Convenience Sampling

Launch The tumultuous town mayor wants to re-route the town bus routes, so he goes to the two nearest bus stops and asks riders for their opinions.

Launch Describe the good and not-so-good parts of this approach. Good: The mayor gets opinions from actual bus riders. The riders are nearby so the mayor gets opinions quickly. Not-so-good: The riders are a small sample of all riders. The riders may only be concerned about their route.

Convenience Sampling It doesn’t take much time to find a sample of your friends or of people in the area. How do you sample in a way that is convenient? What are the advantages and disadvantages of convenience sampling?

Convenience Sampling

Convenience Sampling Convenience sampling is a sampling method in which you choose members of the population that are convenient and available.

Convenience Sampling STEP 1—COLLECT A CONVENIENCE SAMPLE When a researcher surveys members of the population that are convenient, the sample is a convenience sample. A convenience sample is not necessarily a representative sample.

Convenience Sampling Suppose you are doing research on the students at your school. Are the following examples of convenience sampling? Explain. You put an ad in the school newspaper for your research project. You accept the first ten students who volunteer. Yes; your sample is based on the first 10 students who volunteered, so this is an instance of convenience sampling.

Convenience Sampling Suppose you are doing research on the students at your school. Are the following examples of convenience sampling? Explain. You put the names of all of the students in a hat and pull out ten names at random. No; you are choosing among the entire population at random, so this is not an instance of convenience sampling.

Convenience Sampling You choose the first 20 students you see. Suppose you are doing research on the students in your grade. Which of the description(s) is NOT an instance of convenience sampling? You choose the first 20 students you see. You choose all of the students in your school band. You choose all of the students in your classroom. You choose 10 students from each classroom.

Suppose you are a news reporter investigating the town’s opinion of the new shopping center. What are three ways to choose a convenience sample of town residents to interview? Are the samples that you chose representative samples? Explain.

Convenience Sampling Convenience Sample #1: Ask people in the neighborhood near the new shopping center. Yes, the sample is probably a representative sample because the people in this neighborhood may be mixed enough to represent the population.

Convenience Sampling Convenience Sample #2: Ask shoppers in the new shopping center. No, the sample is not a representative sample because the people shopping in the new shopping center probably like the new mall, so they do not represent the entire population.

Convenience Sampling Convenience Sample #3: Ask people commuting to work/on the street. Yes, the sample is probably a representative sample because the people on the street are likely to be a good mix of the population.

Convenience Sampling Convenience Sample #4: Ask the people in the local deli. Yes, the sample is probably a representative sample because the people at the local deli are probably mixed enough to be an accurate representation of the population.

Convenience Sampling Convenience Sample #5: Ask shoppers in the local strip mall. No, the sample is not a representative sample. The shoppers at the local strip mall are probably still shopping there because they do not prefer to shop at the new shopping center, so they do not represent the entire population.

Convenience Sampling There are about 300 million websites in the world. Use the convenience sample to estimate the total number of websites that get more than a million hits per day. Is your estimate accurate? Explain.

11 20 ___ * 300 million = 165 million The convenience sample is based on a list of your favorite websites and may be biased toward popular websites with higher numbers of hits per day. So 165 million websites may not be an accurate estimate of the actual number.

Use the convenience sample to estimate how many of the 1,165 cars on Highway 60 are red. Is your estimate accurate? 16 40 ___ * 1,165 cars = 466 cars The estimate is fairly accurate because the distribution of car colors on the highway is random. The number of red cars around you is about the same as the number of red cars around any other car on the highway.

Systematic Sampling

Launch Your school holds a schoolwide kickball tournament. Your gym teacher lines your class up and starts picking every third person to make up your class team.

Launch Describe a possible benefit and a possible drawback of this sampling approach. Benefit: This method for picking people to survey is simple and easy to follow. Students in line have a random chance of being chosen for a team. Drawback: If students catch on to the sampling method, students who want to be on the team may try to switch places in line with those not wanting to be on the team. This will make the sampling method less random and introduce bias.

Launch How could the gym teacher make the sampling method better? Provide one idea. The coach could just pick every third person in a list of last names in alphabetical order. That way, students couldn’t affect the selection process.

Connect Your Learning The gym teacher picked every third person out of a line to form a team. How do you sample systematically? What are the advantages and disadvantages of systematic sampling?

Systematic Sampling Systematic sampling is a sampling method in which you choose every nth member of the population, where n is a predetermined number. A systematic sample is useful when the researcher is able to approach the population in a systematic, or methodical, way.

Systematic Sampling

Systematic Sampling

Systematic Sampling STEP 1: ASSIGN NUMBERS TO POPULATION Assign each member of the population a unique number.

Systematic Sampling population size _____________ sample size STEP 2: FIND THE INTERVAL "n"" To find the interval n, you need to know the population size and the desired sample size. Interval n = population size sample size _____________

Systematic Sampling STEP 2: FIND THE INTERVAL "n" Interval n = n = = 4 Divide the sample into groups of 4. 20 5 ___ population size sample size _____________

Systematic Sampling

**You can't pick a number larger than your interval** Systematic Sampling STEP 3: FIND THE STARTING NUMBER To find the starting number, pick a number from 1 to n, at random. We are going to use a starting number of 3. **You can't pick a number larger than your interval**

Systematic Sampling STEP 4: COLLECT A SYSTEMATIC SAMPLE Collect a systematic sample by choosing the member with the starting number and then every 4th member until you reach the end of the population. A systematic sample takes preparation to collect, but it usually produces a representative sample. **Warning** Someone could introduce bias into the sample by arranging the population to make sure certain members are chosen.

Systematic Sampling

Systematic Sampling Members 3, 7, 11, 15, and 19 make up a systematic sample. Break the population up into groups (aka "intervals"). Take every nth person from each group. They make up your Systematic Sample.

Systematic Sampling Suppose you are doing research on the students at your school. Is each an instance of systematic sampling? Explain. You make a list of students in your class and choose every seventh name, starting from the first name. Yes; you chose your sample using a starting point, the first person, and an interval, 7, so this is an instance of systematic sampling.

Systematic Sampling Suppose you are doing research on the students at your school. Is each an instance of systematic sampling? Explain. You have the students in your class count off by 4’s. You choose the students who counted “3.” Yes; you chose your sample using a starting point, 3, and an interval, 4, so this is an instance of systematic sampling.

Systematic Sampling Suppose you are doing research on the students at your school. Is each an instance of systematic sampling? Explain. You make a list of the students and choose the first ten names on your list. No; you chose the first 10 names, not by jumping intervals, so this is not an instance of systematic sampling.

Systematic Sampling How are convenience and systematic sampling similar? They both produce a sample. How are they different? Systematic sampling produces a representative sample, requires knowledge of the population size, requires picking numbers at random, and requires time and effort.

Systematic Sampling You want to estimate how often books in the science section of the library are checked out. You decide to sample 9 books in the section. Choose a systematic sample. Is your sample a representative sample? Explain.

Systematic Sampling First find the interval. n = 72/9 = 8 Choose the starting number from 1-8 at random. Collect your systematic sample starting from the starting number and then every 8th book from there. The sample is most likely a representative sample because there does not seem to be a relevant pattern to the books that would introduce bias.

Systematic Sampling When might a systematic sample not be a representative sample? A systematic sample might not be a representative sample when there is some sort of pattern to the list of the population.

Systematic Sampling Suppose you want to estimate the number of purple lights in a light display. You decide to take a systematic sample using an interval of 5 lights, starting from the second light.

Systematic Sampling Suppose there are a total of 300 light bulbs in the display. Using your systematic sample, how many purple bulbs do you estimate are in the display? How accurate is your estimate? Explain.

Systematic Sampling The light display repeats colors in the same order every 5 bulbs. Since the interval of the systematic sample is also 5, the sample consists of only yellow light bulbs. Using the systematic sample, there are only yellow lights (and therefore no purple lights) in the display. This estimate is not accurate because the systematic sample is not a representative sample.

Systematic Sampling Suppose you want to estimate the number of purple lights in a light display. You decide to take a systematic sample using an interval of 6 lights, starting from the second light.

Systematic Sampling Suppose there are a total of 300 light bulbs in the display. Using your systematic sample, how many purple bulbs do you estimate are in the display? How accurate is your estimate? Explain.

Systematic Sampling Since the pattern in the display repeats with an interval of 5, each color of light appears the same number of times in the display. The pattern also repeats when collecting the systematic sample, so each color of light appears the same number of times in the sample. The estimate should be fairly accurate.

Systematic Sampling The systematic sample contains 10 reds, 10 yellows, 10 greens, 10 blues, and 10 purples. The constant of proportionality is 10/50 or 1/5. So, there are about 1/5 x 300, or 60 purple light bulbs in the light display.