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A novel approach for conceptualizing and analyzing data from psychological studies is presented and discussed. This approach is centered on model building in an effort to explicate the structures and processes believed to generate a set of observations. These models therefore go beyond the variable-based, path models in use today which are limiting with regard to the types of inferences psychologists can draw from their research. In terms of analysis, the newer approach replaces traditional aggregate statistics such as means, variances, and covariances with methods of pattern detection and analysis. While these methods are person-centered and do not require parametric assumptions, they are both demanding and rigorous. They also provide psychologists with the information needed to draw the primary inference they often wish to make from their research; namely, the

In his erudite and now classic book

In this paper we present a framework for conceptualizing and analyzing data that does not rely on traditional aggregate statistics such as the mean, median, variance, covariation, etc. Instead, this approach—like Exploratory Data Analysis (EDA;

Pick up almost any research paper on human psychology, and there you will find written in the Introduction statements about persons. You will not likely find statements about means, variances, or even covariances; although you might find descriptions of relationships between different attributes or qualities. Even these relationships, however, will be discussed in the context of living persons rather than aggregate statistics. Writing about rejection and interpersonal coping, for example,

Continuing with the topic at hand, rejection can be produced and studied in the laboratory by psychologists (e.g.,

Now imagine over the course of a semester eighty individual students walking into the psychologist’s laboratory and being guided through these same procedures. With each and every student the experimenter’s expectations will be the same, because within her mind is a model. Perhaps it is a model that is only crudely elaborated, but it is a model nonetheless that is meant to explain the thoughts, feelings, and behaviors of each individual student (person) in the study. What might this model look like? The most rigorous way to express the model is via a picture like that shown in Figure

The model also demarcates three important points of interaction between the experimenter and participant. The purpose of the first interaction, from the perspective of the experimenter, is to create within the mind of the participant an expectation of an online interaction with another student across campus. The pentagon enclosing the image of the participant and counterpart joined by a “+” sign represents a simple or complex judgment. In this instance, the participant judges that he will be interacting with the other student, and that the interaction will be positive (given the biography and the experimenter’s instructions). The circle enclosing the image of the counterpart represents certain predicates (predicative adjectives, predicative nouns) based on the biography. For example, the biography describes the counterpart as “a student,” “a psychology major,” “outgoing,” etc. The counterpart student is thus known through the neutral and positive descriptive nouns and adjectives given in the biography.

The purpose of the second interaction (focusing on rejecting the condition) is to inform the participant that the other student has chosen not to participate in the discussion after having read the participant’s biographical statement. It is not perfectly clear or stated plainly, however, if the counterpart is rejecting the participant, but it is the experimenter’s expectation that the participant will interpret this decision as a personal rejection based on his own biographical statement. The phone call is therefore considered to be an efficient cause; that is, a cause that proceeds its effect in time leading to its production or change (denoted by an arrow labeled “Ef” in the model; see

The judged rejection then operates as an efficient cause of negative self-predications (negative self-attributions) by the participant. These negative self-predications are represented by the circle derogatorily labeled “Loser” enclosing the participant in the second interaction of the study. Hurt feelings, represented by a diamond labeled “Hurt” enclosing the participant, also result from the judged rejection. Finally, these experiences occurring simultaneously within the participant cause him (as an efficient cause) to adopt a negative disposition toward the counterpart. This negative disposition may occur consciously, for instance, if the participant were to think disparaging thoughts such as “well, that guy’s a jerk for wasting my time” or “I always knew psychology majors were unstable.”

Finally, the purpose of the third interaction is to provide the participant with an opportunity to make explicit judgments about his rejecting counterpart. As can be seen on the right side of Figure

At the end of the model (bottom right-hand corner of Figure

The integrated (iconic) model in Figure

1’s have been observed for the rejected participants.

If the structured processes in Figure

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Therefore, the structured processes in Figure

A key feature of the inference is that, unlike induction, it appeals to explanation (viz., the structures and processes diagrammed in Figure

The model can be refined by changing its existing components; for example, the exact emotions felt by the participant can be elaborated, or the 6-point scale can be justified and predictions included about how the participant should behave with regard to the scale. The model can be extended by adding additional components; for example, perhaps not every participant will construe the counterpart’s actions as rejection, and the determining factors for making such an interpretation can be added to the model. Of course the entire model itself can be tested against and perhaps superseded by a competing model (such as a Freudian view of hostility). In this regard, in particular, the experimenter is seeking an

D is a collection of data

H (an hypothesis) would, if true, explain D

No other hypothesis can explain D as well as H does

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Therefore, H is probably true

The conclusion is again uncertain, but the continual striving to thoroughly evaluate, improve upon, or replace a given model seems to capture the investigative spirit of modern science, at least as it is idealized. In any case it is easy to see why

The third inference sought by the experimenter is an attempt to draw a conclusion about persons, in general, from her specific sample of individuals in her particular study. The model in Figure

The three types of inference sought by the experimenter in this example are therefore (1) abduction, (2) inference to best explanation, and (3) inductive generalization. All three inferences are facilitated by the integrated, iconic model in Figure

When psychologists argue they are using statistics to generalize beyond their samples, it is important to realize most believe they are generalizing in the manner described above; namely, making an abductive inference to best explanation or making an inductive inference about persons in general. Unfortunately, in the overwhelming majority of cases, nothing could be further from the truth. By using traditional statistical methods that rely on null hypothesis significance testing (NHST; viz., traditional

To demonstrate this ubiquitous type of inference, let us now consider the condition in which the participant is told that his counterpart cannot participate in the online discussion because of a computer malfunction. With this comparison group in place, and following modal research practice (_{0.95}: –0.58, –0.02. The difference is also consistent with expectation, with the rejecting group yielding a lower mean than the non-rejecting group.

What inference can she draw from these results, assuming she has met or properly adjusted for all of the assumptions of the statistical test? Having used NHST, the experimenter posited two populations from which she drew her samples: a population of persons experiencing rejection in the study, and a population of persons not experiencing rejection in the study. The populations in this example, as in most studies in psychology, are entirely imaginary (_{1} and μ_{2}. The null hypothesis is that the two population means are equal (H_{0}: μ_{1} = μ_{2}) and by declaring her results as “statistically significant” she has rejected this hypothesis and concluded (inferred) that the two population means are not equal. She can consider the difference between the population means as a parameter to be estimated as well (viz., μ_{diff} = μ_{1} – μ_{2}) and then provide a point estimate for what she thinks the difference might be (viz., 4.20 – 4.50 = –0.30). She can also provide an interval with an assigned level of confidence for possible values of the difference (viz., CI_{0.95}: –0.58, –0.02).

With the point and interval estimates in hand, it is clear the psychologist is attempting to make an inference to a population parameter (μ_{diff}), which is presumably fixed at some value. This inference is the only one she can rationally make; and the term “rationally” should be used loosely here because the low observed

The experimenter also cannot make an inductive inference to people in general as her hypotheses and analysis are constrained to means. She cannot, therefore, write statements such as “people who are rejected will rate the rejecting person as less popular than those who are not rejected” or “rejected persons, compared to non-rejected persons, considered the counterpart to be unpopular.” In order to be true to her model and analyses, she must restrict her inferential statements to population means or the difference between them. Moreover, she must be careful to avoid the following erroneous conclusions from her statistically significant finding:

Because my result was statistically significant, it will likely replicate across independent samples of participants.

My result is not likely due to chance given the low

The null hypothesis is probably false; that is, the probability the null hypothesis is true is less than five percent.

My research hypothesis is probably true.

A side-by-side comparison of the models in Figures

Sample | SD | SD | _{diff} |
CI_{0.95} |
|||||

1 | 4.20 | 0.40 | 4.50 | 1.21 | –0.30 | 0.33 | –2.10 | 0.037 | –0.58, –0.02 |

2 | 4.20 | 2.24 | 4.80 | 1.34 | –0.60 | 0.33 | –2.06 | 0.042 | –1.18, –0.023 |

3 | 4.20 | 0.89 | 4.50 | 0.93 | –0.30 | 0.33 | –2.10 | 0.038 | –0.58, –0.02 |

What do we really know about these data based on Table

The results from the three studies clearly show different patterns of responses that are simply not detectable in the aggregate statistics or bar charts. What is the experimenter to do? She could switch to a non-parametric procedure, but there are clear incentives for not doing so, including the potential loss of statistical power and the unwarranted perception that such a switch would indicate weakness in her methods and results. A median test in fact yields statistical significance for only the first two data sets. She could switch to a Bayesian analysis which would permit her to compare means while also assessing parameters relevant to the distributions of the samples. For all three data sets the Bayesian analysis in fact indicates “credible differences” between the group means, as the Highest Density Interval excluded 0 in each case. Fundamentally, though, none of these options represents a departure from the variable-based model in Figure

The first step toward a more rigorous analysis of the data that is also consistent with the types of inferences sought through the model in Figure

Given the experimenter’s choices, then, this array presents boundaries on the ways she thinks data can be structured, and it is within this limiting structure she must identify or search for meaningful and robust patterns of observations.

If the model in Figure

Of course other patterns could be put forth as examples, but the point here is that if the experimenter is to work deductively and conduct

For the sake of demonstration, let us assume that the second pattern in Figure

Tallying all of the persons who were consistent with the predicted pattern yields what is known as the percent correct classification (PCC) index in the OOM software. The PCC index for the first sample was only 40%, as only 64 of the 160 joint group/rating observations matched expectation. The PCC index can range from 0 to 100 and is easily interpretable in light of Figure

The results in Figure

The second data set also reveals striking results that were masked by the traditional statistics; specifically, as can be seen in Figure

Figure

The model in Figure

Results for the three data sets, displayed as multigrams, are shown in Figure

The multigram for the first sample shows a convincing pattern with regard to the PCC index (80%). As can be seen in Figure

If the experimenter has all three data sets to work with, however, it is clear that a single pattern has not emerged. The multigram for the second sample in Figure

Second, the idolatry of the mean is disturbing because it reveals that psychologists are operating under a quantitative imperative (

One need only examine the periodic table of the elements or the biochemical pathways of a eukaryotic cell to understand that the scientific study of nature is not restricted to interval and ratio scaled measurement and parametric statistics. The arguments, models, and methods, presented in this paper hopefully elucidate why psychologists should feel confident in venturing beyond the world of means, variances, and covariances without fearing a loss of scientific rigor. Placing the integrated model in Figure

“I believe that the almost universal reliance on merely refuting the null hypothesis as the standard method for corroborating substantive theories in the soft areas is a terrible mistake, is basically unsound, poor scientific strategy, and one of the worst things that ever happened in the history of psychology” (p. 817).

The shift to iconic modeling is also a step toward the types of inferences psychologists truly wish to make from their research: abductive inference, inference to best explanation, and inductive generalization. Variable-based models are meant to show associations between variables and are poor tools for explaining the complex structures and processes of nature. The mean does not provide information about “people in general” and in fact likely describes no one in particular (

Going beyond the world of variable-based modeling and the computation of means, variances, and other parametric statistics is not necessarily a leap into the world of Bayesian statistics or non-parametric analyses; rather, the move is from estimating parameters in the context of sampling variability (as with an independent samples

The final move, then, is from variable-based models to persons. The example study above employed a between-group design, and only two pertinent observations were made for each participant. A more intensive study of the individual is possible, however, using similar methods to conceptualize and analyze multiple observations made for each person.

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.