Critical Thinking Model Answers Property

Understanding Statistical Arguments

 We’ve learned that anecdotal evidence, or stories that we hear from friends and other sources, are not a reliable form of evidence when we are trying to form many types of reasonable conclusions.If a few friends tell me that a particular phone or a brand of tire is a good one, since my sampling of data is so limited, it could easily happen that they are recommending one of the worst products or there are other problems with the choice that would not be revealed with such a small body of evidence.

 We’ve also learned about the virtues of the scientific method for forming reasonable and better justified conclusions about what is real and true.One of most important forms of scientific reasoning, and the foundation of causal reasoning, is the statistical argument.We often need to know how prevalent a property is in a population.Perhaps I want to know how often AT& T phones break down, or how many oak trees in California are diseased or what the income distributions of people in the U.S. are.The best way to find out these facts and many other like them that we must know to understand the world is through a well constructed statisticalargument.

 Consider this example: 

Researchers wanted to know whether 3-D movies cause motion sickness or headaches in a significant number of people who watch them.In ten major cities, at randomly selected movie theaters that were showing 3-D movies, they interviewed people after viewings.Of the 1,253 people they spoke to, 371 people, or about 30%, reported experiencing some discomfort, motion sickness, or headache during the movie.On those grounds, they concluded that 30% of the people who see 3-D movies experience some physical discomfort from them.

 In this case, the larger group of things that the study is interested in is people.That is, the target population in this case is people.It’s not possible to study all people, however, so a sample population is used.A samplepopulation is the smaller group of things that are actually studied and that are used to generalize to the target population.

The property that this study focuses on is “experience some physical discomfort from watching a 3-D movie.”That’s the property in the target population that is the central question of the study.This is the target property.But in this case, as with many others, actually measuring the presence or absence of “experiences some physical discomfort from watching a 3-D movie” can be difficult.The property that a statistical investigation actually measures in the sample population and that the study will take as an indicator of the target property in the target population is the measured property.We can suppose that the researchers asked exiting movie goers if they experienced any discomfort from the movie and the movie goers either responded affirmatively or negatively.(We don’t have much more detail in this short example.)So the measured property in this study is “said they experienced some physical discomfort from watching a 3-D movie.”And the researchers take the presence of this property to be an accurate indicator of the presence of the target property.That is, if a movie goers says that the movie gave her some physical discomfort, then she actually did feel some physical discomfort.

This difference may not seem significant in this case, but there are many instances where the difference between the measured property and the target property is important and can make the difference between a study we should accept and one that we should reject.Suppose that the researchers had asked the exiting movie goers “are you having fun on your evening out with the person you saw the movie with” and then took their answers to be an accurate indicator of whether they actually had fun with that person.If the question and answer were asked out loud, in front of the other person, then we would not expect to get an accurate answer.How a question is asked or how a property is measured can be very important.The conceptual issue here is known as accuracy.For any statistical argument, one of the major issues is how it can answer this question:how accurate is the measured property as an indicator of the target property.Here are some other examples of measured property/target property pairs:

report on a census form having a household income of less than $200k a year/have a household income of less than $200k a year;

has brown, withered leaves on more than 30% of the tree/has Dutch Elm disease;

answered yes to the question “have you ever cheated on your taxes”/cheated on their taxes

reported agreeing with the statement, “The evolution of life on Earth was assisted by God”/believes that evolution on Earth was assisted by God.

When a study is about what people believe, some of the methods that can help improve accuracy are anonymous questionnaires, carefully worded questions, diverse and multiple cross referenced questions, research into different measurement techniques, and so on.

The other major issue for a statistical argument involves something known as representativeness.If the sample population is going to be used to generalize and project onto the target population, then the sample population must be representative.That is, the sample population must be composed so that in ways relevant to the possession of the target property, the sample population resembles the target population.Roughly, we want the sample population to look enough like the target population that if we observe the presence of some property in them, we can reasonably infer that it will be present in the target population.If I am wondering about the extent to which Dutch Elms disease has infected American Elm trees, it would not be representative to only look at one small grove of them that are highly infected in a park in Pennsylvania.The trees in that park are probably not representative of all the trees in the country.So generalizing from them is likely to give me a skewed view of the bigger picture.

In one 1994 study, researchers set out to test whether drinking alcohol on an empty stomach makes you drunker than drinking with a full stomach.In their tests, the had 10 people consume alcohol on different days—once with a full stomach, and once empty.They concluded that if you have an empty stomach you will get drunker faster than if you have just eaten.

What’s troubling about the study is that the sample population is a mere 10 people, and the results from those 10 are used to generalize about all people.With only 10 subjects, it is possible that they found an isolated effect that was pronounced in a few people in their study, but that is not widely present in the population at large. The conclusion of the study may be correct, but the very small sample population raises serious questions about its representativeness.In general, the way to improve representativeness is to make the sample population large.And if the sample population is being composed from the target population, a method to improve representativeness is to use a random sampling method.A random sampling method will give every individual in the target population an equal chance of begin chosen for the sample population.If a survey about American political attitudes is conducted and only Republicans are called from a Republican voter registration list, then Democrats and third party voters do not have any chance of being selected. So the study would not be representative.In the study above, movie goers were chosen from 10 different cities and the theaters were chosen at random.Those two facts improve representativeness more, say, than a casual conversation with a few friends about their experience in 3-D movies.

So a statistical argument will have these eight elements.It will be valuable to be able to pick them out:

Sample population:the group of objects that the study actually measures.

Target population:the larger or largest group of objects that the study seeks to draw a conclusion about.

Measured property:the property or feature in the sample population that is actually measured in the study in question.

Target property:the property or feature in the target population that is central to the overall argument.

Accuracy:in order to be strong, the measured property in a statistical argument must be an accurate indicator of the presence of the target property in the target population.

Representativeness:in order to be strong, the sample population must represent or resemble the target population, with regard to other properties that are connected to the property in question.If the sample is going to be used to generalize about the target population, the sample must look like the target in the relevant ways.

Margin of error:is the extent to which researchers believe the presence of the target property in the target population may vary from the presence of the measured property in the sample population.In the study above, they might conclude that 30% of Americans, plus or minus 3%, are made physically uncomfortable from watching 3-D movies.That means that they expect that the actual rate of the target property in the target population may be as high as 33% and low as 27%.Usually, increasing the sample population, or composing it very carefully brings the margin of error down.

Random sampling:if a sample population is randomly sampled from the target population, that means that every member of the target population had an equal chance of being chosen for the sample.

Here’s an example of how the movie survey above might be reconstructed as a strong, deductive argument:

1.Measured property in sample population:30% of the 1,253 people interviewed in the 10 city survey claimed that watching a 3-D movie  gave them physical discomfort.[EP]

2. Measured property in sample population to target property in sample population:If 30% of the 1,253 people interviewed in the 10 city survey claimed that watching a 3-D movie made gave them physical discomfort, then 30% of the 1,253 people interviewed in the 10 city survey were given physical discomfort from watching a 3-D movie.[IP]

3.Preliminary conclusion about the sample:30% of the 1,253 people interviewed in the 10 city survey claimed that watching a 3-D movie were given physical discomfort from watching a 3-D movie.[1,2]

4.Target property in the sample to target property in the target population: If 30% of the 1,253 people interviewed in the 10 city survey claimed that watching a 3-D movie were given physical discomfort from watching a 3-D movie, then 30% of the people who see 3-D movies experience some physical discomfort from them.[IP]

5.Conclusion about the target population:30% of the people who see 3-D movies experience some physical discomfort from them.[3,4]

Practice Examples:

1.  Lung Cancer Survival

In a broad survey of the medical records of more than 10,000 cancer patients across the country, researchers at Johns Hopkins have concluded that 82% of stage 0 lung cancer patients whose cancer is detected early survive.Over the course of several years, the records of 10,452 patients were carefully reviewed to determine at what stage the cancer was detected, how it was treated, and what the survival rates were.“Early detection” was defined as cancer that was confined to a small area of one lung.“Survival” was defined to mean surviving 5 or more years after diagnosis.

Sample population:10,452 patients in the Johns Hopkins study

Measured property:had medical files that indicated survival from lung cancer 5 or more years.

Target population:people with lung cancer that is detected early

Target property:survived five or more years.

Measured Propety in the Sample Population:82% of the 10,452 patients in the Johns Hopkins study had medical files that indicated survival from lung cancer 5 or more years.

Target property in the Target Population:82% of people with lung cancer that is detected early survive for five or more years.

2.  Americans and Smoking

In a recent Gallup poll, it was concluded that 21% of Americans smoke.Interviews with more than 75,000 individuals across the United States indicated that about 16,000 of them smoke at least one cigarette or cigar a day. Gallup interviewed no fewer than 1,000 U.S. adults nationwide each day during 2008. These results are based on 75,073 surveys conducted from Jan. 2, 2008, to March 17, 2008. For results based on this sample, the maximum margin of sampling error is ±1 percentage point. In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls.

Sample population:_____________________________________________________

Measured property:_____________________________________________________

Target population:______________________________________________________

Target property: ________________________________________________________

Measured Propety in the Sample Population:________________________________

Target property in the Target Population:___________________________________

 3.  California Oak Trees and Sudden Oak Death

 A strange malady that quickly turns the leaves of California Oak trees brown and then kills the tree has been sweeping through northern California.In preliminary results of a study on Sudden Oak Death, that is caused by the pathogen Phytophthora ramorum, 26% of oak trees in in four study locations in Marin and Sonoma counties had the disease.Observations were done by people in the field looking for brown or dead leaves, and “bleeding” of viscous sap from intact bark.

Sample population:_____________________________________________________

Measured property:_____________________________________________________

Target population:______________________________________________________

Target property: ________________________________________________________

Measured Propety in the Sample Population:________________________________

Target property in the Target Population:___________________________________

Critical Thinking


What is Critical Thinking?

When examining the vast literature on critical thinking, various definitions of critical thinking emerge. Here are some samples:

  • "Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action" (Scriven, 1996 ).
  • "Most formal definitions characterize critical thinking as the intentional application of rational, higher order thinking skills, such as analysis, synthesis, problem recognition and problem solving, inference, and evaluation" (Angelo, 1995, p. 6 ).
  • "Critical thinking is thinking that assesses itself" ( Center for Critical Thinking, 1996b ).
  • "Critical thinking is the ability to think about one's thinking in such a way as 1. To recognize its strengths and weaknesses and, as a result, 2. To recast the thinking in improved form" (Center for Critical Thinking, 1996c ).

Perhaps the simplest definition is offered by Beyer (1995) : "Critical thinking... means making reasoned judgments" (p. 8). Basically, Beyer sees critical thinking as using criteria to judge the quality of something, from cooking to a conclusion of a research paper. In essence, critical thinking is a disciplined manner of thought that a person uses to assess the validity of something (statements, news stories, arguments, research, etc.).


Characteristics of Critical Thinking

Wade (1995) identifies eight characteristics of critical thinking. Critical thinking involves asking questions, defining a problem, examining evidence, analyzing assumptions and biases, avoiding emotional reasoning, avoiding oversimplification, considering other interpretations, and tolerating ambiguity. Dealing with ambiguity is also seen by Strohm & Baukus (1995) as an essential part of critical thinking, "Ambiguity and doubt serve a critical-thinking function and are a necessary and even a productive part of the process" (p. 56).

Another characteristic of critical thinking identified by many sources is metacognition. Metacognition is thinking about one's own thinking. More specifically, "metacognition is being aware of one's thinking as one performs specific tasks and then using this awareness to control what one is doing" (Jones & Ratcliff, 1993, p. 10 ).

In the book, Critical Thinking, Beyer elaborately explains what he sees as essential aspects of critical thinking. These are:

  • Dispositions: Critical thinkers are skeptical, open-minded, value fair-mindedness, respect evidence and reasoning, respect clarity and precision, look at different points of view, and will change positions when reason leads them to do so.
  • Criteria: To think critically, must apply criteria. Need to have conditions that must be met for something to be judged as believable. Although the argument can be made that each subject area has different criteria, some standards apply to all subjects. "... an assertion must... be based on relevant, accurate facts; based on credible sources; precise; unbiased; free from logical fallacies; logically consistent; and strongly reasoned" (p. 12).
  • Argument: Is a statement or proposition with supporting evidence. Critical thinking involves identifying, evaluating, and constructing arguments.
  • Reasoning: The ability to infer a conclusion from one or multiple premises. To do so requires examining logical relationships among statements or data.
  • Point of View: The way one views the world, which shapes one's construction of meaning. In a search for understanding, critical thinkers view phenomena from many different points of view.
  • Procedures for Applying Criteria: Other types of thinking use a general procedure. Critical thinking makes use of many procedures. These procedures include asking questions, making judgments, and identifying assumptions.

Why Teach Critical Thinking?

Oliver & Utermohlen (1995) see students as too often being passive receptors of information. Through technology, the amount of information available today is massive. This information explosion is likely to continue in the future. Students need a guide to weed through the information and not just passively accept it. Students need to "develop and effectively apply critical thinking skills to their academic studies, to the complex problems that they will face, and to the critical choices they will be forced to make as a result of the information explosion and other rapid technological changes" (Oliver & Utermohlen, p. 1 ).

As mentioned in the section, Characteristics of Critical Thinking , critical thinking involves questioning. It is important to teach students how to ask good questions, to think critically, in order to continue the advancement of the very fields we are teaching. "Every field stays alive only to the extent that fresh questions are generated and taken seriously" (Center for Critical Thinking, 1996a ).

Beyer sees the teaching of critical thinking as important to the very state of our nation. He argues that to live successfully in a democracy, people must be able to think critically in order to make sound decisions about personal and civic affairs. If students learn to think critically, then they can use good thinking as the guide by which they live their lives.


Teaching Strategies to Help Promote Critical Thinking

The 1995, Volume 22, issue 1, of the journal, Teaching of Psychology , is devoted to the teaching critical thinking. Most of the strategies included in this section come from the various articles that compose this issue.

  • CATS (Classroom Assessment Techniques): Angelo stresses the use of ongoing classroom assessment as a way to monitor and facilitate students' critical thinking. An example of a CAT is to ask students to write a "Minute Paper" responding to questions such as "What was the most important thing you learned in today's class? What question related to this session remains uppermost in your mind?" The teacher selects some of the papers and prepares responses for the next class meeting.
  • Cooperative Learning Strategies: Cooper (1995) argues that putting students in group learning situations is the best way to foster critical thinking. "In properly structured cooperative learning environments, students perform more of the active, critical thinking with continuous support and feedback from other students and the teacher" (p. 8).
  • Case Study /Discussion Method: McDade (1995) describes this method as the teacher presenting a case (or story) to the class without a conclusion. Using prepared questions, the teacher then leads students through a discussion, allowing students to construct a conclusion for the case.
  • Using Questions: King (1995) identifies ways of using questions in the classroom:
  • Reciprocal Peer Questioning: Following lecture, the teacher displays a list of question stems (such as, "What are the strengths and weaknesses of...). Students must write questions about the lecture material. In small groups, the students ask each other the questions. Then, the whole class discusses some of the questions from each small group.
  • Reader's Questions: Require students to write questions on assigned reading and turn them in at the beginning of class. Select a few of the questions as the impetus for class discussion.
  • Conference Style Learning: The teacher does not "teach" the class in the sense of lecturing. The teacher is a facilitator of a conference. Students must thoroughly read all required material before class. Assigned readings should be in the zone of proximal development. That is, readings should be able to be understood by students, but also challenging. The class consists of the students asking questions of each other and discussing these questions. The teacher does not remain passive, but rather, helps "direct and mold discussions by posing strategic questions and helping students build on each others' ideas" (Underwood & Wald, 1995, p. 18 ).
  • Use Writing Assignments: Wade sees the use of writing as fundamental to developing critical thinking skills. "With written assignments, an instructor can encourage the development of dialectic reasoning by requiring students to argue both [or more] sides of an issue" (p. 24).
  • Dialogues: Robertson andRane-Szostak (1996) identify two methods of stimulating useful discussions in the classroom:
    • Written dialogues: Give students written dialogues to analyze. In small groups, students must identify the different viewpoints of each participant in the dialogue. Must look for biases, presence or exclusion of important evidence, alternative interpretations, misstatement of facts, and errors in reasoning. Each group must decide which view is the most reasonable. After coming to a conclusion, each group acts out their dialogue and explains their analysis of it.
    • Spontaneous Group Dialogue: One group of students are assigned roles to play in a discussion (such as leader, information giver, opinion seeker, and disagreer). Four observer groups are formed with the functions of determining what roles are being played by whom, identifying biases and errors in thinking, evaluating reasoning skills, and examining ethical implications of the content.
  • Ambiguity: Strohm & Baukus advocate producing much ambiguity in the classroom. Don't give students clear cut material. Give them conflicting information that they must think their way through.

References & Resources

  • Angelo, T. A. (1995). Beginning the dialogue: Thoughts on promoting critical thinking: Classroom assessment for critical thinking. Teaching of Psychology, 22(1), 6-7.
  • Beyer, B. K. (1995). Critical thinking. Bloomington, IN: Phi Delta Kappa Educational Foundation.
  • Center for Critical Thinking (1996a). The role of questions in thinking, teaching, and learning. [On-line]. Available HTTP: http://www.criticalthinking.org/University/univlibrary/library.nclk
  • Center for Critical Thinking (1996b). Structures for student self-assessment. [On-line]. Available HTTP: http://www.criticalthinking.org/University/univclass/trc.nclk
  • Center for Critical Thinking (1996c). Three definitions of critical thinking [On-line]. Available HTTP: http://www.criticalthinking.org/University/univlibrary/library.nclk
  • Cooper, J. L. (1995). Cooperative learning and critical thinking. Teaching of Psychology, 22(1), 7-8.
  • Jones, E. A. & Ratcliff, G. (1993). Critical thinking skills for college students. National Center on Postsecondary Teaching, Learning, and Assessment, University Park, PA. (Eric Document Reproduction Services No. ED 358 772)
  • King, A. (1995). Designing the instructional process to enhance critical thinking across the curriculum: Inquiring minds really do want to know: Using questioning to teach critical thinking. Teaching of Psychology, 22 (1) , 13-17.
  • McDade, S. A. (1995). Case study pedagogy to advance critical thinking. Teaching Psychology, 22(1), 9-10.
  • Oliver, H. & Utermohlen, R. (1995). An innovative teaching strategy: Using critical thinking to give students a guide to the future.(Eric Document Reproduction Services No. 389 702)
  • Robertson, J. F. & Rane-Szostak, D. (1996). Using dialogues to develop critical thinking skills: A practical approach. Journal of Adolescent & Adult Literacy, 39(7), 552-556.
  • Scriven, M. & Paul, R. (1996). Defining critical thinking: A draft statement for the National Council for Excellence in Critical Thinking. [On-line]. Available HTTP: http://www.criticalthinking.org/University/univlibrary/library.nclk
  • Strohm, S. M., & Baukus, R. A. (1995). Strategies for fostering critical thinking skills. Journalism and Mass Communication Educator, 50 (1), 55-62.
  • Underwood, M. K., & Wald, R. L. (1995). Conference-style learning: A method for fostering critical thinking with heart. Teaching Psychology, 22(1), 17-21.
  • Wade, C. (1995). Using writing to develop and assess critical thinking. Teaching of Psychology, 22(1), 24-28.

Other Reading

  • Bean, J. C. (1996). Engaging ideas: The professor's guide to integrating writing, critical thinking, & active learning in the classroom. Jossey-Bass.
  • Bernstein, D. A. (1995). A negotiation model for teaching critical thinking. Teaching of Psychology, 22(1), 22-24.
  • Carlson, E. R. (1995). Evaluating the credibility of sources. A missing link in the teaching of critical thinking. Teaching of Psychology, 22(1), 39-41.
  • Facione, P. A., Sanchez, C. A., Facione, N. C., & Gainen, J. (1995). The disposition toward critical thinking. The Journal of General Education, 44(1), 1-25.
  • Halpern, D. F., & Nummedal, S. G. (1995). Closing thoughts about helping students improve how they think. Teaching of Psychology, 22(1), 82-83.
  • Isbell, D. (1995). Teaching writing and research as inseparable: A faculty-librarian teaching team. Reference Services Review, 23(4), 51-62.
  • Jones, J. M. & Safrit, R. D. (1994). Developing critical thinking skills in adult learners through innovative distance learning. Paper presented at the International Conference on the practice of adult education and social development. Jinan, China. (Eric Document Reproduction Services No. ED 373 159)
  • Sanchez, M. A. (1995). Using critical-thinking principles as a guide to college-level instruction. Teaching of Psychology, 22(1), 72-74.
  • Spicer, K. L. & Hanks, W. E. (1995). Multiple measures of critical thinking skills and predisposition in assessment of critical thinking. Paper presented at the annual meeting of the Speech Communication Association, San Antonio, TX. (Eric Document Reproduction Services No. ED 391 185)
  • Terenzini, P. T., Springer, L., Pascarella, E. T., & Nora, A. (1995). Influences affecting the development of students' critical thinking skills. Research in Higher Education, 36(1), 23-39.

On the Internet

  • Carr, K. S. (1990). How can we teach critical thinking. Eric Digest. [On-line]. Available HTTP: http://ericps.ed.uiuc.edu/eece/pubs/digests/1990/carr90.html
  • The Center for Critical Thinking (1996). Home Page. Available HTTP: http://www.criticalthinking.org/University/
  • Center for Critical Thinking (1996a). The role of questions in thinking, teaching, and learning. [On-line]. Available HTTP: http://www.criticalthinking.org/University/univlibrary/library.nclk
  • Center for Critical Thinking (1996b). Structures for student self-assessment. [On-line]. Available HTTP: http://www.criticalthinking.org/University/univclass/trc.nclk
  • Center for Critical Thinking (1996c). Three definitions of critical thinking [On-line]. Available HTTP: http://www.criticalthinking.org/University/univlibrary/library.nclk
  • Ennis, Bob (No date). Critical thinking. [On-line], April 4, 1997. Available HTTP: http://www.cof.orst.edu/cof/teach/for442/ct.htm
  • Montclair State University (1995). Curriculum resource center. Critical thinking resources: An annotated bibliography. [On-line]. Available HTTP: http://www.montclair.edu/Pages/CRC/Bibliographies/CriticalThinking.html
  • No author, No date. Critical Thinking is ... [On-line], April 4, 1997. Available HTTP: http://library.usask.ca/ustudy/critical/
  • Scriven, M. & Paul, R. (1996). Defining critical thinking: A draft statement for the National Council for Excellence in Critical Thinking. [On-line]. Available HTTP: http://www.criticalthinking.org/University/univlibrary/library.nclk
  • Sheridan, Marcia (No date). Internet education topics hotlink page. [On-line], April 4, 1997. Available HTTP: http://sun1.iusb.edu/~msherida/topics/critical.html

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