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Appendix B: Statistical Methods Chapter Outline Demonstration/Activity: Illustrating Descriptive Statistics .................................................................................. Demonstration/Activity: Introducing Students to Variability ............................................................................... Demonstration/Activity: Creating a Normal Distribution .................................................................................... Demonstration/Activity: Correlating Student Data .............................................................................................. Demonstration/Activity: Hypothesis Testing and “Telepathy” ............................................................................. References for Additional Demonstrations/Activities ..........................................................................................
DEMONSTRATION/ACTIVITY: ILLUSTRATING DESCRIPTIVE STATISTICS Beers (1987) presented a useful exercise for introducing descriptive statistics. Choose a variable that will describe your students in some meaningful way. Height is a good example, because all of your students should know their value for that variable. Have the class report their heights aloud and in unison. Of course, this method of reporting will result in great confusion and no interpretable data, just as usually is the case when we begin working with a data set. Beers suggested saying something like: “That sounded just like what data look like when they are first gathered. Data are just a pile of numbers waiting to be organized” (p. 193). Quiz the class about what they think should be done with the class data so that the entire group can make some sense of the numbers. With a little coaxing on your part, someone is likely to suggest making a chart, and someone will suggest finding the average. The first comment allows you to introduce the notion of a frequency distribution, like the one in Figure B.1(a) in the text. Depending on the variable you use in class, you can create a simple or grouped frequency distribution for the data. The second comment allows you to talk about measures of central tendency. Using height as your class variable is a good choice because most introductory psychology courses are imbalanced in terms of gender. If your class is, you can talk about the problem of using the mean as the measure of central tendency for the class data. If you compute the mean and median height, you will typically be able to demonstrate a negatively skewed distribution, as in Figure B.3(b) in the text. After you have computed the measures of central tendency, ask the class if these numbers are all that are needed to describe the class’s height. If no one mentions the need for a measure of variability, ask them how someone could look at the class’s mean or median height and know whether everyone in the class was exactly that tall, or if there was a mixture of people of different height. This prompt should help elicit a comment about the spread, or variability, of the scores. At this point, you can introduce the concept of variability and standard deviation. If you are brave, you might calculate the standard deviation of the class’s scores. Beers, S. E. (1987). Descriptive statistics. In V. P. Makosky, L. G. Whittemore, & A. M. Rogers (Eds.), Activities handbook for the teaching of psychology: Vol. 2 (pp. 193–194). Washington, DC: American Psychological Association.
DEMONSTRATION/ACTIVITY: INTRODUCING STUDENTS
Trice, Trice, and Ogden (1990) wrote about three exercises they use to teach students about statistical variability. This section describes one of their exercises, which can be used with a large group to introduce variability at either a superficial or a deep level. You will need a large piece of wrapping paper, poster board, or something similar for each student. Place a cup in the center of each sheet of paper and have students pitch 5 to 10 pennies at the cup from a close distance. Then they should mark the location of each penny and remove it. Have them repeat this sequence from a greater distance. This time they should mark the location of each penny in a different color and remove it. Have the students measure the distance of each penny from the cup for the two different distance conditions. Students can compare the ranges, average deviations, or standard deviations for the two conditions, depending on the degree of statistical sophistication you want your students to possess. Presumably you will find greater class variability in the farther tosses. Individual students, of course, may show different patterns of variability. Trice, A. D., Trice, O. A., & Ogden, E. P. (1990). Teaching the concept of statistical variability. In V. P. Makosky, C. C. Sileo, L. G. Whittemore, C. P. Landry, & M. L. Skutley (Eds.), Activities handbook for the teaching of psychology: Vol. 3 (pp. 189–191). Washington, DC: American Psychological Association.
Fernald and Fernald (1990) described an in-class exercise designed to quickly introduce the concept of the normal distribution and to generate a normal curve. Save your pennies for a few months so that you can take to class a large number of cups, each containing 15 pennies. The more students who get to participate in this exercise, the better. Tell the students that they are going to flip the pennies, but you want them to make a prediction first. Ask them which outcome—5, 7, or 13 heads—will occur most frequently and which will occur least frequently. Then have the 114
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Full file at http://testbank360.eu/solutionmanualpsychology8th editionwayneweiten class toss the pennies on their desk and count the number of heads obtained. You should collect at least 50 to 100 sets of observations, so in small classes students will need to participate more than once. After the coin tosses, you can describe the normal distribution. Because scores in the middle of the distribution are more frequent than those at the ends, 7 heads is more likely than 5 heads, which is more likely than 13 heads. Ask for a show of hands by those who obtained 7, 5, and 13 heads in their tosses. The display should be convincing. Using TM B-1, plot the distribution of heads for the entire class. If you have collected sufficient data, the plot of the connected points should resemble a normal curve. The peak of the curve should be at 7 and 8, with a mean of approximately 7.5. You probably will not have anyone obtain 0 or 15 heads (only 2 chances in 32,768 tosses of 15 coins). However, you should inform the class that such an outcome is possible—it simply has a very low probability. If students can become comfortable with the concept of the normal distribution, this knowledge will be useful to them throughout the course. Later in the course, when students mention an unusual occurrence that does not fit the norm, you can remind them of the normal curve and the fact that outliers do occur in the population but are statistically unusual. Fernald, P. S., & Fernald, L. D. (1990). Normal probability curve. In V. P. Makosky, C. C. Sileo, L. G. Whittemore, C. P. Landry, & M. L. Skutley (Eds.), Activities handbook for the teaching of psychology: Vol. 3 (pp. 181–182). Washington, DC: American Psychological Association.
DEMONSTRATION/ACTIVITY: CORRELATING STUDENT DATA One approach to teaching statistical concepts is to involve students personally in the material. This type of active learning increases interest in the topic so that students become part of the learning process, curious and questioning as children are. The topic of correlation has the potential to create this interest if it is approached in the right way. Two examples work quite nicely to illustrate correlated variables: (1) height and shoe size or (2) first exam and second exam scores. Ask your class to imagine someone who is 7 feet tall (or made 98 on the first exam). Ask them to predict what size shoe this person wears (or what the person scored on the second exam). In either case, students will typically respond with a large number. Ask the class to imagine another hypothetical person who is 4 feet tall (or who scored 40 on the first exam). What do they predict for this person’s shoe size (or second exam score)? This prediction is likely to be a smaller number. Now ask them why they made those predictions. If the correct answer is not forthcoming, inform them they have assumed there is a relationship between the two variables, in particular a positive correlation. The beauty of using height/shoe size or first exam/second exam for your example of correlation is that either pairing can also be used for an in-class example. You can have students write their height and shoe size anonymously on a slip of paper to be collected at the end of a class period so that you can calculate the correlation and create a scatter plot before the next class meeting. Once you have given two exams, you can correlate them for the classroom example. You can also clarify the prediction process with either pair of scores. When computing the correlation of the scores, the computer will likely give you regression information. You can use the regression equation in class to demonstrate how you could predict someone’s height from his or her shoe size, or vice versa, or how you could predict someone’s second exam score from their first score.
DEMONSTRATION/ACTIVITY: HYPOTHESIS TESTING
Bates (1991) designed an entertaining classroom exercise to teach hypothesis testing. A situation is created in which it appears that a visitor to the class possesses telepathic powers. Students generate hypotheses regarding how the “feat” was accomplished and then test their hypotheses. Because of students’ interest in telepathy, this exercise generates enthusiastic participation. Bates had a colleague attend class one day, with advance warning given that this person has a psychic link with the instructor. With the colleague outside the room, a student volunteer, using a standard deck of cards, lays out 3 rows of 5 cards face up. Another student selects one card as the target card. The “psychic” enters the room and is questioned by Bates about the cards, one by one. The “psychic” is able to select the target card through Bates’s use of the questions “Is it this card?” or “Is it that one?” Of course, this is a simple trick rather than a psychic demonstration. Bates STATISTICAL METHODS
designates the top and bottom rows as “this rows” and the middle row as “that row.” The card being pointed to is not the target card as long as Bates uses the correct modifier for that row when pointing to it. The target card is identified when the incorrect modifier is used for a particular row. In Bates’s example, asking “Is this the card?” when pointing to a card in the middle row or asking “Is that the card?” about a card in the top or bottom row would signal that the target card was the subject of the query. After the demonstration, students are divided into small groups and asked to generate at least two testable hypotheses designed to answer the question of how the visitor performed the feat. At the next class meeting, the groups meet again to design a test that could falsify each of their hypotheses. After groups have designed their tests, Bates and his colleague are available for hypothesis testing. The groups take turns “specifying a set of conditions under which the playing card ‘thought transfer’ should occur” (p. 96). In the interest of time, if the conditions would make the transfer impossible, Bates simply tells the group. When all groups have tested their hypothesis, they are allowed to retest one or to test a revised or new hypothesis. If a group thinks they have a solution, a group member takes the visitor’s place to see if they are correct. The last 15 minutes of class are devoted to completing a worksheet about the experience. Students discuss the outcomes of their tests, modified hypotheses, and any conclusions they can reach about the psychic ability demonstrated. Bates reported that students learn the principle of hypothesis testing well from this exercise, particularly because it deals with empirical events that can be manipulated easily to derive quick feedback. He also noted that this exercise creates greater student interest and participation than any other he has used. Bates, J. A. (1991). Teaching hypothesis testing by debunking a demonstration of telepathy. Teaching of Psychology, 18, 94–97.
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Full file at http://testbank360.eu/solutionmanualpsychology8th editionwayneweiten REFERENCES
• From Teaching of Psychology: The student as data generator, by P. Hettich (1974), 1, 35–36 Instructional techniques in the introductory statistics course: The first class meeting, by K. W. Jacobs (1980), 7, 241–242 The Greyhound strike: Using a labor dispute to teach descriptive statistics, by M. A. Shatz (1985), 12, 85–86 Teaching the relevance of statistics through consumer-oriented research, by B. Beins (1985), 12, 168–169 Elaborating selected statistical concepts with common experience, by K. A. Weaver (1992), 19, 178–179 Correlational analysis and interpretation: Graphs prevent gaffes, by B. F. Peden (2001), 28, 129–131 Microsoft Excel as a tool for teaching basic statistics, by C. B. Warner & A. M. Meehan (2001), 28, 295–298 Personal ad content analysis teaches statistical applications, by D. W. Rajecki (2002), 29, 119–122
• From Activities Handbook for the Teaching of Psychology, by L. T. Benjamin, Jr., & K. D. Lowman (Eds.), 1981, Washington, DC: American Psychological Association: Sampling and probability, by L. Snellgrove, pp. 12–13 Hypothesis testing, Anonymous, pp. 14–15 Hypothesis testing—To “coin” a term, by W. J. Hunter, pp. 16–17 Randomization, by D. J. Stang, pp. 18–19
• From Activities Handbook for the Teaching of Psychology: Vol. 2, by V. P. Makosky, L. G. Whittemore, & A. M. Rogers (Eds.), 1987, Washington, DC: American Psychological Association: Using a labor dispute to teach descriptive statistics, by M. A. Shatz, pp. 195–198 ESP, central tendency, and probability, by M. Wertheimer, pp. 199–200 Sampling fluctuation demonstration, by J. V. Couch, pp. 201–203 The regression effect, by J. Karylowski, pp. 204–206 A demonstration of correlation and prediction, by J. R. Wallace, p. 207
• From Activities Handbook for the Teaching of Psychology: Vol. 3, by V. P. Makosky, C. C. Sileo, L. G. Whittemore, C. P. Landry, & M. L. Skutley (Eds.), 1990, Washington, DC: American Psychological Association: Probability and chance variation, by J. A. Jegerski, pp. 183–184 On the average, by K. Salzinger, pp. 185–186 Measures of central tendency in daily life, by L. L. Schwartz, pp. 187–188