In the reflective model, the attribute is seen as the common cause of observed scores (e.g. depression causes people feeling sad). In the formative model, observed scores define or determine the attribute (e.g. depression occurs when people feel sad a lot). Reflective models are presented as measurement models. A latent variable is introduced to account for the covariance between other variables. In the reflective model, variables are regarded as exchangeable save for measurement parameters (e.g. reliability) and correlations between the variables are spurious in the reflective model. The correlation only exists because variables are related and might be the same thing. Formative models differ from reflective models because the variables are not exchangeable. This is because variables are hypothesised to capture different aspects of the same construct. There is also no assumption about whether the variables should correlate.There are three problems with the conceptualization of reflective and formative models:TimeIn reflective and formative models, time is not explicitly represented. The precedence criteria for causal relationships is not taken into account. Inability to articulate processesThe processes of causal mechanisms cannot be described and tested using these models.Relations between observablesCausal relationships between observable variables are neglected in these models as the models do not account for these relationships, although it is likely that there is a causal relationship between at least some observable variables.The network model states that observable variables of latent variables should be seen as autonomous causal entities in a network of dynamical systems. ...

The danger of using a dichotomous system when it comes to mental disorders is not treating people who require treatment or treating people who do not require treatment. It is unclear where the boundary between disorder and no disorder is and this is not progressive for science and research as a whole. Equivalence classes refers to sets of individuals who are exchangeable with respect to the attribute of interest. Measurement starts with categorization. The continuity hypothesis states that in between any two positions lies a third that can be empirically confirmed (1) and that there are no gaps in the continuum (2). In a continuous interpretation, the distinction between people that have a disorder and do not have a disorder depends on the imposition of a cut-off score that does not reflect a gap in the inherent attribute itself (e.g. difference between average length and being tall). However, there is no way of measuring how depressed someone is (i.e. there is no scale). Local independence states that given a specific level of a latent variable, the observed variables are uncorrelated (e.g. guilt and suicide ideation is uncorrelated in healthy individuals). The form of the latent structure can be assessed by inspecting particular consequences of the model for specific statistical properties of items (1) and on the basis of the global fit measures that allow one to compare whether a model with a categorical latent structure fits better than a model with a continuous latent structure on the observed data.(2). Taxometrics refers to inspecting particular consequences of the model for specific statistical properties of items. If an underlying construct is continuous, then the covariance between any two observed variables should be the same regardless of the exact range. This analysis can be done by choosing a variable and denoting it as the index variable. In other words, the covariance between A and B should be the same on different levels of...

Non-parametric tests can be used when the assumptions of the regular statistical tests have been violated. Non-parametric tests use fewer assumptions and are robust. A non-parametric test has less power than parametric tests if the sampling distribution is normally distributed.Ranking the data refers to giving the lowest score the rank of 1, the next highest score a rank of 2 and so on. This eliminates the effect of outliers. It does neglect the difference in magnitude between the scores. If there are two scores that are the same, there are tied ranks. These scores are ranked by the value of the average potential rank for those scores (e.g. rank 3 and 4 will become rank 3.5). There are several alternatives to the four most used non-parametric tests:Kolmogorov-Smirnov ZIt tests whether two groups have been drawn from the same population. It has more power than the Mann-Whitney test when the sample sizes are less than 25 per group.Moses Extreme ReactionIt tests the variability of scores across the two groups and is a non-parametric form of the Levene’s test.Wald-Wolfowitz runsIt looks at clusters of scores in order to determine whether the groups differ. If there is no difference, the ranks should be randomly interspersed.Sign testIt does the same as the Wilcoxon-signed rank test but it is only based on the direction of the difference. The magnitude of change is neglected. It lacks power unless the sample size is really small.McNemar’s testIt uses nominal, rather than ordinal data. It is useful when looking for changes in people’s scores. It compares the number of people who changed their response in one direction to those who changed in the opposite direction. Marginal homogeneityIt is an extension of McNemar’s test and is similar to the Wilcoxon test.Friedman’s 2-way ANOVA by ranks (k samples)It is a non-parametric ANOVA to compare two groups but has low power compared to the Wilcoxon signed-rank test.Median testIt assesses...

Probabilities are long-run relative frequencies for the collective, rather than an individual. Probabilities do not apply to theories, as individual theories are not collectives. Therefore, the null hypothesis cannot be assigned a probability. A p-value does not indicate the probability of the null hypothesis being true. Power or a p-value is not necessary in Bayesian statistics, as a degree of plausibility can be assigned to theories and the data tells us how to adjust these plausibilities. It is only needed to determine a factor by which we should change the probability of different theories given the data. The probability of a hypothesis being true is the prior probability (P(H)). The probability of a hypothesis given the data is the posterior probability (P(H|D)). The probability of obtaining the exact data given the hypothesis is the likelihood (P(D|H)). Therefore, the posterior probability is the likelihood times the prior probability. The likelihood principle states that all information relevant to inference contained in data is provided by the likelihood. In a distribution, the p-value is the area under the curve at a certain point. The likelihood is the height of the distribution at a certain point. The p-value is influenced by the stopping rule (1), whether or not the test is post-hoc (2) and how many other tests have been conducted (3). These things do not influence the likelihood. The Bayes factor is the ratio of the likelihoods. The Bayes factor is driven to 0 if the null hypothesis is true, whereas the p-values fluctuate randomly if the null hypothesis is true and data-collection continues. The Bayes factor is slowly driven towards the ‘truth’. Therefore, the Bayes factor gives a notion of sensitivity. It distinguishes evidence that there is no relevant effect from no evidence of a relevant effect. It can be used to determine the practical significance of an effect. Adjusting conclusions according to when the hypothesis was...

Good science requires statistical tools and informed judgement about what model to construct, what hypotheses to test and what tools to use. There is no universal method of scientific inference, but, rather, a toolbox of useful scientific methods. Besides that, the danger of Bayesian statistics is that this will become a new universal method of statistics. Lastly, statistical methods are not simply applied to a discipline, they change the discipline itself.In natural sciences, the probabilistic revolution shaped theorizing. In social sciences, it led to scientists mechanizing scientists’ inferences. Inference revolution refers to the idea that inference from sample to population was considered the most important part of research. This revolution led to a dismissive attitude towards replication. There are three meanings of significance:Mere conventionThis means that it is convenient for researchers to use 5% as a standard level of significance. Alpha levelThis means that significance refers to the long-term relative frequency of making a type-I error. Exact level of significanceThis is the exact level of significance and is used in null hypothesis testing using a nil and not a null of zero difference. There are three interpretations of probability:A relative frequencyThis is a long-term relative frequency.PropensityThis is the physical design of an object (e.g. dice) Reasonable degree of subjective beliefThis is the degree an individual believes in somethings.Bayesian statistics should not be used in an automatic way, like frequentism. Objections to the use of Bayes rule are that frequency-based prior probabilities do not exist (1), that the set of hypotheses needed for the prior probability distribution is not known (2) and that researchers’ introspection does not confirm the calculation of probabilities (3).Fishing expeditions refers to the idea that hypothesis finding is the same as hypothesis testing, characterised by...