Lesson 7

Lesson 7: Interpreting Statistical Data

 

Focus

 

Survey and poll results are frequently used to sway public opinion. For that reason, it is important that you are able to interpret survey results and decide for yourself whether you agree or disagree with the survey results or the survey methodology (i.e., how the survey was conducted).

 

Technology has allowed for surveys and polls to be set up in a very short period of time. The polls or surveys can start generating responses almost immediately.

 

 

Users of social networking sites such as Facebook can set up a survey to help them decide which movie they should see that night. Users of restaurant rating apps can look at the number of “likes” to help decide which sushi place sells the best lunch. Tweets to a celebrity fashion critic’s Twitter account can give insight into public opinion on a new fashion trend.

 

Even news agencies use surveys and polls on their websites, Facebook pages, and Twitter accounts to gauge their viewers’ responses to current news stories. Information that used to take a specialized group of people days or weeks to gather can now be accomplished in the span of a 30-minute newscast.

 

But how confident can you be in the results of these informal surveys or polls? For instance, what is the probability that if a student polls all her friends on Facebook about whether she should go and see the new horror movie, her friends are going to say “YES!”? (Is this because it is a good movie or because her friends have a similar taste in movies?) Have you ever seen the confidence level or margin of error listed for these types of informal polls or surveys?

 

In Lesson 6 you began to consider the importance of reliability of results. Recall the survey you did in that lesson in which you looked at how confident you felt you need to be in the skills of your doctor, dentist, or sandwich maker. Do you feel that you need to have the same level of confidence in your doctor and an employee in a fast-food restaurant? If you are using data to help you make a decision, it would be good to know that you can have confidence in that data.

 

In this lesson you will investigate factors that affect the level of confidence in statistical data. In a society where you are constantly presented with opinion polls, surveys, and the opportunity to “like” or “dislike” from most mobile devices, it is important that you consider levels of confidence if you are going to make a decision based on the data.

 

This lesson will help you answer the following critical questions:

• What factors affect the level of confidence in statistical data?
  
  
• When presented with statistics in the media, what should you consider before making decisions based on the data presented?

Assessment

• Module 4 Project

All assessment items you encounter need to be placed in your course folder.

 

Materials and Equipment

• calculator

Discover

 

It is usually not possible to test every single product, survey every member of a population, or examine every single situation.

 

In previous lessons, you looked at how quality control departments use statistics to set standards based on collected data. This information helps ensure that products meet company standards and the standards set by regulatory agencies (e.g., government). But how much product has to be sampled to instill sufficient confidence in the statistical data and, ultimately, confidence in the safety of the product?

 

For example, does every bottle of orange juice leaving a plant need to be tested by a quality control department in order for the consumer to be confident that the product is safe? Does every jar of jam need to be checked to ensure that it has the correct amount of jam in it so the consumer feels he or she receives fair value? Does every millilitre of water leaving a wastewater treatment facility have to be tested to be confident that the water is safe for the environment?

 

Statisticians and quality control technicians have to determine how large of a sample they need to test so they can be sufficiently confident in the results. A pharmaceutical manufacturer, for example, needs to determine how many drug capsules should be tested to have an acceptable level of confidence that all of the capsules produced are safe and effective. There is a fine line between testing enough product to be confident that the drugs are safe and testing too much product because this can get expensive and waste product.

 

Try This 1

 

Use the Sample Size applet to investigate what sample sizes would be required for a given population, confidence intervals, and confidence levels.

 

 

Explore

 

The only way to be 100% confident that results represent a population is to measure or survey every member of the population. For example, a census can be conducted and every person in a population can be surveyed. But it is very expensive to conduct a census. It is also very expensive to measure each and every product ever created. For instance, a clothing manufacturer might use a machine to see how much force it takes to rip a pair of pants. If the manufacturer tested every pair of pants they made, there wouldn’t be any pants left to sell. An entire population would be destroyed. Instead, a sample of the population can be tested.

 

The data gathered by quality control departments from sampling drug capsules, cereal boxes, or ultimate discs is all done through random sampling. Capsules, cereal boxes, and ultimate discs are taken throughout the day and tested to create the data that companies use to make decisions about quality control. If a company chooses to take its entire sample at one time and from one machine, the company may not get a realistic picture of what is happening in the entire production facility. The level of confidence in a set of data relies in part on random sampling.

 

Consider the following situation.

 

Angelica’s favourite sport is hockey, and she plays in a competitive league. Suppose she wants to know what sport teenagers in her area like to play most. She decides to ask her friends on Facebook. After 2 h, 45 of her friends have replied. Most of her friends have chosen hockey as their favourite sport to play. Is this a random sample? How reliable are these results? Do these results accurately reflect the population of teenagers in Angelica’s area?

 

Since Angelica plays hockey, it is likely that many of her Facebook friends are from some of the hockey teams she has played on in the past. This sample does not accurately reflect the views of all of the teeenagers in her area. This is not a random sample, so these results are not very reliable and you should have limited confidence in them.

 

Now suppose Angelica wants to improve the reliability of these results. Since all of her closest friends have already replied, she decides to ask the students in her homeroom class. Out of the 25 students in her class, 18 of them choose rugby—surprisingly, they are all on the rugby team. What does this do to the confidence in the first result? It definitely does not support the original results.

 

 

If Angelica really wants to know what sport teenagers in her area like to play the most, she will need to look at how she could randomly choose people to answer this question so that her results are reliable and she could have a high level of confidence in the results. Perhaps she could randomly ask students in her school by using class lists from the office and picking every fourth person on the list. This would allow her to ask 25% of the student population. She would then have a much higher level of confidence in the results and could make some accurate predictions about what sport most teenagers in her area enjoy playing. In fact, any random method to generate this data would help improve the level of confidence in the results.

 

Once results are gathered from a random sample, the results can be generalized to the population. You can have a very large random sample or have a lot of smaller random samples where you combine the results. If you do not have a random sample that is large enough, then the margin of error and confidence interval may be too large and you cannot accurately generalize the results to the population. Statisticians can use small sample sizes, as long as the sample is truly random. If the sample is not random, the results cannot be accurately predicted for the entire population and the confidence intervals are unreliable.

 

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Read “Example 4: Analyzing statistical data to support a position” on page 300 of your textbook. Kylie used a number line to graph the overlap of the confidence intervals. As you read the example, think about what method you would use to show the overlap of the confidence intervals.

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Self-Check 2

 

Complete “Practising” question 4 on page 302 of the textbook. Answer

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Connect

 

Project Connection

 

Surveys and polls can be informal with little to no scientific basis, or they can be based on reliable data that accurately represents a population. Survey and poll results are frequently used to sway public opinion, so it is important that you are able to interpret survey results and decide for yourself whether you agree or disagree with the survey results or how the survey was conducted.

 

Open the Module 4 Project. You will find and interpret the results of a survey or poll.

 

Lesson 7 Summary

 

 

It is not possible to test an entire population. Instead, random samples can be tested and the results can be used to generalize the results for the population. The more samples you collect, the more confident you become in predicting the result of the next sample and the more accurately the results represent the population.

 

For a given confidence level, the larger your sample size, the smaller your confidence interval and margin of error. The size of the confidence interval is based on the sample size, confidence level, and population size. When a population is small, population size has a greater effect on the size of the sample required.

 

If the confidence level remains the same and a smaller confidence interval and margin of error are needed, then a larger sample is required.

 

Surveys and polls can be set up by just about anyone in a matter of minutes. Since the results are frequently used to try and sway your opinion, it is important that you are able to interpret survey results and decide whether or not the survey accurately represents the true population so that you have enough confidence in the results. Having this knowledge gives you more control over how you choose to react to the many media influences in your life.

 

Now refer to the Module 4 Summary for an overview of concepts you investigated in this module.