Scientific & Statistical Reasoning – Summary interim exam 3 (UNIVERSITY OF AMSTERDAM)
Discovering statistics using IBM SPSS statistics by Andy Field, fifth edition – Summary chapter 6
Bias can be detrimental for the parameter estimates (1), standard errors and confidence intervals (2) and the test statistics and p-values (3). Outliers and violations of assumptions are forms of bias.
An outlier is a score very different from the rest of the data. They bias parameter estimates and have an impact on the error associated with that estimate. Outliers have a strong effect on the sum of squared errors and this biases the standard deviation.
There are several assumptions of the linear model:
- Additivity and linearity
The scores on the outcome variable are linearly related to any predictors. If there are multiple predictors, their combined effect is best described by adding them together. - Normality
The parameter estimates are influenced by a violation of normality and the residuals of the parameters should be normally distributed. It is normality for each level of the predictor variable that is relevant. Normality is also important for confidence intervals and for null hypothesis significance testing. - Homoscedasticity / homogeneity of variance Homoscedasticity / homogeneity of variance
This impacts the parameters and the null hypothesis significance testing. It means that the variance of the outcome variable should not change between levels of the predictor variable. Violation of this assumption leads to bias in the standard error. - Independence
This assumption means that the errors in the model are not related to each other. The data has to be independent.
The assumption of normality is mainly relevant in small samples. Outliers can be spotted using graphs (e.g. histograms or boxplots). Z-scores can also be used to find outliers.
The P-P plot can be used to look for normality of a distribution. It is the expected z-score of a score against the actual z-score. If the expected z-scores overlap with the actual z-scores, the data will be normally distributed. The Q-Q plot is like the P-P plot but it plots the quantiles of the data instead of every individual score.
Kurtosis and skewness are two measures of the shape of the distribution. Positive values of skewness indicate a lot of scores on the left side of th distribution. Negative values of skewness indicate a lot of scores on the right side of the distribution. The further the value is from zero, the more likely it is that the data is not normally distributed.
Normality can be checked by looking at the z-scores of the skewness and kurtosis. It uses the following formula:
Levene’s test is a one-way ANOVA on the deviation scores. The homogeneity of variance can be tested using Levene’s test or by evaluating a plot of the standardized predicted values against the standardized residuals.
REDUCING BIAS
There are four ways of correcting problems with the data:
- Trim the data
Delete a
Discovering statistics using IBM SPSS statistics by Andy Field, fifth edition – Summary chapter 8
Variance of a single variable represents the average amount that the data vary from the mean. The cross-product deviation multiplies the deviation for one variable by the corresponding deviation for the second variable. The average value of the cross-product deviation is the covariance. This is an averaged sum of combined deviation. It uses the following formula:
A positive covariance indicates that if one variable deviates from the mean, the other variable deviates in the same direction. A negative covariance indicates that if one variable deviates from the mean, the other variable deviates in the opposite direction.
Covariance is not standardized and depends on the scale of measurement. The standardized covariance is the correlation coefficient and is calculated using the following formula:
A correlation coefficient of values 0.1 represents a small effect. Values of 0.3 represent a medium effect and values of 0.5 represent a large effect.
In order to test the null hypothesis of the correlation, namely that the correlation is zero, z-scores can be used. In order to use the z-scores, the distribution must be normal, but the r-sampling distribution is not normal. The following formula adjusts r in order to make the sampling distribution normal:
The standard error uses the following formula:
This leads to the following formula for z:
The null hypothesis of correlations can also be tested using the t-score with degrees of freedom N-2:
The confidence intervals for the correlation uses the same formula as all the other confidence intervals. These values have to be converted back to a correlation efficient using the following formula:
CORRELATION
Normality in correlation is only important if the sample size is small (1), there is significance testing (2) or there is a confidence interval (3). The assumptions of correlation are normality (1) and linearity (2).
The correlation coefficient squared (R2) is a measure of the amount of variability in one variable that is shared by the other. Spearman’s correlation coefficient (rs) is a non-parametric statistic that is sued to minimize the effects of extreme scores or the effects of violations of the assumptions. Spearman’s correlation coefficient works best if the data is ranked. Kendall’s tau, denoted by τ, is a non-parametric statistic that is used when the data set is small with a large set of tied ranks.
A biserial or point-biserial correlation is used when a relationship between two variables is investigated when one of the two variables is dichotomous (e.g. yes
.....read moreDiscovering statistics using IBM SPSS statistics by Andy Field, fifth edition – Summary chapter 9
Any straight line can be defined by the slope (1) and the point at which the line crosses the vertical axis of the graph (intercept) (2). The general formula for the linear model is the following:
Regression analysis refers to fitting a linear model to data and using it to predict values of an outcome variable (dependent variable) from one or more predictor variables (independent variables). The residuals are the differences between what the model predicts and the actual outcome. The residual sum of squares is used to assess the ‘goodness-of-fit’ of the model on the data. The smaller the residual sum of squares, the better the fit.
Ordinary least squares regression refers to defining the regression models for which the sum of squared errors is the minimum it can be given the data. The sum of squared differences is the total sum of squares and represents how good the mean is as a model of the observed outcome scores. The model sum of squares represents how well the model can predict the data. The larger the model sum of squares, the better the model can predict the data. The residual sum of squares uses the differences between the observed data and the model and shows how much of the data the model cannot predict.
The proportion of improvement due to the model compared to using the mean as a predictor can be calculated using the following formula:
This value represents the amount of variance in the outcome explained by the model relative to how much variation there was to explain. The F-statistic can be calculated using the following formulas:
‘k’ represents the degrees of freedom and denotes the number of predictors.
The F-statistic can also be used t test the significance of with the null hypothesis being that is zero. It uses the following formula:
Individual predictors can be tested using the t-statistic.
BIAS IN LINEAR MODELS
An outlier is a case that differs substantially from the main trend in the data. Standardized residuals can be used to check which residuals are unusually large and can be viewed as an outlier. Standardized residuals are residuals converted to z-scores. Standardized residuals greater than 3.29 are considered an outlier (1), if more than 1% of the sample cases have a standardized residual of greater than 2.58, the level of error in the model may be unacceptable (2) and if more than 5% of the cases have standardized residuals with an absolute value greater than 1.96, the model may be a poor representation of the data (3).
The studentized residual is the unstandardized residual divided
.....read moreDiscovering statistics using IBM SPSS statistics by Andy Field, fifth edition – Summary chapter 11
Moderation refers to the combined effect of two or more predictor variables on an outcome. This is also known as an interaction effect. A moderator variable is one that affects the relationship between two others. It affects the strength or direction of the relationship between the variables.
The interaction effect indicates whether moderation has occurred. The predictor and the moderator must be included for the interaction term to be valid. If, in the linear model, the interaction effect is included, then the individual predictors represent the regression of the outcome on that predictor when the other predictor is zero.
The predictors are often transformed using grand mean centring. Centring refers to transforming a variable into deviations around a fixed point. This fixed point is typically the grand mean. Centring is important when the model contains an interaction effect, as it makes the bs for lower-order effects interpretable. It makes interpreting the main effects easier (lower-order effects) if the interaction effect is not significant.
The bs of individual predictors can be interpreted as the effect of that predictor at the mean value of the sample (1) and the average effect of the predictor across the range of scores for the other predictors (2) when the variables are centred.
In order to interpret a (significant) moderation effect, a simple slopes analysis needs to be conducted. It is comparing the relationship between the predictor and outcome at low and high levels of the moderator. SPSS gives a zone of significance. Between two values of the moderator the predictor does not significantly predict the outcome and below and above the values it does.
The steps for moderation are the following if there is a significant interaction effect: centre the predictor and moderator (1), create the interaction term (2), run a forced entry regression with the centred variables and the interaction of the two centred variables (3).
The simple slopes analysis gives three models. One model for a predictor when the moderator value is low (1), one model for a predictor when the moderator value is at the mean (2) and one model for a predictor when the moderator value is high (1).
If the interaction effect is significant, then the moderation effect is also significant.
MEDIATION
Mediation refers to a situation when the relationship between the predictor variable and an outcome variable can be explained by their relationship to a third variable, the mediator. Mediation can be tested through three linear models:
- A linear model predicting the outcome from the predictor variable (c).
- A linear model predicting the mediator from the predictor variable (a).
- A linear model predicting the outcome from both the predictor variable and the mediator (predictor = c’ and mediator = b).
There are four conditions for mediation: the predictor variable must significantly predict the outcome variable (in model 1)(1), the predictor variable must significantly predict the mediator
.....read moreFoster (2010). Causal inference and developmental psychology.” – Article summary
The problem of causality is difficult in developmental psychology, as many questions of that field regard factors that a person cannot be randomly assigned to (e.g. single parent family). Causal inference refers to the study and measurement of cause-and-effect relationships outside of random assignment.
In the current situation in developmental psychology, it is unclear among researchers whether causality can be implied and why. Causal inferences are necessary for the goals of developmental psychology because causal inferences can improve the lives of people (1), can help distinguish between associations and causal claims for laypeople (2) and causal thinking is unavoidable (3).
The directed acyclic graph (DAG) is a tool which is useful in moving from associations to causal relationships. It is particularly useful in identifying covariates and understanding the anticipated consequences of incorporating these variables.
The DAG is a symbolic representation of dependencies among variables. The causal Markov assumption states that the absence of a path (in the DAG) implies the absence of a relationship. In the DAG, models that represent data with fewer links are preferred to the more complex (parsimony). If two variables are simultaneously determined, the DAG could incorporate this possibility by treating the two as reflecting a common cause.
Variables (in the DAG) can be related in three ways:
- Z is a common cause of X and Y
In this case, Z needs to be controlled for. - Z is a common effect of X and Y
This is a collider. Conditioning on a collider creates a spurious relationship between X and Y. This relationship can suppress or inflate a true causal effect. - Z mediates the effect of X on Y
“Pearl (2018). Confounding and deconfounding: Or, slaying the lurking variable.” - Article summary
Confounding bias occurs when a variable influences both who is selected for the treatment and the outcome of the experiment. If a possible confounding variable is known, it is possible to control for the possible confounding variable. Researchers tend to control for all possible variables, which leaves the possibility of controlling for the thing you are trying to measure (e.g. controlling for mediators).
Confounding needs a causal solution, not a statistical one and causal diagrams provide a complete and systematic way of finding that solution. If all the confounders are controlled for, a causal claim can be made. However, it is not always sure whether all confounders are controlled for.
Randomization has two clear benefits. It eliminates confounder bias and it enables the researcher to quantify his uncertainty. Randomization eliminates confounders without introducing new confounders. In a non-randomized study, confounders must be eliminated by controlling for them, although it is not always possible to know all the possible confounders.
It is not always possible to conduct a randomized controlled experiment because of ethical, practical or other constraints. Causal estimates of observational studies can provide with provisional causality. This is causality contingent upon the set of assumptions that the causal diagram advertises.
Confounding stands for the discrepancy between what we want to assess (the causal effect) and what we actually do assess using statistical methods. A mediator is the variable that explains the causal effect of X on Y (X>Z>Y). If you control for a mediator, you will conclude that there is no causal link, when there is.
There are several rules for controlling for possible confounders:
- In a chain junction (A -> B -> C), controlling for B prevents information from A getting to C and vice versa.
- In a fork or confounding junction (A <- B -> C), controlling for B prevents information from A getting to C and vice versa.
- In a collider (A -> B <- C), controlling for B will allow information from A getting to C and vice versa.
- Controlling for a mediator partially closes the stream of information. Controlling for a descendant of a collider partially opens the stream of information.
A variable that is associated with both X and Y is not necessarily a confounder.
“Shadish (2008). Critical thinking in quasi-experimentation.” - Article summary
A common element in all experiments is the deliberate manipulation of an assumed cause followed by an observation of the effects that follow. A quasi-experiment is an experiment that does not uses random assignment of participants to conditions.
An inus condition is an insufficient but non-redundant part of an unnecessary but sufficient condition. It is insufficient, because in itself it cannot be the cause, but it is also non-redundant as it adds something that is unique to the cause. It is an insufficient cause.
Most causal relationships are non-deterministic. They do not guarantee that an effect occur, as most causes are inus conditions, but they increase the probability that an effect will occur. To different degrees, all causal relationships are contextually dependent.
A counterfactual is something that is contrary to fact. An effect is the difference between what did happen and what would have happened. The counterfactual cannot be observed. Researchers try to approximate the counterfactual, but it is impossible to truly observe it.
Two central tasks of experimental design are creating a high-quality but imperfect source of counterfactual and understanding how this source differs from the experimental condition.
Creating a good source of counterfactual is problematic in quasi-experiments. There are two tools to attempt this:
- Observe the same unit over time
- Make the non-random control groups as similar as possible to the treatment group
A causal relationship exists if the cause preceded the effect (1), the cause was related to the effect (2) and there is no plausible alternative explanation for the effect other than the cause (3). Although quasi-experiments are flawed compared to experimental studies, they improve on correlational studies in two ways:
- Quasi-experiments make sure the cause precedes the effect by first manipulating the presumed cause and then observing an outcome afterwards.
- Quasi-experiments allows to control for some third-variable explanations.
Campbell’s threats to valid causal inference contains a list of common group differences in a general system of threats to valid causal inference:
- History
Events occurring concurrently with treatment could cause worse performance. - Maturation
Naturally occurring changes over time, not too be confused with treatment effects. - Selection
Systematic differences over conditions in respondent characteristics. - Attrition
A loss of participants can produce artificial effects if that loss is systematically correlated with conditions. - Instrumentation
The instruments of measurement might differ or change over time. - Testing
Exposure to a test can affect subsequent scores on a test. - Regression to the mean
An extreme observation will be less extreme on the second observation.
Two flaws of falsification are that it requires a causal claim to be clear, complete and agreed upon in all its details and it requires observational procedures to perfectly reflect the theory that is being tested.
“Kievit et al. (2013). Simpson’s paradox in psychological science: A practical guide.” - Article summary
Simpson’s paradox states that the direction of an association at the population-level may be reversed within subgroups of that population. Inadequate attention to the Simpson’s paradox may lead to faulty inferences. The Simpson’s paradox can arise because of differences in proportions on subgroup levels compared to population levels. It also states that a pattern (association) does not need to hold within a subgroup.
The paradox is related to a lot of things, including causal inference. A generalized conclusion (e.g. extraversion causes party-going) might hold for the general population, but does not mean that this inference can be drawn at the individual level. A correlation across the population does not need to hold in an individual over time.
In order to deal with Simpson’s paradox, the situations in which the paradox occurs frequently have to be assessed. There are several steps in preventing Simpson’s paradox:
- Consider when it occurs.
- Explicitly propose a mechanism, determining at which level it is presumed to operate.
- Assess whether the explanatory level of data collection aligns with the explanatory level of the proposed mechanism.
- Conduct an experiment to assess the association between variables.
In the absence of strong top-down knowledge, people are more likely to make false inferences based on Simpson’s paradox.
Dienes (2008). Understanding psychology as a science.” – Article summary
A falsifier of a theory is any potential observation statement that would contradict the theory. There are different degrees of falsifiability, as some theories require fewer data points to be falsified than others. In other words, simple theories should be preferred as these theories require fewer data points to be falsified. The greater the universality a theory, the more falsifiable it is.
A computational model is a computer simulation of a subject. It has free parameters, numbers that have to be set (e.g. number of neurons used in a computational model of neurons). When using computational models, more than one model will be able to fit the actual data. However, the most falsifiable model that has not been falsified by the data (fits the data) should be used.
A theory should only be revised or changed to make it more falsifiable. Making it less falsifiable is ad hoc. Any revision or amendment to the theory should also be falsifiable. Falsifia
Standard statistics are useful in determining probabilities based on the objective probabilities, the long-run relative frequency. This does not, however, give the probability of a hypothesis being correct.
Subjective probability refers to the subjective degree of conviction in a hypothesis. The subjective probability is based on a person’s state of mind. Subjective probabilities need to follow the axioms of probability.
Bayes’ theorem is a method of getting from one conditional probability (e.g. P(A|B)) to the inverse. The subjective probability of a hypothesis is called the prior. The posterior is how probable the hypothesis is to you after data collection. The probability of obtaining the data given the hypothesis is called the likelihood (e.g. P(D|H). The posterior is proportional to the likelihood times the prior. Bayesian statistics is updating the personal conviction in light of new data.
The likelihood principle states that all the information relevant to inference contained in data is provided by the likelihood. A hypothesis having the highest likelihood does not mean that it has the highest probability. A hypothesis having the highest likelihood means that the data support the hypothesis the most. The posterior probability is not reliant on the likelihood.
The probability distribution of a continuous variable is called the probability density distribution. It has this name, as a continuous variable has infinite possibilities and probabilities in this distribution gives the probability of any interval.
A likelihood could be a probability or a probability density and it can also be proportional to a probability or a probability density. Likelihoods provide a continuous graded measure of support for different hypotheses.
In Bayesian statistics (likelihood analysis), the data is fixed but the hypothesis can vary. In significance testing, the hypothesis is fixed (null hypothesis) but the data can vary. The height of the curve of the distribution for each hypothesis is relevant in calculating the likelihood. In significance testing, the tail area of
.....read more“Marewski & Olsson (2009). Formal modelling of psychological processes.” - Article summary
One way of avoiding the null hypothesis testing ritual in science is to increase the precision of theories by casting them as formal models. Rituals can be characterized by a repetition of the same action (1), fixations on special features (2), anxieties about punishment for rule violation (3) and wishful thinking (4). The null hypothesis testing ritual is mainly maintained because many psychological theories are too weak to make precise predictions besides the direction of the effect.
A model is a simplified representation of the world that aims to explain observed data. It specifies a theory’s predictions. Modelling is especially suited for basic and applied research about the cognitive system. There are four advantages of formally specifying the theories as models:
- Designing strong tests of theories
Modelling theories leads to being able to make quantitative predictions about a theory, which then leads to comparable, competing predictions between theories which allows for comparison and testing of theories. - Sharpening research questions
Null hypothesis testing allows for vague descriptions of theories and specifying the theories as models requires more precise research questions. These vague descriptions make theories difficult to test and sharpening the research questions makes it easier to test the theories. - Going beyond linear theories
Null hypothesis testing is especially applicable to simple hypotheses. The statistical tools available are used to create theories, mostly linear theories and by specifying the theory as a model, this is not necessary anymore. - Using more externally valid designs to study real-world questions
Modelling can lead to more externally valid designs, as confounds are not eliminated in the analysis, but built into the model.
Goodness-of-fit measures cannot make the distinction between variation in the data as a result of noise or as a result of the psychological process of interest. A model can end up overfitting the data, capturing the variance of the psychological process of interest and variance as a result of random error. The ability of a model to predict new data is the generalizability. The complexity of a model refers to a model’s inherent flexibility that enables to fit diverse patterns of data. The complexity of a model is related to the degree to which a model is susceptible to overfitting. The number of free parameters (1) and how parameters are combined in the model (2) contribute to the model’s complexity.
Increased complexity makes a model more likely to overfit while the generalizability to new data decreases. Increased complexity can also lead to better generalizability of the data, but only if the model is complex enough and not too complex. A good fit to current data does not predict a good fit to other data.
The irrelevant specification problem refers to the difficulty bridging the gap between description of theories and formal implementations. This can lead to unintended discrepancies between theories and their formal counterparts. The Bonari paradox refers to when models become more complex and
.....read more“Dennis & Kintsch (2008). Evaluating theories.” - Article summary
A theory is a concise statement about how we believe the world to be. There are several things to look at when evaluating theories:
1. Descriptive adequacy
Does the theory accord with the available data?
2. Precision and interpretability
Is the theory described in a sufficiently precise fashion that it is easy to interpret?
3. Coherence and consistency
Are there logical flaws in the theory? Is it consistent with theories of other domains?
4. Prediction and falsifiability
Can the theory be falsified?
5. Postdiction and explanation
Does the theory provide a genuine explanation of existing results?
6. Parsimony
Is the theory as simple as possible?
7. Originality
Is the theory new or a restatement of an old theory?
8. Breadth
Does the theory apply to a broad range of phenomena?
9. Usability
Does the theory have applied implications?
10. Rationality
Are the claims of the theory reasonable?
Postdiction refers to predictions under controlled conditions.
"Furr & Bacharach (2014). Estimating and evaluating convergent and discriminant validity evidence.” - Article summary
There are four procedures to present the implications of a correlation in terms of our ability to use the correlations to make successful predictions:
- Binomial effect size display (dichotomous)
This illustrates the practical consequences of using correlations to make decisions. It can show how many successful and unsuccessful predictions can be made on the basis of a correlation. It uses the following formula:
- Binomial effect size display can be used to translate a validity correlation into an intuitive framework. However, it frames the situation in terms of an ‘equal proportions’ situation.
- Taylor-Russell tables (dichotomous)
These tables inform selection decisions and provide a probability that a prediction will result in a successful performance on a criterion. The size of the validity coefficient (1), selection proportion (2) and the base rate (3) are required for the tables. - Utility analysis
This frames validity in terms of a cost-benefit analysis of test use. - Analysis of test sensitivity and test specificity
A test is evaluated in terms of its ability to produce correct identifications of a categorical difference. This is useful for tests that are designed to detect a categorical difference.
Validity correlations can be evaluated in the context of a particular area of research or application.
A nomological network refers to the interconnections between a construct and other related construct. There are several methods to evaluate the degree to which measures show convergent and discriminate associations:
- Focusses associations
This method focusses on a few highly relevant criterion variables. This can make use of validity generalization. - Sets of correlations
This method focusses on a broad range of criterion variables and computes the correlations between the test and many criterion variables. The degree to which the pattern of correlations ‘makes sense’ given the conceptual meaning of the construct is evaluated. - Multitrait-multimethod matrices
This method obtains measures of several traits, each measured through several methods. The purpose is to set clear guidelines for evaluating convergent and discriminant validity evidence. This is done by evaluating trait variance and method variance. Evidence of convergent validity is represented by monotrait-heteromethod correlations.
The correlations between measures are called validity coefficients. Validity generalization is a process of evaluating a test’s validity coefficients across a large set of studies. Validity generalization studies are intended to evaluate the predictive utility of test’s scores across a range of settings, times and situations. These studies can reveal the general level of predictive validity (1), reveal the degree of variability among the smaller individual studies (2) and it can reveal the source of the variability among studies (3).
| Method used to measure the two constructs | |
“Furr & Bacharach (2014). Estimating practical effects: Binomial effect size display, Taylor-Russell tables, utility analysis and sensitivity / specificity.” – Article summary
Validity refers to the degree to which evidence and theory support the interpretations of test scores entailed by the proposed uses (e.g. to what degree does it measure what it is supposed to measure). Items of a test itself cannot be valid or invalid, only the interpretations can be valid or invalid.
Validity is a property of the interpretation (1), it is a matter of degree (2) and the validity of a test’s interpretation is based on evidence and theory (3). Validity influences the accuracy of our understanding of the world, as research conclusions are based on the validity of a measure.
Construct validity refers to the degree to which test scores can be interpreted as reflecting a particular psychological construct. Face validity refers to the degree to which a measure appears to be related to a specific construct, in the judgement of nonexperts, test takers and representatives of the legal system. Convergent validity refers to the degree to which test scores are correlated with tests of related constructs.
Validity is important for the accuracy of our understanding of the world (1), decisions on societal level (e.g. laws based on ‘invalid’ research) and decisions on individual level (3) (e.g. college admissions).
The validity of test score interpretation depends on five types of evidence: test content (1), consequences of use (2), association with other variables (3), response processes (4) and internal structure (5).
Test content can be seen as content validity. There are two threats to content validity:
- A test including construct-irrelevant content
The inclusion of content that is not relevant to the construct of interest reduces validity. - Construct underrepresentation
A test should include the full range of content that is relevant to the construct.
Construct underrepresentation can be constrained by practical issues (e.g. time of a test). The internal structure of a test refers to the way the parts of a test are related to each other. There should be a proper match between the actual internal structure of a test and the internal structure a test should have. The internal structure can be examined through the correlations among items in the test and among the subscales in the test. This can be done using factor analysis.
Factor analysis helps to clarify the number of factors within a set of items (1), reveals the associations among the factors within a multidimensional test (2) and identifies which items are linked to which factors (3). Factors are dimensions of the test.
Response processes refers to the match between the psychological processes that respondents actually use when completing a measure and the processes that they should use.
In order to assess validity, the association with other variables (e.g. happiness and self-esteem) should be assessed. If a positive relationship is to be expected between two variables, then, in order for the interpretation of a measure to be valid, this relationship needs to exist. The association with other variables involves the match between a measure’s actual associations with other measures
.....read more“Furr & Bacharach (2014). Scaling.” - Article summary
Scaling refers to assigning numerical values to psychological attributes. Individuals in a group should be similar to each other in the regard of sharing a psychological feature. There are rules to follow in order to put people in categories:
- People in a category must be identical with respect to the feature that categorizes the group (e.g. hair colour).
- The groups must be mutually exclusive
- The groups must be exhaustive (e.g. everyone in the population can fall into a category).
Each person should fall into one category and not more than one. If numerals are used to indicate order, then the numerals serve as labels indicating rank. If numerals have the property of quantity, then they convey information about the exact amounts of an attribute. Units of measurement are standardized quantities. The three levels of groups are identity (1), order (2) and quantity (3).
There are two possible meanings of the number zero. It can be the absolute zero (1) (e.g. a reaction time of 0ms) or it can be an arbitrary quantity of an attribute (2). This is called the arbitrary zero. The arbitrary zero does not represent the absence of anything, rather, it is a point on a scale to measure that feature. A lot of psychological attributes use the arbitrary zero (e.g. social skill, self-esteem, intelligence).
An unit of measurement might be arbitrary because unit size may be arbitrary (1), some units of measurement are not tied to any one type of object (2) (e.g. centimetres can measure anything with a spatial property) and some units of measurement can be used to measure different features of the same object (3) (e.g. weight and length).
One assumption of counting is additivity. This requires that unit size does not change. This would mean that an increase of one point is equal at every point. This is not always the case, as an IQ test asks increasingly difficult questions to increase one point of IQ. Therefore, the unit size changes.
Counting only qualifies as measurement if it reflects the amount of some feature or attribute of an object. There are four scales of measurement:
- Nominal scale
This is used to identify groups of people who share a common attribute that is not shared by people in other groups (e.g. ‘0’ for male and ‘1’ for female). It assesses the principle of identity. - Ordinal scale
This is used to rank people according to some attribute. It is used to make rankings within groups and cannot be used to make comparisons between groups, as this would require quantity. It assesses the principle of identity and order. - Interval scale
This is a scale that is used to represent quantitative difference between people. It assesses the principle of identity, order and quantity. - Ratio scales
This is a scale that has an absolute zero point. It satisfies the principle of identity, order, quantity and has an absolute zero.
Psychological attributes might not be able to be put
.....read more“Mitchell & Tetlock (2017). Popularity as a poor proxy for utility.” - Article summary
Before the existence of the IAT, indirect measures of prejudice were developed in order to overcome response bias and psychologists began to examine automatic processes that may contribute to contemporary forms of prejudice. After the existence of the IAT, implicit prejudice became the same thing as widespread unconscious prejudices that are more difficult to spot and regularly infect intergroup interactions.
The IAT has been used throughout different areas of society and is a very popular mean of describing implicit prejudice. Prejudice extends beyond negative or positive associations with an attitude object to include motivational and affective reactions to in-group and out-group members. IAT does not have a strong predictive validity. The IAT score is a poor predictor of discriminating behaviour.
There are no guidelines for how to interpret the scores on the IAT. This is referred to as the score interpretation problem. The test scores are dependent on arbitrary thresholds and it is not possible to link them to behaviour outcomes.
The focus of the IAT on implicit gender stereotypes is (not implicit sexism) is problematic because implicit measures of gender stereotypes are not a good predictor of discriminatory behaviour (1), only a very limited set of implicit gender stereotypes has been examined (2) and no explanation is provided about how conflicts between automatic evaluative associations and automatic semantic associations are resolved (3).
Individuating information, getting personal information about a certain group, exerts effects to counter explicit biases. It does the same with regard to implicit biases.
Subjective evaluation criteria are not associated with discrimination. Therefore, the solution that only objective measures must be used in decision making to counter (implicit) bias is unnecessary. This is referred to as the subjective judgement problem.
“LeBel & Peters (2011). Fearing the future of empirical psychology: Bem’s (2011) evidence of psi as a case study of deficiencies in modal research practice.” - Article summary
Psi refers to the anomalous retroactive influence of future events on an individual’s current behaviour. There are three important deficiencies in modal research practice: an overemphasis on conceptual replication (1), insufficient attention to verifying the integrity of measurement instruments and experimental procedures (2) problems with the implementation of null hypothesis testing (3).
The interpretation bias refers to a bias towards interpretations of data that favour a researcher’s theory. A potential consequence of this is an increased risk of reported false positives and a disregard of true negatives. The knowledge system of psychology consists of theory relevant beliefs (1), this is about the mechanisms that produce behaviour and method-relevant beliefs (2), this is about the procedures through which data is obtained.
Deficiencies in modal research practice bias systematically bias the interpretation of confirmatory data as theory relevant (1) and the interpretation of disconfirmatory data as method relevant (2).
Central beliefs are beliefs on which many other beliefs depend. Conservatism refers to choosing the theoretical explanation consistent with the data that requires the least amount of restructuring of the existing knowledge system.
If method-relevant beliefs are central in a knowledge system, it becomes more difficult to blame methodology related errors for disconfirmatory results. If theory-relevant beliefs become central, it poses the threat of becoming a logical assumption. A hypothesis under test should be described in a way that is falsifiable and not logically necessary.
An overemphasis on conceptual replication at the expense of direct replication weakens method-relevant beliefs in the knowledge system. A statistical significant result is often followed by a conceptual replication. A failure of the conceptual replication leads to the question whether the negative result was due to the falsity of the underlying theory or to methodological flaws introduced by changes in conceptual replication.
The failure to verify the integrity of measurement instruments and experimental procedures weakens method-relevant beliefs and leads to ambiguity in the interpretation of results. The null hypothesis can be viewed as a straw man, as two identical populations are almost not possible. Basing theory choices on null hypothesis significance tests detaches theories from the broader knowledge system.
In order to overcome the flaws of the modal research practice, method-relevant beliefs must be strengthened. There are three ways in order to do this:
- Stronger emphasis on direct replication
A direct replication leads to greater confidence in the results. They are necessary to ensure that an effect is real. - Verify integrity of methodological procedures
Method-relevant beliefs are more difficult to reject if the integrity of methodological procedures are verified and this leads to a less ambiguous interpretation of results. This includes routinely checking the internal consistency of the scores of any measurement instrument that is used. This includes the use of objective markers of instruction comprehension. - Use stronger forms of NHST
The null hypothesis should be a theoretically derived point value of the focal variable, instead
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