Bet Hedging Hypothesis Statement - Sports Betting

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Bet Hedging Hypothesis Statement

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Supportive Hypotheses and Related Statements

Supportive Hypotheses and Related Statements

Recall the provisional statements about adult literacy education based upon Rescher’s “duly-hedged synthesis” as a first-cut resolution to our problem, which fuses elements of learning to read with that of learning to learn.

1. Literacy facilitates knowledge acquisition in the grappling with and mastery of print-based texts.

2. Literacy is enhanced to the extent to which individuals gain the capacity to read and write print-based texts.

  1. Growth in literacy is experienced to the extent to which readers progressively comprehend and draw meaning from texts and appropriate them into their lives.

4. Literacy has a technological component in the mastery of reading, writing and the comprehension of texts and a metaphorical dimension that resides in transactions between the reader and the text in which meaning making and significance lies beyond the text into that of appropriation, however variously that may be defined.

Each of these statements, as working hypotheses of the “duly hedged synthesis” requires additional clarification, including the grappling with new contradictions that may arise as the investigative proceeds. Let us take these statements one at a time.

Literacy facilitates knowledge acquisition in the grappling with and mastery of print-based texts.

· Knowledge acquisition may refer to understanding and progressively attaining the skills and knowledge needed for the technical mastery of reading and writing.

· Literacy may refer to the enhanced ability to read to the extent of providing an independent resource that students can apply to texts that they encounter either in the instructional program or outside of it without assistance from others.

· Knowledge acquisition may refer to the mastery of the content of print-based texts at varying levels of literal and inferential comprehension.

· Literacy may refer to the knowledge needed for such acquisition regardless as to how much or how little a student learns to read.

· While both learning to read and learning to learn are valid indicators of literacy, educators need to determine where priorities should be placed in terms of various student need and ability and what focal points of concentration stimulate what aspects of learning for any given student or groups of students.

Literacy is enhanced to the extent to which individuals gain the capacity to read and write print-based texts.

· If not by definition, it is at least a strong inference among most adult literacy educators and students that literacy includes the ability to read and write print-based texts and may even be its main purpose.

· All things being equal, increased capacity to read and write texts enhances literacy, whether a literal or metaphorical definition of literacy is adopted.

· The extent to which adult literacy students increase their ability to read print-based texts varies widely. Such variability needs to be factored into the reading and writing aspects of a given program and corresponding modes of assessment and accountability regardless of reading methodologies and the instructional content selected.

Growth in literacy is experienced to the extent to which readers progressively comprehend and draw meaning from texts and appropriate them into their lives.

· The capacity to comprehend and draw meaning from print-based texts in a supportive instructional environment does not depend on the ability to read the text independently.

· Students who have enhanced their ability to read and write have gained additional skills in comprehending and drawing meaning from texts in their ability to study independently. As a general rule, this capacity enhances a student’s mastery of the content embedded in printed texts.

· There may or may not be any intrinsic correlations between comprehending the authorial meaning(s) of a text and a student drawing meaning from it. While literacy may be enhanced through either, as a general rule, it is strengthened most so when reasonable inferences between the two can be made.

Literacy has a technological component in the mastery of reading, writing and the comprehension of texts, and a metaphorical dimension that resides in transactions between the reader and the text in which meaning making and significance lies beyond the text into that of appropriation, however variously that may be defined.

· Literacy, in the most comprehensive of definitions includes both the technological mastery of reading and writing, along with that of comprehension and deriving meaning from print-based texts.

· Taking the capacities of students into account, literacy progresses most when all of these dimensions are factored in, in which none of them serves as the privileged foundation of the definition.

· Even adults who remain at beginning levels of reading and writing ability who do not even come to approximating independent fluency can benefit as a result of the progress they achieve in the areas of comprehension and meaning making, although how durable such learning is and its significance requires much research.

· The extent to which even advanced students who progress in their reading and writing benefit in doing so also requires discriminating analysis. The salience to which gains in reading ability short of the GED certification open up opportunity structures for life improvement requires careful analysis in which the separation of variables may prove difficult.

· Even if little in the realm of opportunity structures is attained, being able to read, write, and comprehend print-based texts and appropriating such knowledge for one’s own purposes has a certain value in itself (although how much so remains in question) as a form of self development that may or may not have broader societal impact.

· What is determined as efficacious in relation to adult literacy education may have as much to do with values of individual students and programs that seek to support them as with specific impacts subject to objective forms of direct measurability.

· Literacy is a cultural metaphor of considerable pluralistic range and scope of knowledge acquisition that includes the technical capacity of reading and writing as an important, but undetermined variable of the broader definition encapsulated in the term, “multiliteracies.”

· Definitions of literacy that programs appropriate will be shaped by the sum total of cultural, social, political, economic, and intellectual influences interacting on them. In short, the cultural matrix as a variant in adult literacy education is unavoidable.

The Postpositivist Temper

These four hypotheses and 19 related statements presuppose a provisional acceptance of a “duly-hedged synthesis” that literacy is appropriately defined as a transactional relation between learning to read and write and broader content learning stemming from topics within and suggested by print-based texts. While both of these aspects of literacy are critical, neither is accepted as the foundational baseline of the definition. If anything is, based upon the precepts I have lain out, it is the tension between the radical particularity of student need, interest, and aptitude and the broader cultural matrix that gives shape to that which achieves social and political legitimacy through which definitions and purposes of adult literacy education are mediated.

In this respect, whatever value there is in adult literacy as an educational phenomenon, which, on my reading, is a great deal, I am also proposing that literacy, however it is defined, has a semiotic reference, which needs to be grasped as an ecological sign system manifested in a range of psycho-socio contexts (Barton, 1994). This is the case, I am positing even if one defines literacy as mastery of reading and writing in which the technologies themselves possess cultural symbolic reference, which include, but also point beyond their literal meaning. Consequently, there is no “autonomous” literacy outside a contextual frame, but a definition that is socially and culturally shaped all the way down (Street, 1988). On this claim I am radicalizing the logical assumptions of the New Literacy Studies in accepting both definitions of literacy proposed in this paper in symbolically significant mediational terms as pointing beyond themselves into the realm of their cultural significance (Barton, 1994).

To move beyond these core suppositions of literacy (the “duly-hedged synthesis”), including the 19 bulleted statements would be the beginning of shifting into an actual research project. That cannot be undertaken here, but what merits further discussion is the salience of postpositivist research design. In the briefest of terms this mediating school seeks maximum precision consistent with the complexity of the problem under investigation in the quest for truth as a regulative ideal. This is the core definition of “competent inquiry” in the postpositivist mode.

In the scientific pole of this research design, there is a tendency to limit problems to those that are susceptible to “piecemeal social engineering” or “middle range theories” (Pawson & Tilley, 1997; Phillips & Burbules, 2000). Such a limiting propensity contradicts the broader philosophical tenets of postpositivism in which research is designed in accordance to the needs of the problem under investigation, however complexly these may intrude into the cultural matrix, consequently, into the realm of values even at the level of political culture. The provisional statements about adult literacy education proposed in this paper require examination of highly specific (yet complex) matters, for example, on how adults at different levels of reading ability learn, or expand on their ability to read. Some of the statements also require broad cultural interpretations on the construction of meaning mediated via a power/knowledge nexus within the context of the politics and sociology of adult literacy programs and networks. On this assumption, the construction of literacy in the external environment feeds back into the field with obvious consequences for the ways in which programs are shaped and the ways in which literacy is defined in highly specific instructional setting (Demetrion, 2004). This also requires highly competent postpositivist analysis if this school of research is going to gain the credibility it needs to achieve its mediational vision.

In the example provided in this paper, the quality of the research design (stemming from the core definition of literacy, to the four supportive hypotheses and 19 related statements) is in the competence of the set up, including the salience of the problem posed. The issue is not whether the frame that I have provided could be improved, but the extent to which it lays out in detail, sequence, and scope, something of the dimensions of a significant problem and viable pathways toward its exploration and potential resolution at least in the Peircian sense of long-range cumulative research. Assuming these to be relatively sound, at least for the sake of the current discussion, then the research to be undertaken needs to draw on whatever methodologies are required to probe into the relevant content.

Fidelity to the scientific methodology is the key, as laid out, for example, in Popper’s six points, Dewey’s “patterns of inquiry,” and Rescher’s network model. Critical in postpositivist design is a problem focus, the stimulation of imagination in the making of bold conjectures, attunement to the significance of provisional hypothesis formation in pushing an investigation forward, the correlative role of guided experimentation, and the capacity to discern which data in which contexts is relevant to the problem at hand. Also needed is searing and, as relevant, comparative analysis of any given theory or study, acceptance of falsification as a core criteria as subtly defined by Popper and Dewey, a probing into alternative scenarios suggested by the data or a given hypothesis, a drive for problem resolution, and the search for truth, however provisional, as a regulative ideal. These ideals are embodied in Dewey, Popper, and Rescher, whose collective reflections make a substantial contribution to postpositivist design. My purpose in this paper is less to draw out the subtle distinctions and potential points of conflict among these scientifically oriented philosophers, than to illustrate how their collective work contributes to the development of a broad-based postpositivist temper. Any research project on adult literacy that stems from the framework provisionally laid out here will be credible to the extent that it follows along its pathways.

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Mating portfolios: bet-hedging, sexual selection and female multiple mating, Paco Garcia-Gonzalez

Mating portfolios: bet-hedging, sexual selection and female multiple mating

Polyandry (female multiple mating) has profound evolutionary and ecological implications. Despite considerable work devoted to understanding why females mate multiply, we currently lack convincing empirical evidence to explain the adaptive value of polyandry. Here we provide a direct test of the controversial idea that bet-hedging functions as a risk-spreading strategy that yields multi-generational fitness benefits to polyandrous females. Unfortunately, testing this hypothesis is far from trivial, and the empirical comparison of the across-generations fitness payoffs of a polyandrous (bet hedger) versus a monandrous (non-bet hedger) strategy has never been accomplished because of numerous experimental constraints presented by most ‘model’ species. In the present study we take advantage of the extraordinary tractability and versatility of a marine broadcast spawning invertebrate to overcome these challenges. We are able to simulate multi-generational (geometric mean) fitness among individual females assigned simultaneously to a polyandrous and monandrous mating strategy. Our approaches, which separate and account for the effects of sexual selection and pure bet-hedging scenarios, reveal that bet-hedging, in addition to sexual selection, can enhance evolutionary fitness in multiply-mated females. In addition to offering a tractable experimental approach for addressing bet-hedging theory, our study provides key insights into the evolutionary ecology of sexual interactions.

Estación Biológica de Doñana

Consejo Superior de Investigaciones Científicas

Hypothesis Testing - Significance levels and rejecting or accepting the null hypothesis

Hypothesis Testing (cont. )
Hypothesis Testing
The null and alternative hypothesis

In order to undertake hypothesis testing you need to express your research hypothesis as a null and alternative hypothesis. The null hypothesis and alternative hypothesis are statements regarding the differences or effects that occur in the population. You will use your sample to test which statement (i.e., the null hypothesis or alternative hypothesis) is most likely (although technically, you test the evidence against the null hypothesis). So, with respect to our teaching example, the null and alternative hypothesis will reflect statements about all statistics students on graduate management courses.

The null hypothesis is essentially the "devil's advocate" position. That is, it assumes that whatever you are trying to prove did not happen (hint: it usually states that something equals zero). For example, the two different teaching methods did not result in different exam performances (i.e., zero difference). Another example might be that there is no relationship between anxiety and athletic performance (i.e., the slope is zero). The alternative hypothesis states the opposite and is usually the hypothesis you are trying to prove (e.g., the two different teaching methods did result in different exam performances). Initially, you can state these hypotheses in more general terms (e.g., using terms like "effect", "relationship", etc.), as shown below for the teaching methods example:

Depending on how you want to "summarize" the exam performances will determine how you might want to write a more specific null and alternative hypothesis. For example, you could compare the mean exam performance of each group (i.e., the "seminar" group and the "lectures-only" group). This is what we will demonstrate here, but other options include comparing the distributions, medians, amongst other things. As such, we can state:

Now that you have identified the null and alternative hypotheses, you need to find evidence and develop a strategy for declaring your "support" for either the null or alternative hypothesis. We can do this using some statistical theory and some arbitrary cut-off points. Both these issues are dealt with next.

Hypothesis Testing
Significance levels

The level of statistical significance is often expressed as the so-called p-value. Depending on the statistical test you have chosen, you will calculate a probability (i.e., the p-value) of observing your sample results (or more extreme) given that the null hypothesis is true. Another way of phrasing this is to consider the probability that a difference in a mean score (or other statistic) could have arisen based on the assumption that there really is no difference. Let us consider this statement with respect to our example where we are interested in the difference in mean exam performance between two different teaching methods. If there really is no difference between the two teaching methods in the population (i.e., given that the null hypothesis is true), how likely would it be to see a difference in the mean exam performance between the two teaching methods as large as (or larger than) that which has been observed in your sample?

So, you might get a p-value such as 0.03 (i.e., p = .03). This means that there is a 3% chance of finding a difference as large as (or larger than) the one in your study given that the null hypothesis is true. However, you want to know whether this is "statistically significant". Typically, if there was a 5% or less chance (5 times in 100 or less) that the difference in the mean exam performance between the two teaching methods (or whatever statistic you are using) is as different as observed given the null hypothesis is true, you would reject the null hypothesis and accept the alternative hypothesis. Alternately, if the chance was greater than 5% (5 times in 100 or more), you would fail to reject the null hypothesis and would not accept the alternative hypothesis. As such, in this example where p = .03, we would reject the null hypothesis and accept the alternative hypothesis. We reject it because at a significance level of 0.03 (i.e., less than a 5% chance), the result we obtained could happen too frequently for us to be confident that it was the two teaching methods that had an effect on exam performance.

Whilst there is relatively little justification why a significance level of 0.05 is used rather than 0.01 or 0.10, for example, it is widely used in academic research. However, if you want to be particularly confident in your results, you can set a more stringent level of 0.01 (a 1% chance or less; 1 in 100 chance or less).

Hypothesis Testing
One- and two-tailed predictions

When considering whether we reject the null hypothesis and accept the alternative hypothesis, we need to consider the direction of the alternative hypothesis statement. For example, the alternative hypothesis that was stated earlier is:

The alternative hypothesis tells us two things. First, what predictions did we make about the effect of the independent variable(s) on the dependent variable(s)? Second, what was the predicted direction of this effect? Let's use our example to highlight these two points.

Sarah predicted that her teaching method (independent variable: teaching method), whereby she not only required her students to attend lectures, but also seminars, would have a positive effect (that is, increased) students' performance (dependent variable: exam marks). If an alternative hypothesis has a direction (and this is how you want to test it), the hypothesis is one-tailed. That is, it predicts direction of the effect. If the alternative hypothesis has stated that the effect was expected to be negative, this is also a one-tailed hypothesis.

Alternatively, a two-tailed prediction means that we do not make a choice over the direction that the effect of the experiment takes. Rather, it simply implies that the effect could be negative or positive. If Sarah had made a two-tailed prediction, the alternative hypothesis might have been:

In other words, we simply take out the word "positive", which implies the direction of our effect. In our example, making a two-tailed prediction may seem strange. After all, it would be logical to expect that "extra" tuition (going to seminar classes as well as lectures) would either have a positive effect on students' performance or no effect at all, but certainly not a negative effect. However, this is just our opinion (and hope) and certainly does not mean that we will get the effect we expect. Generally speaking, making a one-tail prediction (i.e., and testing for it this way) is frowned upon as it usually reflects the hope of a researcher rather than any certainty that it will happen. Notable exceptions to this rule are when there is only one possible way in which a change could occur. This can happen, for example, when biological activity/presence in measured. That is, a protein might be "dormant" and the stimulus you are using can only possibly "wake it up" (i.e., it cannot possibly reduce the activity of a "dormant" protein). In addition, for some statistical tests, one-tailed tests are not possible.

Hypothesis Testing
Rejecting or failing to reject the null hypothesis

Let's return finally to the question of whether we reject or fail to reject the null hypothesis.

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