on 19-Jul-2017 (Wed)

In a frequency distribution It is important to consider the number of intervals to be used. If too few intervals are used, too much data may be summarized and we may lose important characteristics; if too many intervals are used, we may not summarize enough.

I explore the notion of Abbasid metapoetry, sug- gesting that the term, as defined by twentieth-century critics, appropriately describes the relationship of Abbasid poets to their predecessors

Poetry and the debates around poetry became a common feature of every court. These debates had their impact on the attitudes of poets towards their craft, which necessarily led to more conscious and deliberate poetry that con- stantly addresses its references and calls attention to its processes. Moreover, the poet became an authority on poetry, often presiding over discussions of his work and that of others. Knowledge of poetry became a specialized field. Poets and poems were compared, examined, and weighed against each other. The reception of poetry became a specialized skill not everyone could lay claim to. This is what al-Amidi calls al- 'ilm bi al-shi'r 11 (knowledge of poetry, criticism), a science whose experts often included poets.

In Abbasid metapoesis, one must avoid forcing the term on earlier poetry. In the Arabic tradition, whose common poetic themes is the boast, most boast poems include long descriptions of what good poetry is and who a great poet is. Thus, one must distinguish between thematic metapoetry, meaning poems whose subject or theme is poetry, and a metapoetry that is deeper and much more critical in nature, although it is not always signaled or marked as clearly as the former. I call this second type "referential or contextual metapoesis," to reflect a consciousness in the manner a poet engages his poetic references.

Abbasid poetry not a continuation of what came before: the Abbasid experience is a step away from the archetypal qasidah.

The keyword mnemonic demands considerable creative effort if the learner is to go beyond the words for which suggested conversions of words to images are available. Retrieval practice could offer an alternative technique for learning vocabulary, one that is less demanding and might be applied by a wider range of learners to a wider range of vocabulary.

When a distribution has one value that appears most frequently, it is said to be unimodal. A data set that has two modes is said to be bimodal.

Harmonic Mean

The harmonic mean of n numbers x_i (where i = 1, 2, ..., n) is:

The special cases of n = 2 and n = 3 are given by:

and so on.

For n = 2, the harmonic mean is related to arithmetic mean A and geometric mean G by:

Another benefit derives from the comprehensibility of the images: Without meaning, memory is poor (Bransford & Johnson, 1973; Bartlett, 1932), and novel foreign words are, by definition, not understood by the learner. The keyword ideas and sounds, though, are understandable and therefore, more memorable than the foreign words.

The effectiveness of the keyword method also appears to depend upon the quality of the keyword image

When compared with items that had also been presented just once but had not received retrieval practice, Landauer and Bjork found that all retrieval schedules enhanced recall at a later test, and that performance was best with an expanding schedule.

Another potential benefit of retrieval practice is a motivational one. If practice is scheduled to enable high levels of success, learners have a more positive learning experience and may approach the task more confidently and enthusiastically.

Within Nelson and Narens’s (1994) influential framework, students are characterized as confronting three types of decisions—selection of kind of processing, allocation of study time, and termination of study. We have expanded that framework to include deci- sions about study strategies and scheduling

In business and elsewhere, we often encounter probabilities stated in terms of odds—for instance, “the odds for E” or the “odds against E.” For example, as of November 2013, analysts’ fiscal year 2014 EPS forecasts for JetBlue Airways (NASDAQ: JBLU) ranged from $0.55 to $0.69. Suppose one analyst asserts that the odds for the company beating the highest estimate, $0.69, are 1 to 7. Suppose a second analyst argues that the odds against that happening are 15 to 1. What do those statements imply about the probability of the company’s EPS beating the highest estimate? We interpret probabilities stated in terms of odds as follows:

• Probability Stated as Odds. Given a probability P(E),

  1. Odds for E = P(E)/[1 − P(E)]. The odds for E are the probability of E divided by 1 minus the probability of E. Given odds for E of “a to b,” the implied probability of E is a/(a + b).

In the example, the statement that the odds for the company’s EPS for FY2014 beating $0.69 are 1 to 7 means that the speaker believes the probability of the event is 1/(1 + 7) = 1/8 = 0.125.

• 2. Odds against E = [1 − P(E)]/P(E), the reciprocal of odds for E. Given odds against E of “a to b,” the implied probability of E is b/(a + b).

The statement that the odds against the company’s EPS for FY2014 beating $0.69 are 15 to 1 is consistent with a belief that the probability of the event is 1/(1 + 15) = 1/16 = 0.0625.

To further explain odds for an event, if P(E) = 1/8, the odds for E are (1/8)/(7/8) = (1/8)(8/7) = 1/7, or “1 to 7.” For each occurrence of E, we expect seven cases of non-occurrence; out of eight cases in total, therefore, we expect E to happen once, and the probability of E is 1/8. In wagering, it is common to speak in terms of the odds against something, as in Statement 2. For odds of “15 to 1” against E (an implied probability of E of 1/16), a $1 wager on E, if successful, returns $15 in profits plus the $1 staked in the wager. We can calculate the bet’s anticipated profit as follows:

Win:	Probability = 1/16; Profit =$15
Loss:	Probability = 15/16; Profit =–$1
Anticipated profit = (1/16)($15) + (15/16)(–$1) = $0

Weighting each of the wager’s two outcomes by the respective probability of the outcome, if the odds (probabilities) are accurate, the anticipated profit of the bet is $0.

What to study ?
which items to study is one of the two most frequently investigated components of self-regulated study (the other is deciding how long to persevere once a choice has been made)

How Long to Study
Once an item has been selected for study, two more decisions must be made: (1) how long to persist before moving on to another item and (2) when to stop studying the item altogether.

Deciding when to stop studying . It seems simple: Stop studying when you know the information. Often, however, people stop studying when they do not know the information—when, for example, they are under time pressure or they feel that the information is either not learnable or not worth learning

Perhaps most surprising is that the participants dropped items that they seemed to realize they did not really know.

our participants seemed to be of two minds: They dropped items they knew at the time, but they also seemed aware that they might forget those items by the time of the test. If they knew that they might forget those items, why not leave them in the deck for further study? Our hypothesis is that the participants believed, wrongly, that there was little to gain from restudying an answer once they could recall it, even if the answer might other- wise be forgotten

A subsequent experiment supported this hypothesis. When participants were asked to type in answers as they studied, 58% of dropped items were dropped after a sin- gle correct recall (and 20% after not having been recalled at all!). Such a strategy is far from optimal: Items that are close to being recallable (i.e., in the region of prox- imal learning) on a later test should be prioritized, not dropped.

spacing practice and self-testing, both of which are de- sirable difficulties—that is, manipulations that introduce difficulties during study, but enhance long-term learning (Bjork, 1994)

separating successive study sessions rather than massing such sessions—has large positive ef- fects on long-term memory (see, e.g., Cepeda, Pashler, Vul, Wixted, & Rohrer, 2006; Dempster, 1988). But what do students choose to do? Choosing to space study activities requires a belief that most students may not have—that spacing is advanta- geous

students would choose massed practice if given a choice, however counterproductive that choice might be.

Choosing to self-test . Self-testing can be a very effec- tive study strategy, especially in the interest of long-term

retention (see, e.g., Bjork, 1975; Roediger & Karpicke, 2006). The act of retrieving information from memory increases, sometimes dramatically, the likelihood that information can be retrieved again in the future. When adopting self-testing as a study strategy, it is important to choose the right time to test oneself, because the more difficult the retrieval (provided it succeeds), the larger the benefits;

To understand the meaning of a probability in investment contexts, we need to distinguish between two types of probability: unconditional and conditional. Both unconditional and conditional probabilities satisfy the definition of probability stated earlier, but they are calculated or estimated differently and have different interpretations. They provide answers to different questions.

In analyses of probabilities presented in tables, unconditional probabilities usually appear at the ends or margins of the table, hence the term marginal probability. Because of possible confusion with the way marginal is used in economics (roughly meaning incremental), we use the term unconditional probability throughout this discussion.

Suppose the question is “What is the probability that the stock earns a return above the risk-free rate (event A)?” The answer is an unconditional probability that can be viewed as the ratio of two quantities. The numerator is the sum of the probabilities of stock returns above the risk-free rate. Suppose that sum is 0.70. The denominator is 1, the sum of the probabilities of all possible returns. The answer to the question is P(A) = 0.70.

Now suppose we want to know the probability that the stock earns a return above the risk-free rate (event A), given that the stock earns a positive return (event B). With the words “given that,” we are restricting returns to those larger than 0 percent—a new element in contrast to the question that brought forth an unconditional probability. The conditional probability is calculated as the ratio of two quantities. The numerator is the sum of the probabilities of stock returns above the risk-free rate; in this particular case, the numerator is the same as it was in the unconditional case, which we gave as 0.70. The denominator, however, changes from 1 to the sum of the probabilities for all outcomes (returns) above 0 percent. Suppose that number is 0.80, a larger number than 0.70 because returns between 0 and the risk-free rate have some positive probability of occurring. Then P(A | B) = 0.70/0.80 = 0.875. If we observe that the stock earns a positive return, the probability of a return above the risk-free rate is greater than the unconditional probability, which is the probability of the event given no other information.

When students were asked how they decided what to study next, 59% chose “Whatever’s due soonest/overdue,” and only 11% chose “I plan my study schedule ahead of time, and I study whatever I’ve scheduled.” Similarly, 86% of students re- sponded “no” when they were asked whether they usually returned to course material to review it after a course had ended—although the ideal answer to this question is yes. The responses of the meager 14% of students who said “yes” may be partly attributable to courses that spanned multiple academic terms.

Self-testing . Overall, the results of our survey sug- gest that students either do not appreciate the benefits of spacing, or simply do not make choices to mass or space at all but rather attend to whatever is most urgent.

A large percentage of participants (68%) seemed to realize the metacognitive benefits of testing, because their response to this question was “to figure out how well I have learned the information I’m studying.” Interestingly, however, only 18% thought of testing as a learning event

Dropping material from further study . Our work on flashcards suggests that people often stop studying something once they feel they know it at the present time, meaning that they often stop too soon

To review, an unconditional probability is the probability of an event without any restriction; it might even be thought of as a stand-alone probability. A conditional probability, in contrast, is a probability of an event given that another event has occurred.