. In option (C), we’re asking all the patients who came for an appointment on a Saturday. Many of these might not have been prescribed the drug. Also using this sample, we’re not interviewing any patients from any other day. Option (D) has a similar problem to option (C) in that we have no way of knowing if these patients have been prescribed the drug.

Option (E), on the other hand, is the correct answer. We are generating a list at random from the patient registry. This will include all the patients that have been prescribed the drug by the doctor. Each member of the population has an equal chance of being selected.

We will now summarize the key points from this video. We began this video by defining what we mean by a biased and unbiased sample. In a biased sample, one or more parts of the population are favored over others, whereas in an unbiased sample, each member of the population has an equal chance of being selected. We also saw that a representative sample is a subset of the population that reflects the characteristics of the larger group. In order for our sample to be fair and results accurate, we want an unbiased and representative sample.

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