东郊椰林风景区
Running head: GENERATING SEQUENCES
A Program for Generating Randomized Simple and Context-Sensitive Sequences
Gilbert Remillard
Morehead State University
ACCEPTED:Behavior Rearch Methods
上海南京东路
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Department of Psychology日记作文300字
601 Ginger Hall
Morehead State University老刘李红
Morehead, KY 40351
石嘴山日报Email: g.remillard@moreheadstate.edu
Phone: 1-606-783-2379丝绸之路终点
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Abstract
This article introduces Sequence Generation 2008 (SeqGen2008), a Windows-bad quence generator. SeqGen2008 can generate simple quences satisfying ur-defined event probabilities or frequencies. The program can also generate context-nsitive quences satisfying ur-defined transition matrices that specify the probabilities or frequencies with which distinct events are to follow specific contexts. An analysis of the properties and behavior of the algorithms employed by SeqGen2008 reveals that the algorithms are unbiad in their generation of quences.
A Program for Generating Randomized Simple and Context-Sensitive Sequences
Sequences compod of m distinct events with each event occurring one or more times are common in psychological rearch. Typically, the events are stimuli or experimental conditions. Sequence generation, in many cas, involves ordering events in a quence either by randomly lecting the events with replacement from a pool or by listing the events and randomly shuffling the
list. The two simple approaches do not consider context (i.e., preceding events) when lecting the next event in the quence. The disregard of context has two disadvantages. The first is a potential reduction in power via the introduction of noi in the data (van Casteren & Davis, 2006), and the cond is a risk of introducing confounds. The are discusd more fully in the next ction of the paper. Context-nsitive quence generation, in contrast, permits tighter control over the quential structure and so may be the better approach when generating quences of events in a within-subject design (Emerson & Tobias, 1995; Remillard & Clark, 1999; van Casteren & Davis, 2006). This form of quence generation, however, is less common than the two simple approaches described above, perhaps becau it is more difficult to implement or it is not implemented by popular experiment-generation software (e.g., E-Prime).
Another issue in the realm of quence generation is the adequacy of the algorithms ud to generate quences. For example, there are numerous ways to randomly shuffle a list of events, but not all algorithms are unbiad (Castellan, 1992). The majority of studies that prent participants with quences of events do not describe the algorithms that were ud to generate the quences. Conquently, one cannot ascertain whether the process of generating quences was biad or unbiad in the studies. Even if acceptable algorithms were ud, there is no evidence that they were implemented correctly.
The preceding discussion suggests a need for software that implements both context-nsitive quence generation and unbiad algorithms. The prent article introduces such software. The article is divided into four major ctions. The first ction describes five quence-generation methods—two common methods that disregard context and three context-nsitive methods that rearchers might find uful. The cond ction prents a Windows application that implements the five methods. The third ction describes the algorithms that underlie the various methods of quence generation. The final ction prents the results of Monte-Carlo simulations. The simulations were run to ensure the algorithms were implemented correctly and exhibited no bias in their generation of quences.
Sequence-Generation Methods
Simple probabilities. This is quence generation where each distinct event has a fixed probability of being lected on each trial. For example, a rearcher may wish to generate 500-trial quences with events 1—8 each having a 1/8 probability of being lected on each trial (e Table 1, tier 1), or events 1—3 having probabilities 8/10, 1/10, and 1/10, respectively, of being lected on each trial (e Table 1, tier 2). A disadvantage of the method is that obrved relative frequencies (RFs) and expected RFs can differ considerably, especially when quences are short.1 However, obrved R
Fs will tend to approach expected RFs as quences becomes longer.
Simple frequencies. This is quence generation where each distinct event occurs a pre-specified number of times in the quence. For example, a rearcher may wish to generate 15-trial quences with events 1—5 each occurring three times in a quence (e Table 1, tier 3), or generate 180-trial quences with events 1—4 occurring 60, 60, 30, and 30 times, respectively, in a quence (e Table 1, tier 4). Clearly, simple frequencies generation can produce quences
with obrved RFs that match expected RFs. For example, a rearcher may wish to generate a 400-trial quence with events 1—5 having obrved RFs 2/10, 5/10, 1/10, 1/10, and 1/10, respectively. This could be achieved by generating a 400-trial quence with events 1—5 occurring 80, 200, 40, 40, and 40 times, respectively, in the quence.
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ppt模板制作Inrt Table 1 here
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Simple probabilities and simple frequencies generation are common in psychological rearch. How
ever, they fail to consider context. The event lected on a trial is generally independent of the events lected on preceding trials. This disregard of context has two disadvantages. The first is a potential reduction in power. For example, consider a rearcher who generates 20, 90-trial quences (one quence per participant) with conditions 1—3 each occurring 30 times in a quence. For each participant, the quence is generated by randomly shuffling the 90 trials. Now, simply by chance, condition 2 may be more likely to precede condition 1 than condition 3 for some participants, and vice versa for other participants. As a result, the performance difference between conditions 1 and 3 might vary across participants if there are order effects. This would inflate the error term (i.e., the Subject x Condition interaction) in an analysis of variance and diminish power. The cond disadvantage of disregarding context is the risk of introducing confounds. For example, if, in the preceding scenario, condition 2 is more likely to precede condition 1 than condition 3 for the large majority of participants, then this would reprent a confound. The likelihood of this type of confounding will tend to increa as the number of participants decreas.
The next three quence-generation methods are context nsitive. The event lected on a trial is dependent on the events lected on preceding trials. The cond method below can overcome the disadvantages outlined above.
Contextual probabilities. This is quence generation where the probability of an event being lected on trial t is dependent on the context (i.e., on the events lected on trials t – n, ..., t – 2, t – 1). Table 2 prents three transition matrices, each specifying the conditional probabilities with which events are to follow contexts. The first matrix has four events and four contexts of size 1. The row for context 3 specifies that events 1—4 have probabilities 8/16, 4/16, 0/16, and 4/16, respectively, of being lected on trial t given that event 3 is lected on trial t – 1. The probabilities for context 3 could have been written in a different but equivalent manner; for example, 2 1 0 1 /4 or 50 25 0 25 /100. The zeroes in the matrix indicate that the rearcher does not wish an event to occur twice in succession.
The cond matrix has three events and nine contexts of size 2. The row for context 1-2 specifies that events 1—3 have probabilities 5/10, 2/10, and 3/10, respectively, of being lected on trial t given that events 1 and 2 are lected on trials t – 2 and t – 1, respectively. Finally, the third matrix has two events and six contexts of size 3. The row for context 2-1-2 specifies that events 1 and 2 each have probability 25/50 of being lected on trial t given that events 2, 1, and 2 are lected on trials t – 3, t – 2, and t – 1, respectively. Again, the probabilities could have been written in a different but equivalent manner; for example, 1 1 /2 or 50 50 /100. The zeroes in the matrix indicate that the r
earcher does not wish an event to occur three times in succession. Contextual probabilities generation has been ud in studies examining the human capacity for acquiring quential structure (e.g., Schvaneveldt & Gomez, 1998; Soetens, Melis, & Notebaert, 2004).
