Misleading Uses of Statistics

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  • 0:05 Misleading Uses of Statistics
  • 0:43 Issues with Sampling…
  • 3:35 Issues with Data…
  • 6:27 Lesson Summary
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Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

It can be too easy to present statistics in a way that is misleading. This lesson will cover the ways in which a statistic can be misleading and how to avoid and identify misleading statistics.

Misleading Uses of Statistics

Jack is working on building a nonprofit organization to rescue unwanted Easter bunnies. He is putting together information and research to present to potential board members. Jack wants to make sure he is putting the best information forward without misleading the board members. While statistics can be a powerful tool, they are often dismissed because of people who want to abuse and misuse the data. Jack will need to understand the misleading uses of statistics in order to avoid this problem.

In this lesson, you will learn about problems that happen with sampling and surveys, and issues with data interpretation. First, let's discuss the issues that can occur with sampling and surveys where statistics can be misleading.

Issues with Sampling and Surveys

Jack decides to conduct a survey to collect information about the need for an Easter bunny rescue. He decides to survey a few close friends, asking them 10 yes-or-no questions about bunny rescue. Let's take a look at some problems this may present when analyzing Jack's data.

First, Jack has a bad sample. He can't assume that his group of friends are an unbiased and fully representative mix of the population. This is known as a non-representative sample, which is a sample selected by a method that specifically excludes certain groups from the research, whether intentionally or unintentionally. Sometimes, it is difficult to conduct surveys that are completely representative of the population. However, it is important to be aware of these factors and the groups that could be left out when collecting data.

Next, Jack has a bad survey that has a few problems:

  • Limiting questions
  • Leading questions
  • Social desirability

Yes-or-no questions don't always give a good picture of the data that is being collected from the sample. These questions limit the response of the participant. For example, let's say that one of Jack's survey questions says, 'Every year, thousands of Easter bunnies are abandoned because they are no longer wanted as an Easter gift. If every rescue person were willing to house just two bunnies, we could make a great difference. Are you willing to house two bunnies? Yes or No?'

This is a limiting question. The participants of the survey may be willing to house one rescue bunny, but unable to house two. Answering 'yes' or 'no' does not give Jack the full picture of this data and limits the information he can gather. Additionally, there may be some participants who are willing to foster a bunny or spend time volunteering. If Jack is looking for information about how many surveyed participants are interested in getting involved in bunny rescue, then this question limits the information he can gather.

Leading questions are another problem that can produce misleading statistics. Leading questions are questions that encourage the answers desired by the researcher. For example, Jack's question above leads the participant into volunteering to house bunnies. A better, less leading question, might be 'What do you think might be some solutions to solve the abandoned bunny problem?' This is an open invitation for participants to respond in their own way and does not force them into answering in a certain way.

Another issue is social desirability, which refers to the tendency of participants to answer inaccurately, based on the way they feel they should answer, rather than provide a truthful response. For example, participants may answer favorably to questions such as, 'Do you think the bunny abandonment issue is important?' because they don't want to look like jerks who don't care about bunnies! However, sometimes participants might not be genuinely interested in a particular issue, and this would give misleading data to the amount of participation that a nonprofit business will have in the future.

Next, let's talk about issues that one can have with data after it has been collected.

Issues with Data Interpretation

Jack can mislead his audience into interpreting his data inaccurately in a few ways:

  • Misleading graphs
  • Ranking issues
  • Qualifying issues

Graphs are a great way to display information that a researcher has collected. However, it is very easy to display information in an incorrect or confusing way. To avoid this, Jack will need to answer a few questions about his data:

  1. How is the independent variable being measured?
  2. How is the dependent variable being measured?
  3. What types of data are the independent and dependent variables?

Once Jack understands the data being used in the survey, he can better understand how to organize his data. For more specific information about graphs and data, check out our lessons on tables and plots.

Constructing a graph correctly is the first step in avoiding misleading statistics. Check out this graph

Pets Abandoned Graph

Can you find anything misleading about this graph? Notice the left side of the graph. See how the intervals are irregular? The graph goes from zero to three to seven to ten and so forth . This makes the difference between the number of bunnies abandoned and the number of other animals abandoned look quite different. However, take a look at the same data in a different graph, this one with regular intervals:

Numbers of Pets Abandoned Graph

Although the data shows us that the number of abandoned animals has increased over time, the difference between the number of bunnies and the number of other animals is really quite small.

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