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This turns out to be the case. First note that the equation: or: describes an ellipse. The gradient of F z evaluated at z0 is: This vector is thus normal or orthogonal to the ellipse at z0 see figure 1.

With the help of the vector b, which is defined in section 1. We will now show that the representations of 9 correspond to solving 5 in a weighted least-squares sense. For different values of c we get different ellipses and the larger the value of c is, the larger the ellipse see figure 1.

Example 4: Consider again the problem defined in section 1. Let us denote these new base vectors as d1 and d2. With the help of the base vectors d1 and d2, the vectors y, a and e can then be constructed from the scalars y1, y2, a1, a2, e1 and e2 as: , 12 ,. This is shown in figure 1. Note that the vectors of 12 are not the same as those of They do however have the same components.

If this is the case, then every weighted least-squares problem can be interpreted as a problem of orthogonal projection! For a proof, see the intermezzo at the end of this section. In figure 1. Now that we have established the fact that weighted least-squares estimation can be interpreted as orthogonal projection, it must also be possible to interpret the oblique projectors of equation 8 as orthogonal projectors. From now on we will assume that it is clear from the context which inner-product is taken and therefore also denote the matrix as Pa.

Proof: The proof is by induction. Since W is symmetric positive definite, it will be clear that A is also symmetric positive definite. A simple example of a Cholesky decomposition is: 1.

In our discussions so far no assumptions regarding the probabilistic nature of the observations or measurement errors were made. Since functions of random variables are again random variables, it follows that if the observation vector is assumed to be a random vector y note: the underscore indicates that we are dealing with random variables and substituted for y in 16 , the left-hand sides of 16 also become random variables: 17 These random variables are called least-squares estimators, whereas if y is replaced by its sample value y one speaks of least-squares estimates.

From your lecture notes in statistics you know how to derive the probability density functions of the estimators of 17 from the probability density function of y. You know furthermore how to compute the means and covariance matrices of y. This is particularly straight- forward in case of linear functions see also appendix E and F. The result 18 holds true irrespective the type of probability distribution one assumes for y. We will assume that the randomness of the observation vector y is a consequence of the random nature of the measurement errors.

Thus we assume that y can be written as the sum of a deterministic, i. This assumption seems acceptable if the measurement errors are zero "on the average".

Note that this unbiasedness property of least-squares estimators is independent of the choice for the weight matrix W! Application of the "propagation law of covariances" to 17 gives: 22 As you know from your lecture notes in Statistics, the variance of a random variable is a measure for the spread of the probability density function around the mean value of the random variable. It is a measure of the variability one can expect to see when independent samples are drawn from the probability distribution.

It is therefore in general desirable to have estimators with small variances. This is particularly true for our least-squares estimators. The least-squares estimates were derived from the deterministic principles of "orthogonality" and "minimum distance". That is, no probabilistic considerations were taken into account in the derivation of least-squares estimates.

Nevertheless, it was established in the previous section that least-squares estimators do have some "optimal properties" in a probabilistic sense. They are unbiased estimators independent of the choice for the weight matrix W, and their variance can be minimized by choosing the weight matrix as the inverse of the covariance matrix of the observations.

Moreover, they are linear estimators, i. In order to find out how large the class of best linear unbiased estimators is is there only one? Thus instead of starting from the least-squares principle of "orthogonality" we start from the conditions of linearity, unbiasedness and best.

Let us therefore look at the class of linear and unbiased estimators. Linear estimation theory 29 From taking the expectation of 26 follows, with 25 and 27 that: or 29 Thus for LU-estimators the vector l has to satisfy 29 see figure 1. For instance, every vector l of the form: where c is arbitrary, is permitted.

Let us now include the "B-property". We will now give an alternative derivation of the solution Equation 29 is the equation of a line with a direction vector orthogonal to a see figure 1. Since the vector b Figure 1. This concludes our alternative derivation of The least-squares principle is a deterministic principle where no probability assumptions concerning the vector of observations is made. In contrast with the least-squares principle, the principle of best linear unbiased estimation does make use of some probability assumptions.

In particular it is based on assumptions concerning the mean and covariance matrix of the random vector of observables y. We cannot guarantee that Psychology and the Challenges of Life Binder Ready Version book is available in the library, click Get Book button to download or read online books.

Join over This text is an unbound, three hole punched version. In the 13th edition of Psychology and the Challenges of Life: Adjustment and Growth, Binder Ready Version, 13th Edition authors Jeffrey Nevid and Spencer Rathus continue to reflect on the many ways in which psychology relates to the lives we live and the important roles that psychology can play in helping us adjust to the many challenges we face in our daily lives. Throughout, the authors explore applications of psychological concepts and principles in meeting life challenges such as managing our time, developing our self-identity, building and maintaining friendships and intimate relationships, adopting healthier behaviors and lifestyles, coping with stress, and dealing with emotional problems and psychological disorders.

In the 13th edition of Psychology and the Challenges of Life: Adjustment and Growth, Binder Ready Version, 13th Edition authors Jeffrey Nevid and Spencer Rathus continue to reflect on the many ways in which psychology relates to the lives we live. In the 14th edition of this market leading title, Psychology and the Challenges of Life: Adjustment and Growth, authors Spencer Rathus and Jeffrey Nevid continue to reflect on the many ways in which psychology relates to the lives we live and the important roles that psychology can play in helping.

A long-respected standard in the psychology of adjustment, Psychology and the Challenges of Life, Eleventh Edition has been thoroughly updated and contemporized to provide students the ability to reflect on how psychology relates to the lives we live and the roles that psychology can play in helping us with the.

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The text's integrated emphasis on diversity promotes a more inclusive view of personal adjustment. Princeton's star player, who had just appeared on the cover of Time magazine, left the game with a broken nose.

Soon thereafter, a Dartmouth player was taken off the field with a broken leg. By the end of the game— which Princeton won— both sides had racked up a sizable number of penalties. Following the game, tempers flared and bitter accusations were traded. Partisans on both sides wrote scathing editorials. For example, four days after the game, a writer for the Daily Princetonian Princeton's student newspaper declared: "This observer has never seen quite such a disgusting exhibition of so-called 'sport.

Princeton, obviously the better team, had no reason to rough up Dartmouth. Throughout the ensuing week, Dartmouth and Princeton students continued to fiercely debate what had happened and who was responsible.

Into that turmoil stepped Albert Hastorf a social psychologist then at Dartmouth and Hadley Cantril a Princeton survey researcher. Capitalizing on the controversy, Hastorf and Cantril conducted what is now a classic study of selective perception.

They began by asking Dartmouth students and Princeton students the following question, among others: "From what you saw in the game or the movies, or from what you have read, which team do you feel started the rough play?

Of the Dartmouth students, 53 percent asserted that both sides started it, and only 36 percent said that Dartmouth started it. In contrast, 86 percent of the Princeton students felt that Dartmouth had started it, and only 11 percent said that both sides were initiators. To explore this question, they asked a new group of students at each school to watch a film of the game and to record any infractions they noticed.

Students from both schools watched the very same film, and they used the same rating system to record any observed infractions. As you can see in Figure 1. Dartmouth students observed nearly the same number of infractions on both sides 4. In fact, there was such a discrepancy in perceptions that when Princeton sent a copy of the film to several Dartmouth alumni for a group showing, one Dartmouth alumnus who previewed the film could not see any of the Dartmouth infractions and, in confusion, sent Princeton a telegram asking for the rest of the film!

Based on these differences in perception, Hastorf and Cantril , pp. It is inaccurate and misleading to say that different people have different 'attitudes' concerning the same 'thing,' For the 'thing' simply is not the same lor dillerenl people whether the 'thing' is a football game, a presidential candidate, Communism, or spinach.

Vallone, Ross, and Lepper called this phenomenon the "hostile media effect," and they first studied it in the context of the presidential election between Jimmy Carter and Ronald Reagan. Three days before the election, they asked registered voters to indicate whether media coverage of the candidates had been biased, and if so, to indicate the direction of the bias.

What they found is that approximately one-third of the respondents felt that media coverage had been biased, and in roughly 90 percent of these cases, respondents felt that the media had been biased against the candidate they supported.

The news segments were drawn from six different evening and late-night news programs broadcast nationally in the United States over a ten-day period. In support of the hostile media effect, Vallone, Ross, and Lepper found that each side saw the news coverage as biased in favor of the other side. Pro-Arab students thought the news segments were generally biased in favor of Israel, pro-Israeli students thought the segments were biased against Israel, and neutral students gave opinions that fell between the two groups.

Moreover, pro-Arab students felt that the news programs had excused Israel "when they would have blamed some other country," whereas pro-Israeli students felt the programs blamed Israel "when they would have excused some other country. For example, pro-Arab and pro-Israeli students differed in their perceptions of the number of favorable and unfavorable references that had been made to Israel during the news programs.

On the average, pro-Arab students reported that 42 per-cent of the references to Israel had been favorable and only 26 percent had been unfavorable. Pro- Israeli students, on the other hand, recalled 57 percent of the relerences to Israel as having been unfavorable and only 16 percent as having been favorable. Furthermore, pro-Israeli stu-dents though!

Vallone, Ross, and Lepper concluded that partisans tend to view media coverage of controversial events as unfairly biased and hostile to the position they advocate. They also speculated that similar biases in perception might arise in the context of mediation, arbitration, or other situations in which two sides are heavily committed to prior positions.

This speculation makes good sense. As we will see in Chapter 2, when people become committed to a particular cause or a course of action, their perceptions often change in order to remain consistent with this commitment. Even the simple identification of a playing card— or the perception of one's own intoxication— depends critically on cognitive and motivational factors.

Consequently, before making an important judgment or decision, it often pays to pause and ask a few key questions: Am I motivated to see things a certain way?

What expectations did I bring into the situation? Would I see things differently without these expectations and motives? Have I consulted with others who don't share my expectations and motives? By asking such questions, decision makers can expose many of the cognitive and motivational factors that lead to biases in perception. To understand the theory of cognitive dissonance and see how dissonance can influence judgment and decision making, consider a story told by Nathan Ausubel ; see also Deci, , pp.

To drive him out of town, a gang of youths visited the shop each day, standing in the entrance and shouting, "Jew! The next time that the gang came to threaten him, the tailor announced that anyone who called him a Jew would get a dime.

He then handed dimes to each member of the gang. Delighted with their new incentive, members of the gang returned the next day, shouting "Jew! The gang left satisfied because, after all, a nickel was a nickel. Then, on the following day, the tailor gave out only pennies to each gang member, again explaining that he could afford no more money than that. Well, a penny was not much of an incentive, and members of the gang began to protest.

When the tailor replied that they could take it or leave it, they decided to leave it, shouting that the tailor was crazy if he thought that they would call him a Jew for only a penny! Why would members of the gang harass the tailor for free but not for a penny? According to the theory of cognitive dissonance, people are usu- ally motivated to reduce or avoid psychological inconsistencies.

When the tailor announced that he was happy to be called a Jew, and when he changed the gang's motivation from anti- semitism to monetary reward, he made it inconsistent or "dissonance-arousing" for gang members to please him without financial compensation. In the absence of a sufficiently large payment, members of the gang could no longer justify behaving at variance with their objective which was to upset the tailor, not to make him happy.

Sixty male undergraduates at Stanford University were randomly assigned to one of three experimental conditions. And in the control condition, participants simply engaged in the tedious tasks.

What were the tasks? First, students spent half an hour using one hand to put 12 spools onto a tray, unload the tray, refill the tray, unload the tray again, and so on. Then, after thirty minutes were up, they spent the remainder of the hour using one hand to turn each of 48 pegs on a pegboard— one-quarter turn at a time! Each participant was seen individually, and the experimenter simply sat by, stopwatch in hand, busily making notes on a sheet of paper. Once the student had finished his tasks, the experimenter leaned back in his chair and said: I'd like to explain what this has been all about so you'll have some idea of why you were doing this.

There are actually two groups in the experiment. In one, the group you were in, we bring the subject in and give him essentially no introduction to the experiment. But in the other group, we have a student that we've hired that works for us regularly, and what I do is take him into the next room where the subject is waiting— the same room you were waiting in before— and I introduce him as if he had just finished being a subject in the experiment. The fellow who works for us then, in conversation with the next subject, makes these points It was very enjoyable, I had a lot of fun, 1 enjoyed myself, it was very interesting.

Following this explanation, the experimenter asked subjects in the control condition to rate how enjoyable the tasks had been. You see, we've got another subject waiting [looks at watch] who is supposed to be in that other condition. If you would be willing to do this for us, we'd like to hire you to do it now and then be on call in the future, if something like this should ever happen again. We can pay you a dollar [or twenty dollars, depending on condition] for doing this for us, that is, for doing it now and then being on call.

Do you think you could do that for us? In this instance, the dissonant cognitions were: 1. The task was extremely boring. Festinger proposed that people try whenever possible to reduce cognitive dissonance.

He regarded dissonance as a "negative drive state" an aversive condition , and he presented cognitive dissonance theory as a motivational theory despite the word "cognitive". According to the theory, subjects in the experiment should be motivated to reduce the inconsistency between the two thoughts listed above.

Of course, there wasn't much subjects could do about the second thought. On the other hand, the tediousness of the task afforded subjects some room to maneuver. Tediousness, you might say, is in the eye of the beholder. Bern's self-perception theory is based on two main premises: 1. People discover their own attitudes, emotions, and other internal states partly by watching themselves behave in various situations.

To the extent that internal cues are weak, ambiguous, or uninter-pretable, people are in much the same position as an outside observer when making these inferences.

The difference between self-perception theory and dissonance theory is that self-perception theory explains classical dissonance findings in terms of how people infer the causes of their behavior, whereas cognitive dissonance theory explains these findings in terms of a natural motivation to reduce inner conflict, or dissonance. According to Bern, subjects in the Festinger and Carlsmith study could have experienced no tension whatsoever and still given the same pattern of results.

A great deal of research has been conducted comparing these theories cf. Bern, , but it is still an open question as to which theory is more accurate or more useful in explaining "dissonance phenomena. In the final analysis, it probably makes sense to assume that both theories are valid in a variety of situations but following psychological tradition, I will use dissonance terminology as a shorthand for findings that can be explained equally well by self-perception theory.

As the next sections demonstrate, cognitive dissonance influences a wide range of judgments and decisions. Most dissonance-arousing situations fall into one of two general categories: predecisional or postdeci-sional. In the first type of situation, dissonance or the prospect of dissonance influences the decisions people make. In the second kind of situation, dissonance or its prospect follows a choice that has already been made, and the avoidance or reduction of this dissonance has an effect on later behavior.

They are involved in an accident. The father is killed, and the son is in critical condition. The son is rushed to the hospital and prepared for the operation. The doctor comes in, sees the patient, and exclaims, "I can t operate; it's my son! Most people would say it is not. They would reason that the patient cannot be the doctor's son if the patient's father has been killed. At least, they would reason this way until it occurred to them that the surgeon might be the patient's mother.

Moreover, according to the theory of cognitive dissonance, you should be motivated to reduce that dissonance by behaving in a more nonsexist way than ever. In , Jim Sherman and Larry Gorkin used the female surgeon story to test this hypothesis. Sherman and Gorkin randomly assigned college students to one of three conditions in an experiment on "the relationship between attitudes toward social issues and the ability to solve logical problems. In the non-sex-role condition, students were given five minutes to solve an equally difficult problem concerning dots and lines.

And in the control condition, students were not given a problem to solve. In the sex-role and non-sex-role conditions, the experimenter provided the correct solution after five minutes had passed roughly 80 percent of the subjects were not able to solve the assigned problem within five minutes. Next, subjects were told that the experiment was over, and they were presented with booklets for another experimenter's study about legal decisions the students had been told previously that they would be participating in "a couple of unrelated research projects".

Subjects were informed that the principal investigator of the other study was in South Bend, Indiana, and that they should put the completed booklets in envelopes addressed to South Bend, seal the envelopes, and drop them in a nearby mailbox. Then subjects were left alone to complete the booklet on legal decisions.

In reality, the experiment on legal decisions was nothing more than a way to collect information on sexism without subjects detecting a connection to the first part of the experiment. Subjects read about an affirmative action case in which a woman claimed that she had been turned down for a university faculty position because of her gender. Then they indicated what they thought the verdict should be, how justified they thought the university was in hiring a man rather than the woman, and how they felt about affirmative action in general.

Sherman and Gorkin found that, compared with subjects in the control group and subjects who were presented with the problem concerning dots and lines, subjects who had failed to solve the female surgeon problem were more likely to find the university guilty of sexual discrimination, less likely to see the university as justified in hiring a male for the job, and more supportive of affirmative action policies in general. In other words, after displaying traditional sex-role stereotypes, students tried to reduce their dissonance by acting more "liberated" or, in terms of self-perception theory, trying to show themselves that they were not sexist.

This method of dissonance reduction, called "bolstering," has also been used successfully to promote energy conservation. Kantola, G. Syme, and N. Campbell found that heavy users of electricity cut their consumption significantly when they were informed of their heavy use and reminded of an earlier conservation endorsement they had made.

What Doob et al. Doob and his associates explained this finding in terms of customer "adaptation levels" and the need to avoid dissonance.

Furthermore, according to dissonance theory, the more people pay for something, the more they should see value in it and feel pressure to continue buying it. The net result is similar to that found with many of the behavioral traps discussed in Chapter To test this hypothesis, Knox and Inkster asked people to rate their horse's chances of winning on a 7-point scale in which 1 indicated that the chances were "slight" and 7 indicated that the chances were "excellent.

This finding raises an interesting question: Does voting for a c;indi date increase your confidence that the candidate will win the election? In , Oded Frenkel and Anthony Doob published a study exploring this question. Frenkel and Doob used the same basic procedure as Knox and Inkster ; they approached people immediately before and immediately after they voted.

In one experiment they surveyed voters in a Canadian provincial election, and in another they queried voters in a Canadian federal election. In keeping with the results of Knox and Inkster, Frenkel and Doob , p.

Research on cognitive dissonance is not only bountiful and entertaining, it is directly applicable to many situations. For example, retail stores often explicitly label introductory offers so as to avoid the kind of adaptation effects found by Doob et al. Similarly, many political campaigns solicit small commitments in order to create postdecisional dissonance this strategy is sometimes known as the "foot-in-the-door technique".

In the remainder of this book, we will discuss several other applications and findings from cognitive dissonance theory. One of the leading authorities on dissonance research is Elliot Aronson, a student of Festinger and an investigator in many of the early dissonance experiments for readers interested in learning more about the theory of cognitive dissonance, a good place to begin is with Aronson, , It is therefore appropriate to conclude this chapter with a statement by Aronson , p.

If you want someone to form more positive attitudes toward an object, get him to commit himself to own that object 2. Before when the American Psychological Association adopted guidelines for nonsexist lan- guage , this literary practice was common in psychology.

According to the theory of cognitive dissonance, the pressure to feel consistent will often lead people to bring their beliefs in line with their behavior. In Chapter 3, we will see that, in many cases, people also distort or forget what their initial beliefs were. It's a poor sort of memory that only works backwards," the Queen remarked.

See Item 19 of the Reader Survey for your answer. Roughly 85 percent of the college students in a study by P. Memories are not like copies of our past experiences on deposit in a memory bank. Instead, they are constructed at the time of withdrawal Loftus, ; Myers, The "materials" used in this split-second reconstruction are logical inferences that fill in missing detail, associated memories that blend in with the original memory, and other relevant information.

To verify that memory is reconstructive; try an exercise suggested by Myers : Close your eyes and recall a scene in which you experienced something pleasurable. Don't read any further until you have finished replaying your experience. Did you see yourself in thr scene? Most people do. But if you saw yourself, then you must have reconstructed the scene unless, of course, you were looking at yourself during the original experience. In the first experiment, 45 students were asked to view seven different film clips depicting a traffic accident.

The clips ranged from five to thirty seconds in length and were borrowed from longer driver's education films. After each film clip, students answered a series of questions, including one on how fast the cars had been traveling. One-fifth of the students answered the question: "About how fast were the cars going when they contacted each other? Thus, Loftus and Palmer concluded that the form of a question— even when changed by only one word— can markedly affect how people reconstruct their memory of an event.

If anything, results from the second experiment were even more dramatic. This time, Loftus and Palmer had students watch a one-minute film that included a four-second, multiple-car crash.

Fifty students were asked: "About how fast were the cars going when they smashed into each other? Then the students returned one week later and, without viewing the film again, answered a series of questions. The key question Loftus and Palmer were interested in was whether students remembered having seen any shattered glass during the car crash. Loftus and Palmer found that asking students how fast the cars were going when they "smashed" not only led to faster estimates, but that one week later, a greater proportion of the students remembered the accident as having involved broken glass.

The results, which show statistically reliable differences among the experimental conditions, are shown in Table 3. What is interesting about these results is that the accident never involved broken glass— subjects who estimated the speed of smashing cars reconstructed the accident so that it involved broken glass! In , John Bransford and Jeffrey Franks further showed that memories are not stored separately from one another.

Bransford and Franks initially presented college students with a list of sentences about an event. For example, one of the lists— reprinted on page 7 of the Reader Survey— went like this: The ants ate the sweet jelly which was on the table. Then, after five minutes or so, students were presented with another list of sentences and asked to indicate which sentences were in the first list.

They were also asked to rate their confidence in each answer on a scale from 1 to 5. Item 34 in the Reader Survey contains a second list o! As it happens, the only sentence that appeared in the first set was Item 34c: "The ants ate the sweet jelly. Were you? What is significant about the sentence in Item 34b is that it contains combinations of relations that are not contained in any individual sentence from the first set.

The original sentences never explicitly stated that the jelly in the kitchen was sweet, or that the ants in the kitchen ate the sweet jelly. The sentence in Item 34b can only be derived by combining separate sentences from the first set. Thus, people do not simply memorize sentences; they construct and memorize a general scenario. Once one piece of information is integrated with others, it is sometimes difficult to remember which information was new and which was already known.

For example, if they learn about the results of a psychological experiment, they tend to regard the findings as having been fairly predictable all along— or at least more predictable than they would have judged before learning of the results one of the reasons why this book has a Reader Survey! Moreover, if people are asked to behave as though they know nothing about the outcome of an experiment, they still respond more like people who know about the results than people who do not.

That is, if they are asked to estimate in retrospect how likely they once thought the results were to occur, they assign higher probabilities than do people predicting the experimental outcome in advance.

This tendency is known as "hindsight bias," or the "I-knew-it-all-along" effect. Hindsight bias is the tendency to view what has already happened as relatively inevitable and obvious— without realizing that retrospective knowledge of the outcome is influencing one's judgments. One of the first studies on hindsight bias was published in by Baruch Fischhoff and Ruth Beyth.

In the first phase of the experiment, several groups of Israeli students were asked to estimate the probability of 15 different outcomes for either the China trip or the Soviet trip— before the trip took place.

For example, students who were asked about the China trip estimated the chances that the United States would establish a diplomatic mission in Peking, that President Nixon would meet Mao at least once, that President Nixon would announce the trip a success, and so forth. Similarly, students who were asked about Nixon's trip to the Soviet Union estimated outcomes such as the establishment of a joint space program, or the arrest of Soviet Jews trying to speak with Nixon.

In the second phase of the study— two weeks to six months after the trip had taken place— students were asked to recall what their earlier predictions had been. For instance, students who had answered ques-tions about the China trip were told the following:.

We are presently interested in the relation between the quality of people's predictions and their ability to remember their predictions. For this reason, we would like to have you fill out once again the same questionnaire which you completed two weeks ago, giving the same probabilities which you gave then.

If you cannot remember the probability which you then assigned, give the probability which you would have given to each of the various outcomes on the eve of President Nixon's trip to China. Students were also asked to indicate whether, as far as they knew, each outcome had in fact occurred. Fischhoff and Beyth wanted to see if students would remember their predictions as having been more accurate than they actually were.

In general, this is just what Fischhoff and Beyth found. Three-quarters of the students tended to remember having assigned higher probabilities than they actually had to outcomes that they thought had occurred, and the majority of students remembered having assigned lower probabilities to outcomes they believed had not occurred. Hindsight biases were particularly strong when the initial predictions preceded the recall task by several months.

When three to six months separated the prediction and recall tasks, 84 percent of the students showed hindsight biases— after learning the outcome of Nixon's trips, they viewed the outcome as having been more predictable than it actually was. Slovic and Fischhoff found that hindsight biases diminished when people stopped to consider reasons why the results might have turned out differently. Subjects in this research read four brief descriptions of studies drawn from biology, psychology, and meteorology.

Foresight subjects were told that the four studies would be conducted soon, and hindsight subjects were told that the studies had already been conducted. After reading about each study, all subjects then estimated the probability of replicating an outcome obtained on the first experimental trial each trial always had two possible outcomes.

In other words, hindsight subjects were told that a particular outcome had already been observed, and foresight subjects were asked to suppose the outcome occurred. This difference was substantially reduced, however, when hindsight subjects were asked to consider reasons why either experimental outcome might have occurred. See the pros and cons here.

If you're so inclined, you can tweak the assignments taking advantage of a generous bank of additional questions. You can also set up quizzes and exams from separate banks of questions if you want. The homework questions are conveniently sprinkled throughout the eBook chapters, so your students can "read a little, do a little". Plus, the multiple-choice homework questions are automatically graded for you.

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