WSRt, critical thinking - a summary of all articles needed in the fourth block of second year psychology at the uva
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Critical thinking
Article: Dienes, Z, 2011
Bayesian Versus orthodox statistics: which side are you on?
doi: 10.1177/1745691611406920
The orthodox logic of statistics, starts from the assumption that probabilities are long-run relative frequencies.
A long-run relative frequency requires an indefinitely large series of events that constitutes the collective probability of some property (q) occurring is then the proportion of events in the collective with property q.
The logic of Neyman Pearson (orthodox) statistics is to adopt decision procedures with known long-term error rates and then control those errors at acceptable levels.
Thus, setting significance and power controls long-run error rates.
The probability of a theory being true given data can be symbolized as P(theory|data).
This is what orthodox statistics tell us.
One cannot infer one conditional probability just by knowing its inverse. (So P(data|theory) is unknown).
Bayesian statistics starts from the premise that we can assign degrees of plausibility to theories, and what we want our data to do is to tell us how to adjust these plausibilities.
The likelihood
In the Bayesian approach, applies to the truth of theories.
We can answer the questions about:
Neither of these can be do using the orthodox approach.
Likelihood: the probability of obtaining the exact data given the hypothesis.
Posterior is given by likelihood times prior.
The likelihood principle: all information relevant to inference contained in data is provided by the likelihood.
When we are determining how given data changes the relative probability of our different theories, it is only the likelihood that connects the prior to the posterior.
The likelihood is the probability of obtaining the exact data obtained given a hypothesis (P(D|H).
This is different from a p value, which is the probability of obtaining the same or more extreme data given both a hypothesis and a decision procedure.
In orthodox statistics, p values are changed according to the decision procedure; under what conditions one would stop collecting data, whether or not the test is post hoc, how many other test one conducted.
None of these factor influence the likelihood.
The Bayes factor
The Bayes factor pits one theory against another.
Prior probabilities and prior odds can be entirely personal and subjective.
There is no reason why people should agree about these before data are collected if they are not part of the publically presented inferential procedure.
If the priors form part of the inferential procedure, they must be fairly produced and subjected to the tribunal of peer judgement.
One data are collected we can calculate the likelihood for each theory.
These likelihoods are things we want researchers to agree on. Any probabilities that contribute to them should be plausibly or simply determined by determined by the specification of the theories.
The Bayes factor (B): the ratio of likelihoods.
Posterior odds = B x prior odds.
The evidence is continuous and there are not thresholds in Bayesian theory.
B automatically gives a notion of sensitivity, it directly distinguishes data supporting the null from data uninformative about whether the null or you theory was supported.
For both p values associated with a t test and for B, if the null is false, as a number of subjects increases, then test scores are driven in one direction.
When the null hypothesis is true, p values are not driven in any direction, only B us. B is then driven to zero.
Stopping rule
In the Neyman Pearson approach, one must specify the stopping rule in advance.
Once those conditions are met, there is to be no more data collection.
Typically, this means one should use a power calculation to plan in advance how many subjects to run.
The Bayes factor behaves differently from p values as more data are run (regardless of stopping rule).
Planned versus post hoc comparisons
When using Neyman Pearson, it matters whether you formulated your hypothesis before or after looking at the data (post hoc vs. planned comparisons).
Predictions made before rather than after looking at the data are treated differently.
In Bayesian inference, the evidence for a theory is just as strong regardless of its timing relative to the data.
This is because the likelihood is unaffected by the time the data were collected.
The likelihood principle follows from the axioms of probability.
It is not the ability to predict in advance per se that is important, that ability is just an (imperfect) indicator of the prior probability of relevant hypotheses.
When performing Bayesian inference, there is no need to adjust for the timing of predictions per se.
Multiple testing
When using Neyman Pearson, one must correct for how many tests are conducted in a family of tests.
When using Bayes, it does not matter how many other statistical hypotheses are investigated. All that matters is the data relevant to each hypothesis under investigation.
Once one takes into account the full context, the axioms of probability lead to sensible answers.
In the Bayes approach, rather than the Neyman Pearson approach, that is most likely to demand that researchers draw appropriate conclusions from a body of relevant data involving multiple testing.
If we want to determine by how much we should revise continuous degrees of belief, we need to make sure our system of inference obeys the axioms of probability.
If researchers want to think in terms of degree of support data provide for a hypothesis, they should make sure their inferences obey the axioms of probability.
One version of degrees of belief are subjective probabilities.
Subjective probabilities: personal convictions in an opinion.
When probabilities of different propositions form part of the inferential procedure we use in deriving conclusions from data, then we need to make sure that the procedure is fair.
Thus, there has been an attempt to specify objective probabilities that follow from the informational specification of a problem.
In this way, the probabilities become an objective part of the problem, with values that can be argued about, given the explicit assumptions, and that do not depend any further on personal idiosyncrasies.
One notion of rationality is having sufficient justification for one’s beliefs.
If one can assign numerical continuous degrees of justification to beliefs, then some simple minimal desiderata lead to the likelihood principle of inference.
Hypothesis testing violates the likelihood principle.
Bayes factors demand consideration of relevant effect sizes.
Neyman developed two specific measures of sensitivity:
For any continuous measure based on a finite number of subjects, an interval cannot be an infinitesimally small point.
A null result is always consistent with population values other than zero.
That is why a non-significant result cannot on its own lead to the conclusion that the null hypothesis is true.
Theories and practical questions generally specify, even if vaguely, relevant effect sizes.
The research context, usually provides a range of effects that are too small to be relevant and a range of effects that are consistent with theory or practical use.
Researchers have relevant intuitions, and that is why it has made sense to them to assert null hypotheses.
Bayes makes them explicit.
If we want to use null results in any way to count against theories that predict an effect, we must consider the range of effect sizes consistent with the theory.
Effect size is very important in the Neyman Pearson approach.
On the other hand, Fisherian significance testing leads people to ignore effect sizes.
One must specify what sort of effect sizes a theory predicts to calculate a Bayes factor.
Because it takes into account effect size, the Bayes factor distinguishes evidence that there is not relevant effect from no evidence of a relevant effect.
One can only confirm a null hypothesis when one has specified the effect size expected on the theory being tested.
In specifying theoretically expected effect sizes, we should ask ourselves “What size effect does the literature suggest is interesting for this particular domain?” Rather than following the common practice of plucking a standardized effect size of 0.5 out of thin air, researchers should get to know the data of the field.
Confidence intervals themselves have all the problems for Neyman Pearson inference in general (unlike credibility or likelihood intervals).
Because confidence intervals consists of all values non-significantly different from the sample mean, they inherit the arbitrariness of significance testing.
To calculate a Bayes factor in support of a theory, one has to specify what the probability of different effect sizes are, given the theory.
Bayes gives us the apparatus to flexibly deal with different degrees of uncertainty regarding the predicted effect size.
Logically, one needs to know what a theory predicts in order to know how much it is supported by evidence.
Three distributions
In terms of predictions of the theory (or requirements of a practical effect), one has to decide what range of effects are relevant to the theory.
Three ranges:
Different ways of using Bayes factors
Bayes factor is suggested to be used on any data where the null hypothesis is compared with a default theory.
Or when inference is based on the posterior and thus takes into account the priors of hypothesis.
Also for specific hypotheses that interest the researcher and allows priors to remain personal and not part of public inference.
By following Bayes rule, each of these approaches means rational answers are provided for the given assumptions, and researchers may choose each according to their goals and which assumptions seem relevant to them.
Bayes factors are just one form of Bayesian inference, namely a method for evaluating theories against another.
With Bayes factors, one does not have to worry about corrections for multiple testing, stopping rules, or planned versus post hoc comparisons.
Bayes factor just tells you how much support given data provides for one theory over another.
There is no right Bayes factor.
Strictly, each Bayes factor is a completely accurate indication of the support for the data of one theory over another.
The theories are defined by the precise predictions they make.
The crucial question is which of these representations best matches the theory as the researcher has described it and related it to the existing literature.
One constraint on the researcher will be the demand for consistency: arguing for one application of a theory ties one’s hands when it comes to another application.
The solution is to use a default Bayes factor for all occasions, though this amounts to evaluating a default theory for all occasions, regardless of one’s actual theory.
A default Bayes factor will only test your theory if it happens to correspond to the default.
Another solution is to define the predictions according to simple procedures to ensure the theory proposed is tested according to fair criteria.
When using Bayes in multiple testing, one can use the fact that one is testing multiple hypotheses to inform the results if one believes that testing these multiple hypotheses is relevant to the probability of any of them being true.
Calculating a Bayes factor depends on answering the following question about which there may be disagreement: What way of assigning probability distributions of effect sizes as predicted by theories would be accepted by protagonists on all sides of a debate?
Ultimately, the issue is about what is more important to us: using a procedure with known long-term error rates or knowing the degree of support for our theory.
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Critical thinking
Article: Borsboom, Rhemtulla, Cramer, van der Maas, Scheffer and Dolan (2016)
Kinds versus continua: a review of psychometric approaches to uncover the structure of psychiatric constructs
The present paper reviews psychometric modelling approaches that can be used to investigate the question whether psychopathology constructs are discrete or continuous dimensions through application of statistical models.
The question of whether mental disorders should be thought of as discrete categories or as continua represents an important issue in clinical psychology and psychiatry.
But, such categorizations often involve apparently arbitrary conventions.
All measurement starts with categorization, the formation of equivalence classes.
Equivalence classes: sets of individuals who are exchangeable with respect to the attribute of interest.
We may not succeed in finding an observational procedure that in fact yields the desired equivalence classes.
If we break down the classes further, we may represent them with a scale that starts to approach continuity.
The continuity hypothesis formally implies that:
In psychological terms, categorical representations line up naturally with an interpretation of disorders as discrete disease entities, while continuum hypotheses are most naturally consistent with the idea that a construct varies continuously in a population.
In psychology, we have no way to decide conclusively whether two individuals are ‘equally depressed’.
This means we cannot form the equivalence classes necessary for measurement theory to operate.
The standard approach to dealing with this situation in psychology is
Critical thinking
Article: Eaton, Krueger, Docherty, and Sponheim (2013)
Toward a Model-Based Approach to the Clinical Assessment of Personality Psychopathology
This paper illustrates how new statistical methods can inform conceptualization of personality psychopathology and therefore its assessment.
Structural assumptions about personality variables are inextricably linked to personality assessment.
The nature of the personality assessment instrument reflect assumptions about the distributional characteristics of the construct of interest.
Historically, many assumptions about the distributions of data reflecting personality constructs resulted form expert opinion or theory.
Both ‘type’ theories and dimensional theories have been proposed.
Assessment instruments have reflected this bifurcation in conceptualization.
Because the structure of personality assessment is reflective of the underlying distributional assumptions of the personality constructs of interest, reliance solely on expert opinion about these distributions is potentially problematic.
It is critical for personality theory and assessment that underlying distributional assumptions of symptomatology be correct and justifiable.
Critical thinking
Chapter 4 of Understanding Psychology as a science by Dienes
Bayes and the probability of hypotheses
Objective probability: a long-run relative frequency.
Classic (Neyman-Pearson) statistics can tell you the long-run relative frequency of different types of errors.
An alternative approach to statistics is to start with what Bayesians say are people’s natural intuitions.
People want statistics to tell them the probability of their hypothesis being right.
Subjective probability: the subjective degree of conviction in a hypothesis.
Subjective or personal probability: the degree of conviction we have in a hypothesis.
Probabilities are in the mind, not in the world.
The initial problem to address in making use of subjective probabilities is how to assign a precise number to how probable you think a proposition is.
The initial personal probability that you assign to any theory is up to you.
Sometimes it is useful to express your personal convictions in terms of odds rather than probabilities.
Odds(theory is true) = probability(theory is true)/probability(theory is false)
Probability = odds/(odds +1)
These numbers we get from deep inside us must obey the axioms of probability.
This is the stipulation that ensures the way we change our personal probability in a theory is coherent and rational.
This is where the statistician comes in and forces us to be disciplined.
There are only a few axioms, each more-or-less self-evidently reasonable.
H is the hypothesis
D is the data
P(H and D) = P(D) x P(H|D)
P(H and D) = P(H) x P(D|H)
so
P(D) x P(H|D) = P(H) x P(D|H)
Moving P(D) to the other side
P(H|D) = P(D|H) x P(H) / P(D)
This last one is Bayes theorem.
It tells you how to go from one conditional probability to its inverse.
We can simplify this equation if we are interested in comparing the probability of different hypotheses given the same data D.
Then P(D) is just a constant for all these comparisons.
P(H|D) is proportional to P(D|H) x
.....read moreCritical thinking
Article: Dienes, Z, 2011
Bayesian Versus orthodox statistics: which side are you on?
doi: 10.1177/1745691611406920
The orthodox logic of statistics, starts from the assumption that probabilities are long-run relative frequencies.
A long-run relative frequency requires an indefinitely large series of events that constitutes the collective probability of some property (q) occurring is then the proportion of events in the collective with property q.
The logic of Neyman Pearson (orthodox) statistics is to adopt decision procedures with known long-term error rates and then control those errors at acceptable levels.
Thus, setting significance and power controls long-run error rates.
The probability of a theory being true given data can be symbolized as P(theory|data).
This is what orthodox statistics tell us.
One cannot infer one conditional probability just by knowing its inverse. (So P(data|theory) is unknown).
Bayesian statistics starts from the premise that we
.....read moreCritical thinking
Article: Borsboom, D. and Cramer, A, O, J. (2013)
Network Analysis: An Integrative Approach to the Structure of Psychopathology
doi: 10.1146/annurev-clinpsy-050212-185608
The current dominant paradigm of the disease model of psychopathology is problematic.
Current handling of psychopathology data is predicated on traditional psychometric approaches that are the technical mirror of of this paradigm.
In these approaches, observables (clinical symptoms) are explained by means of a small set of latent variables, just like symptoms are explained by disorders.
In this review, we argue that complex network approaches, which are currently being developed at the crossroads of various scientific fields, have the potential to provide a way of thinking about disorders that does justice to their complex organisation.
We know for certain that people suffer from symptoms and that these symptoms cluster in a non-arbitrary way.
For most psychopathological conditions, the symptoms are only empirically identifiable causes of distress.
In order for a disease model to hold, it should be possible to conceptually separate conditions from symptoms.
This isn’t possible for mental disorders.
As an important corollary, this means that disorders cannot be causes of these
Critical thinking
Article: Coyle, A (2015)
Introduction to qualitative psychological research
Introduction
This chapter examines the development of psychological interest in qualitative methods in historical context and point to the benefits that psychology gains from qualitative research.
It also looks at some important issues and developments in qualitative psychology.
At its most basic, qualitative psychological research may be regarded as involving the collection and analysis of non-numerical data through a psychological lens in order to provide rich descriptions and possibly explanations of peoples meaning-making, how they make sense of the world and how they experience particular events.
Qualitative research is bound up with particular sets of assumptions about the bases or possibilities of knowledge.
Epistemology: particular sets of assumptions about the bases or possibilities of knowledge.
Epistemology refers to a branch of philosophy that is concerned with the theory of knowledge and that tries to answer questions about how we can know what we know.
Ontology: the assumptions we make about the nature of being, existence or reality.
Different research approaches and methods are associated with different epistemologies.
The term ‘qualitative research’ covers a variety of methods with a range of epistemologies, resulting in a domain that is characterized by difference and tension.
The epistemology adopted by a particular study can be determined by a number of factors.
Whatever epistemological position is adopted in a study, it is usually desirable to ensure that you maintain this position consistently throughout the wire-up to help produce a coherent research report.
Positivism: holds that the relationship between the world and our sense perception of the world is straightforward. There is a direct correspondence between things in the world and our perception of them provided that our perception is not skewed by factors that might damage that correspondence.
So, it is possible to obtain accurate knowledge of things in the world, provided we can adopt an impartial, unbiased, objective viewpoint.
Empiricism: holds that our knowledge of the world must arise from the collection and categorization of our sense perceptions/observations of the world.
This categorization allows us to develop more complex knowledge
Critical thinking
Article: Gigerenzer, G. & Marewski, J, N. (2015)
Surrogate Science: The Idol of a Universal Method for Scientific Inference
doi: 10.1177/0149206314547522
Introduction
Scientific inference should not be made mechanically.
Good science requires both statistical tools and informed judgment about what model to construct, what hypotheses to test, and what tools to use.
This article is about the idol of a universal method of statistical inference.
In this article, we make three points:
The null ritual
The most prominent creation of a seemingly universal inference method is the null ritual:
Level of significance has three different meanings:
Three meanings of significance
The alpha level: the long-term relative frequency of mistakenly rejecting hypothesis H0 if it is true, also known as Type I error rate.
The beta level: the long-term frequency of mistakenly rejecting H1 if it is true.
Two statistical hypothesis need to be specified in order to be able to determine both alpha and beta.
Neyman and Pearson rejected a mere convention in favour of an alpha level that required a rational scheme.
This is a list of the important terms used in the articles of the fourth block of WSRt, with the subject alternative approaches to psychological research.
Equivalence classes: sets of individuals who are exchangeable with respect to the attribute of interest.
Taxometrics: by inspecting particular consequences of the model for specific statistical properties of (subsets of) items, such as the patterns of bivariate correlations expected to hold in the data
Latent trait models: posit the presence of one or more underlying continuous distributions.
Zones of rarity: locations along the dimension that are unoccupied by some individuals.
Discrimination: the measure of how strongly the item taps into the latent trait.
Quasi-continuous: the construct would be bounded at the low end by zero, a complete absence of the quality corresponding with the construct.
Latent class models: based on the supposition of a latent group (class) structure for a construct’s distribution.
Conditional independence: that inter-item correlations solely reflect class membership.
Hybrid models (of factor mixture models): combine the continuous aspects of latent trait models with the discrete aspects of latent class models.
EFMA: exploratory factor mixture analysis.
Objective probability: a long-run relative frequency.
Subjective probability: the subjective degree of conviction in a hypothesis.
The likelihood principle: the notion that all the information relevant to inference contained in data is provided by the likelihood.
Probability density distribution: the distribution of if the dependent variable can be assumed to vary continuously
Credibility interval: the Bayesian equivalent of a confidence interval
The Bayes factor: the Bayesian equivalent of null hypothesis testing
Flat prior or uniform prior: you have no idea what the population value is likely to be
This magazine contains all the summaries you need for the course WSRt at the second year of psychology at the Uva.
The three most important elements of Bayesian statistics are:
For more information about Bayesian statistics, check out my summary of the fourth block of WSRt
The Bayes factor (B) compares the probability of an experimental theory to the probability of the null hypothesis.
It gives the means of adjusting your odds in a continuous way.
For more information, look at the (free) summary of 'Bayes and the probability of hypotheses' or 'Bayesian versus orthodox statistics: which side are you one?'
Weaknesses of the Bayesian approach are:
For more information, look at the (free) summary of 'Bayesian versus orthodox statistics: which side are you on?'
At its most basic, qualitative psychological research can be seen as involving the collection and analysis of non-numerical data through a psychological lens in order to provide rich descriptions and possibly explanations of peoples meaning-making, how they make sense of the world and how they experience particular events.
For more information, look at the (free) summary of 'Introduction to qualitative psychological research'
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mistake kuqelis contributed on 20-06-2021 14:58
I think the part you mentioned about data and theory might be incorrect check this out:
The probability of a theory being true given data can be symbolized as P(theory | data), and that is what many of us would like to know. This is the inverse of P(data | theory), which is what orthodox statistics tells us.
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