Showing posts with label bias. Show all posts
Showing posts with label bias. Show all posts

Sunday, July 20, 2014

A crisis in cultural psychology? Lack of replications, bias & publication pressures


Social psychology is facing an existential crisis. Ype Poortinga and I took the opportunity to examine how cross-cultural psychology fares in comparison. What is the background? A collective drive for presenting novel, sexy and sensational findings has propelled social psychology into a minefield of public mistrust and claims of being a pseudoscience. The list of sins in the eyes of the public are long: Central methods at the core of the discipline such as priming have been challenged, the drive to find significant differences has led to a neglect of the meaningfulness of psychological findings, publication pressures opened the doors for unscientific data massaging and most notoriously, glamorous stars of the discipline have been found to fabricate their data. There has rarely been a month since the now infamous Staples affair, when the field was not in the spotlight of public and internal scrutiny. This series of events has led to some agonizing soul-searching among psychologists.

Addressing methodological vulnerabilities in research on behavior and culture


Ype Poortinga and myself used the opportunity of the 22nd International conference of Cross-Cultural Psychology (organized by IACCP) to critically examine how cross-cultural psychology as a sister discipline of social psychology is faring. We assembled an A-list of leading cross-cultural psychologists and former editors of the flagship journal for research on culture and psychology (Journal of Cross-Cultural Psychology). Our instructions were simple: we requested them to critically evaluate the methods of our field and comment on ways how our field may move forward. Ype and I also provided a summary of our own concerns about the state of the field. The session was exceptionally well attended and the panel managed to create a lively debate and exchange of views with each other and the audience. This was particularly remarkable given the technical challenges, the double booking of the room and the incredible heat, lack of seats and oxygen in the late afternoon (it felt like a 2 hour sauna session). I have received quite a few requests for our slides, so I am summarizing some key points from our introductory presentation, the talks by Peter Smith, Johnny Fontaine and David Matsumoto as well as discussion that followed the presentations. I will also outline some ideas of the next steps that we are considering taking.



Poortinga and Fischer: Why questionable null-hypotheses and convergent search for evidence erode research on behavior and culture


Null hypothesis significance testing is the modus operandi for conducting research in psychology overall. At the same time, it has come under increasing pressure and scrutiny. Some quotes from some recent papers illustrate the various problems with the state of psychology:


Ioannides (2005): “[A] research finding is less likely to be true when … when effect sizes are smaller; when there is … lesser preselection of tested relationships; … greater flexibility in designs, definitions, outcomes, and analytical modes; … and when more teams are involved in a scientific field in chase of statistical significance”
Vul et al. (2009) report on “voodoo correlations” in fMRI: “We show how … nonindependent analysis [of voxels] inflates correlations while yielding reassuring-looking scattergrams”
Simmons et al. (2011) on “false-positive psychology”: “… flexibility in data collection, analysis, and reporting dramatically increases actual false-positive rates. In many cases, a researcher is more likely to falsely find evidence that an effect exists than to correctly find evidence that it does not”.



The application of the experimental research paradigm with an emphasis on null-hypothesis significance testing is particular problematic in cross-cultural psychology, because some of the basic assumptions of experimental design are violated by default:

a) There is no random assignment of respondents to conditions and

b) The experimenter has little control over conditions and ambient events.




This figure shows these problems in a nice way and clearly highlights that cross-cultural studies do not even meet the conditions for good quasi-experimental designs and have significant
shortcomings. 

Further challenging current experimental practices, Simmons, Nelson and Simonsohn (2011) eloquently exposed the problems of researcher degrees of freedom and the impact of quite innocent appearing research practices on significance levels. They demonstrated how a logically impossible hypothesis (listening to songs about age will decrease the age of listeners) can be empirically supported. Applied to the topic of their investigation, they discovered the psychological equivalent of the proverbial fountain of youth by using questionable research practices. The following figure shows the outcomes of their simulation study and the impact of four researcher degrees of freedom on significance levels. We highlighted the relevance of these conditions for cross-cultural research. 



First, assuming per definition that culture is a shared meaning system, any two cultural variables will be correlated to a significant degree. The very nature of the phenomena under investigation makes finding significant differences more likely. This non-independence is well recognized and the negative impact on significance testing is well recognized in methods circles but not well-understood in general cross-cultural research circles.

Second, a researcher may add 10 more observations or cases to the study if a first examination did not reveal any significant differences. This is probably a more common practice in cultural priming studies, but may be less of an issue in comparative survey studies.

The third questionable practice is controlling for third variables, especially if their impact is not theoretical grounded. In their case study, Simmons et al. used gender as an example, but in cross-cultural psychology it is often GDP at the country level or some demographic variables at the individual level that is entered as a covariate. This is a double-bind of cross-cultural psychology, on one hand we need to control for other variables that may explain any differences between samples, on the other hand, these simulations demonstrated that such practices have a sizable impact on significance levels.

The last questionable practice is to drop (or not) one of the conditions. The equivalent in cross-cultural psychology is to omit samples that may not fit the expected pattern (outlier removal). Talking to other researchers, this seems a common practice.

These individual practices individually increase the likelihood of finding significant results only in a relatively minor way, but the combination of these practices will lead to substantively inflated ratios of significance results: a significant result at the magical .05 significance level is 60% more likely if you combine all four of these questionable practices! Based on conversations with colleagues and observations of publication trends, these practices are common in cross-cultural psychology. This now means that we probably need to question a good number of empirical findings published!

A further issue is that the null hypothesis of no difference is likely to be rejected if there is a difference on any third variable that is related to the dependent variable. In such instances, there is a high rate of Type 1 errors (false positive results). One pressing issue is method bias. In questionnaire studies, response biases such as acquiescence or yes-saying are particularly salient.

The next figure shows the probability of finding a significant result as a function of sample size and the size of the bias. The various lines show the various levels of bias in terms of the standard deviation. If the bias effect is small (e.g., 1/16th of the standard deviation on the DV), increasing sample sizes are not increasing the probability of finding a significant effect by much. However, when bias approaches a .25 of the standard deviation, the probability of finding a significant effect in a sample of 100 participants approaches 60%. You may argue that ¼ of a standard deviation is large. However, it is not an unrealistic scenario given the prevalence and extent of response styles in questionnaire research – see for example our earlier research showing that response styles produce bigger effect sizes than 1/3 of theoretically important research studies.



These two simulation studies suggest that cross-cultural differences might be spurious and driven by method effects. In addition, our field seems to be driven by differences and appears to pay unduly emphasis on differences, without questioning their validity. The next figure shows the emphasis on differences and the lack of studies hypothesizing and finding similarities. This graph is adapted from a review by Brouwers and others, published in JCCP in 2004. As can be seen, the majority of studies expect differences only (N=55) and only 25 studies expected differences and similarities. At the same time, 57 studies found both. Most importantly, given laws of probability, we should also have studies that expect and report only similarities. Brouwers and colleagues did not find a single study that either hypothesized or reported similarities only. Where are these studies?




The points raised so far should not be understood as challenging the experimental methods underlying comparative research. We would urge our colleagues to critically question some of our designs and analytic procedures. In the larger experimental literature, a number of strategies have been proposed, including:

- stricter designs (larger n, Button et al., 2013) for more power
- stricter analysis (p < . 005, Johnson, 2013)
- prevention of experimenter bias (O. Klein et al., 2012)
- more transparency (e.g., pre-registration of hypotheses)
-replication across multiple researchers and labs (R. A. Klein et al., 2014)
We see it as a good sign that replication studies have achieved new status. For example, an earlier attempt of our lab to replicate the culture-level value structure by Schwartz using data from the Rokeach Value Survey faced some real uphill battle in getting it published. The saving grace to get it published seemed to be the appearance of a new value type that was not evident in the earlier Schwartz circle (a replication of this new value type is still outstanding). The new emphasis on replication in my opinion is a major achievement. The first findings of this new wave of replications are coming in. For example, the following graph shows the replication success of a number of studies in the ‘many labs’ replication report. Some of the older studies hold up well to scrutiny, but many of the newer findings, in particular priming studies are not replicable.

What is also noteworthy is that in the original dissemination of these findings, the lack of cross-cultural differences in the patterns was emphasized. Some commentators were quick to jump on that and suggested that careful and experimentally strict replications will do away with cross-cultural differences. We may want to challenge such an assumptions, but these comments clearly demonstrate that we as cross-cultural and cultural psychologists need to engage with the replication debate. We cannot sit back and pretend that the replication crisis does not affect us!



Replications vary along an underlying dimension, with exact replications being at one end and conceptual replications forming the opposing end. The conventional experimental wisdom is to prioritize exact replications or to stick as closely as possible to the original designs (close replications) with large samples sizes to have high power to detect effects. Of course, we know that exact replication in a cross-cultural context is problematic due to the different cultural conditions of participants.

However, an even more important point for us is that the presence of bias (e.g., response styles, speed-accuracy trade-offs) challenges the validity of exact or close replications. A replication of a biased study is a replication of a biased study.

In addition, if we have two samples and we define one sample as belonging to X culture and the other sample as belonging to a Y culture (this could be anything: collectivistic vs individualistic; independent vs interdependent self-construals, honour vs dignity; holistic vs analytic thinking), then any difference on whatever variable will be statistically related to the presumed X-Y difference. Therefore, replications in cross-cultural psychology need to be positioned towards the conceptual replication end and require additional methodological safeguards.

We suggest that cross-cultural replications need to:

-ensure validity of procedures in local context

-empirical checks on the postulated antecedent (what theoretical process is likely to drive these expected patterns and to empirically test these theoretical processes)

-manipulation checks (including a “no-difference” condition, on what variable or set of variables do we NOT expect a difference)

-control on likely alternative explanations (e.g., response styles).



In summary of the points so far, cross-cultural psychology suffers from many of the same shortcomings that have created the crisis in social psychology. A somewhat humorous account borrowing from Dante’s version of hell is provided by this cartoon (by the Neurosceptic, published in Perspectives in Psychological Science). Our research culture that emphasizes differences instead of similarities leads a state of limbo, overselling and post-hoc story-telling. Our narrow orientation towards ghost in the machine variables (such as collectivism, self-construals and values) lead to overselling (everything needs to be explicable by single dimensions, typically of personal relations or self-construals), post-hoc story telling and p-value fishing. From personal experience publishing cross-cultural research, nearly any difference can with a bit of theoretical creativity be related back to individualism-collectivism, self-construals or any of the other fashionable constructs these days. These biases in orientation and the researcher practices and researcher degrees of freedom then lead to p-value fishing and creative outlier utilization. Of course, the absence of no-difference studies suggest a significant file drawer problem.

Our suggestions are therefore:

Better designs (including efforts to reduce bias, testing of alternative theoretical processes, etc.)

Planned replications

Depositing hypotheses and methods in a public archive prior to data collection



Peter Smith: To understand cultural variation let’s sample cultural variations


Peter Smith and colleagues suggested a rather straightforward approach for addressing some of the concerns. Their recommendation was to go beyond two culture comparisons and to sample cultural variation more broadly, e.g., by studying multiple Asian and non-Asian samples that are typically lumped together as collectivist, interdependent, holistic, etc. In addition, Peter and colleagues included more diverse instruments capturing conceptually similar constructs to examine variability in intended constructs across a broader range of instruments. Peter presented some preliminary data that supported the usefulness of this approach. However, he also acknowledged that the current study has some important limitations, including studying students, not having enough samples yet to properly examine effects (e.g., though multi-level modeling) and a high demand on participants (e.g., completing long sets of questionnaires).


Johnny Fontaine: A plea for domain representation


Johnny presented a more technical account of domain representation that examined the meaning of constructs across a larger number of languages and cultural contexts. Using examples from the emotion domain, he showed that we can avoid confusion and biases in meaning through the use of sophisticated non-metric statistical methods in combination with elaborate designs that allow separating situational and personal characteristics. His approach demands a theoretical analysis of possibly important variables that need to be incorporated into the research design. Johnny really got the methods guns blazing in his presentation and I have to admit that the heat of the room by that time had fried my brain. As a consequence, I was not able to follow all the intricate steps in the procedure and not having a seat did not allow me to take good notes (but the graphs looked very convincing). He is working on a manuscript detailing the procedures and I am certainly looking forward to reading it when it is ready.

David Matsumoto: Random thoughts about methodological vulnerabilities in research on behavior and culture.


David broadened the symposium by focusing on the broader research climate in culture and psychology. Most people in this overheating room will have appreciated his first demand: before he started talking he requested everyone to stand up from their seats. Beyond bringing some oxygen into our brains, this also then became a beautiful point of reference for his short and sharp presentation. Here are his three main arguments (my paraphrasing):

Point 1: Study behavior

Point 2: Respect the literature

Point 3: The current pressures on young academics makes following recommendations 1 and 2 challenging


The first point is obvious – our discipline confuses self/other/peer-reports of behavior for behavior. I do not have hard stats here, but from memory – I cannot remember a single cross-cultural social psyc study in the last year or two in JCCP that studied actual behavior. He pointed out that everyone had stood up when he asked at the beginning of his presentation – a success rate of 100%. In contrast, when asking people whether they would stand up in a seminar room when asked by the presenter (e.g., on a scale from 1-7), there would have been significant variability and the mean would definitely been lower than 100%. Drawing upon his own research on emotion display, he argued that triangulation of research method is necessary.

The second point highlights the emphasis of getting to know more about previous research. In the current research environment, researchers need to present novel result and theory. There is no incentive for (or penalty for not) reading older research that may have been conducted 10 or 40 years ago. Journal editors are keen to get citations to recent papers to increase the journal’s Impact Factor. Yet, this leads to impoverished and non-cumulative research.

The last point highlights the constraints that young researchers pre-tenure are facing: more publications in less time. Studies of behavior are time consuming and therefore are less appealing. Reading relevant literature in one’s field or neighboring disciplines is also detracting from writing articles and funding applications. David emphasized that IACCP has a richer intellectual tradition than many mainstream researchers who have discovered culture and now publish in high-impact journals.


Some of the discussion points


The discussion turned repeatedly on a number of points. I will try and summarize some of the key ones that stood out for me.

Representativeness of samples: One key concern that came up repeatedly was that studying students is not appropriate for making claims about cultural processes. Students are not good representatives of the larger population.

Studying nations: One early comment that drew spontaneous applause from the audience was that psychology has failed in studying culture. Instead, psychologists are studying nations. Yet, nations are highly diverse and consist potentially of many subcultures. Various other commentators picked up similar themes throughout the discussion. One issue that is related here was the relative emphasis on between-country/culture differences and the lack of attention to within-country/culture differences. Both Geert Hofstede and Shalom Schwartz were in the audience, but they remained silent – it would have been nice to hear their responses to some of these comments (and both have done some interesting work that would have been informative in this debate).

Lack of strong theory: Peter Richerson argued that psychologists lack strong theory and recommended looking to neighboring disciplines such as biology for inspiration. David Matsumoto defended psychology in his response, suggesting that psychology has some good theories. But he also added that we need truly exploratory work that can understand phenomena on their own terms. My thought on this is that we have not enough strong theory (in a philosophy of science perspective) and that exploratory research with attention to various alternative explanations may bring us closer to developments of stronger theories of culture (e.g., by including the possibilities of no differences, attention to alternative processes beyond the usual suspects in current psychological thinking on culture).

Validity of findings: One point that occurred in various disguises in a number of comments was the importance of validity of findings in the local context. Amina Abubakar was the first to get this point across in the debate: To what extent can cultural psychology and cross-cultural research as a method of choice yield insights into the minds and behaviours of people in a specific context? How applicable and relevant is cross-cultural research for people around the world? This is a major question and needs some serious contemplation as we face a rapidly changing world and need to collectively respond to multiple pressing challenges (e.g., increasing intergroup conflict, climate change, decreasing natural resources).

Next steps


An immediate opportunity following this debate arose the next day after the round-table discussion. Ype challenged the assembly that methods issues need more attention and in response Walt Lonner as the founding editor of JCCP suggested a methods oriented special issue for JCCP. We had a discussion during the coffee break and he invited us to write a proposal for a special issue. Any thoughts for topics and contributors for such a special issue addressing the methods challenges are much welcome (please flick me an email or respond below – I would love to hear from you).

Looking at some other associations (APS comes to mind here), we could adopt some of their criteria for publication – there have been some interesting suggestions and changes in policies recently. Even JPSP now publishes replications (hooray!!!!!!)!

Overall, I think that the overall change in research climate is promising. There has never been a more positive time to discuss how we collectively do research, there is much promise of change in the air and I strongly believe that collectively we can make a positive change. Without this conviction, we would not have had the symposium and such a large crowd keen to brave tropical temperatures and horrible conditions in the late afternoon to debate a topic so passionately. I felt humbled by this enthusiasm of the audience and the positive comments that we received over the next couple of days. I look forward to continuing this debate and hearing your opinions and suggestions!

Tuesday, May 14, 2013

Unpackaging culture & cultural differences

One of the most fascinating questions arises when we observe that individuals in a different cultural system behave or act in a different way. Why do they do that? What is the explanation or reason for showing these particular behaviours or responses? For example, we may have stepped on an exotic island and observe that the inhabitants eat way more chocolate ice cream that we do. Or they may tell you that there are lots of little ghosts out there taking care of them, many more than you ever thought would be possible to inhabit a small island like this. Or they may simple say in some interviews or surveys that they do not like to work as hard as you normally would expect in adult samples. How could we explain any of these differences?




Given the perpetual problem of potential bias in comparative research, we can never really rule out that our observations were simply erroneous - we might have had the wrong instruments, there may have been language problems in interactions (remember Lost in Translation?), we may have mis-interpreted the data or it may have simply been a chance difference. 

One persuasive idea that has been around for quite a while in the social sciences is the idea of unpackaging. The terms goes back to a classic study conducted by Whiting and Whiting (1975). They orchestrated a large ethnographic study of child development among six communities: a New England Baptist community; a Philippine barrio; an Okinawan village; an Indian village in Mexico; a northern Indian caste group; and a rural tribal group in Kenya. They reported differences in a number of psychological processes, socialization and child-rearing patterns. Going beyond just noting these differences, they reasoned that there must be specific contextual variables that could explain the differences found, linking ecological constraints faced by these communities to psychological processes via adaptive socialization practices. For instance, they compared the activities of children from the same families, some of whom were living in cities and others in villages. They also compared families in which young boys helped with baby-tending with those in which girls did the helping. Therefore, these social conditions were linked to observed behavioural differences, leading to one plausible explanation of why they may have occurred in the first place. This is essentially what psychologists study as mediation:  processes and variables that explain the relationship between an independent or predictor variable and the dependent or criterion variable. It is about the causal theoretical processes, the how and why of the observed effects. We often think of mediators as internalized psychological processes of external conditions that lead to other outcomes down the causal chain. In cross-cultural work, it does not necessarily always be an internal psychological variable - it could also be living conditions or social constraints and norms that can act as mediators. 

Put differently, unpackaging studies are extensions of basic cross-cultural comparisons in which the active ingredient presumed to cause the observed differences in psychological processes is directly measured and explicitly tested for its role in explaining the outcome. Have a look at the graphical representation of mediation. Unpackaging culture is one term often found in the literature, others include ‘linkage studies’ (Matsumoto & Yoo, 2006), ‘mediation studies’ (Kirkman, Lowe & Gibson, 2006) or ‘covariate studies/strategies’ (Leung & van de Vijver, 2008).




 For example, Tinsley (2001) found that differences in the conflict management strategies of German, Japanese and US managers were completely mediated by the values held by members of these cultural groups, and Felfe, Yan and Six (2008) reported that individuals’ scores on a ‘collectivism’ scale mediated differences in organizational commitment across samples of Romanian, German and Chinese employees.  

In an ideal test of mediation, the researcher tests whether other relevant variables that are not related to the hypothesis also yield mediation effects. This provides greater certainty in establishing exactly what the causes the results that are obtained. For instance, Y. Chen, Brockner, and Katz (1998) showed that a measure of individual-collective primacy mediated the intergroup effects that they had predicted and found. They then tested whether six other measures derived from the concept of individualism-collectivism also mediated these effects, and found that they did not. Studies of this kind help to clarify the loose and varied ways in which the psychological aspects of individualism and collectivism have been employed by different authors. 

What are some general concerns?
In the above examples, the mediator and dependent or criterion variable were measured using the same or similar methods. If there is some third unmeasured variable that is related or unrelated to the independent variable, we may end up with a situation where it appears that there is mediation, whereas in reality, there is none. Having multiple mediators measured with the same method as the DV may lead to some reassurance about the findings, but ultimately, the best test would be a test using independent methods

Experiments have been much in vogue recently to study cultural differences. One of the major concerns is whether the manipulation was effective or not. This is again the problem of potential bias in comparative studies. If we have a psychological mediator in our experiment that highlights how the manipulation is affecting the DV, then we are much safer grounds in terms of explaining the psychological processes. 

In summary, unpackaging has two important and inter-related features: identification of the theoretical factors or processes that may cause cultural differences in psychological outcomes of interest, and an explicit empirical test of the proposed processes leading to these outcomes. Therefore, it is as much about theory as it is about methods and stats. Having unpackaged an observed difference in behaviour, attitudes or beliefs and having ruled out alternative theoretical explanations (other potential mediators), we can also place much more confidence in our results. I leave it up to you to come up with potentially meaningful variables that we could use in those three semi-silly examples (ice cream, ghosts and motivation). Once you have some mechanism, the next phase would be to test whether the mediator(s) actually do the job. Ideally, this is one of the best ways to rule out measurement bias - explain where the difference came from and that the difference is not driven by artefacts. 


Some more technical explanations are available in Fischer (2009); Leung & Van de Vijver (2008) and Poortinga & Van de Vijver (1987, this is an excellent discussion early discussion with some great multi-method examples). Excellent resources and tutorials for running state-of-the-art mediation analyses are available from on Kristopher Preacher's and Andrew Hayes' websites. Use them!!!!!

Overall, I think this is the most exciting part of cross-cultural research - put on your detective hat and find out where any difference that you perceive in the world ultimately stems from. 


Thursday, October 11, 2012

How to run a Conditional ANOVA


Today is a wee bit heavier on the stats side again. If you are interested in Differential Item Functioning and how to do it with an easy to use tool, this is for you...

Aim: Identify differential item functioning in numerical scores across groups in order to decide whether the items are unbiased and can be used for cross-cultural comparisons.

General approach: Van de Vijver and Leung (1997) describe a conditional technique which can be used if you use Likert-type scales. It uses traditional ANOVA techniques. The independent variables are (1) the groups to be compared and (2) score levels on the total score (across all items) as an indicator of the true observed or ‘latent’ trait (please note that technically it is not a latent variable). The dependent variable is the score for each individual item. Since we are using the total score (divided into score levels) as an IV, the analysis is called ‘conditional’.

Advantages of Conditional ANOVA: It can be easily run in standard programmes such as SPSS. It is simple. It highlights some key issues and principles of differential item functioning. One particular advantage is that working through these procedures, you can easily find out whether score distributions are similar or different (e.g., is an item bias analysis warranted and even possible?).

Disadvantages of Conditional ANOVA: There are many arbitrary choices in splitting variables and score groups (see below) that can make big differences. It is not very elegant. Better approaches that circumvent some of these problems and that can be implemented in SPSS and other standard programmes include Logistic Regression. Check out Bruno Zumbo’s website and manual. I will also try and put up some notes on this soon.

What do we look for? There are three effects that we look for.
First, a significant main effect of score level would indicate that individuals with low score overall also show a lower score on the respective item. This would be expected and therefore is generally not of theoretical interest (think of it as equivalent to a significant factor loading of the item on the ‘latent’ factor).
Second, a significant main effect of country or sample would indicate that scores on this item for at least one group are significantly higher or lower, independent of the true variable score. This indicates ‘uniform DIF’. (Note: this type of item bias can NOT be detected in Exploratory Factor Analysis with Procrustean Rotation).
Third, a significant interaction between country and score level on the item mean indicates that the item discriminates differently across groups. This indicates ‘non-uniform DIF’. The item is differently related to the true ‘latent’ variable across groups. For example, think of an item of extroversion. In one group (let’s say New Yorkers), ‘being the centre of attention at a cocktail party’ is a good indicator of extroversion, whereas for a group of Muslim youth from Mogadishu in Somalia it is not a relevant item of extroversion (since they are not allowed to drink alcohol and probably have never been at a cocktail party, for obvious reasons).
Note: Such biases MAY be detected through Procrustean Rotation, if examining differentially loading items.

Important: What is our criterion for deciding whether an item shows DIF or not?

Statistical Procedure:

The procedure requires in most cases at least four steps.
Step 1: Calculate the sum score of your variable. For example, if you have an extraversion scale with ten items measured on a scale from 1 to 5, you should create the total sum. This can obviously vary between 10 and 50 for any individual. Use the syntax used in class.

For example:

Compute extroversion=sum(extraversion1, extraversion2,…,extraversion10).

Step 2: You need to create score levels. You would like to group equal numbers of individuals into groups according to their overall extroversion score.
Van de Vijver and Leung (1997) recommend having at least 50 individuals per score group and sample. For example, if you have 100 individuals in each group, you can maximally form 2 groups. If you have 5,000 individuals in each of your cultural samples, you could theoretically form up to 100 score levels (well actually not, because you would have only 40 meaningful groups in this example since the difference between maximum and minimum possible score is 40). Therefore, it is up to you how many score levels you create. Having more levels will obviously allow more fine-grained analyses (you can make finer distinctions between extroversion levels in both groups) and probably more powerful (you are more likely to detect DIF). However, because you have fewer people in your analysis, it might also be less stable. Hence, there is a clear trade-off, but don’t despair. If an item is strongly biased, it should show up in your analysis independent of you have fewer or more score levels. If the bias is less severe, analyses might change across different options.

One issue is that if you have less than 50 people in each score group and cultural sample, the results might become quite unstable and you may find interactions that are hard to interpret. In any case, it important to consider both statistical significance as well as effect sizes when interpreting item bias.

A simple way of getting the desired number of equal groups is to use the rank cases option. You find this under ‘Transform’ -> ‘Rank cases’. Transfer your sum score into the variables box. Click on ‘Rank types’. First, unclick ‘Rank’ (it will rank your sample, but this is something that you do not need). Second, click on ‘Ntiles’ and specify the number of groups you want to create. For example, if you have 200 individuals, you could create 4 groups. If you have larger samples, the discussion from above applies (you have to decide about the number of levels, facing the before-mentioned trade-off in terms of power versus stability).

As discussed above, it is strongly advisable to interpret effect sizes (how big is the effect) in addition to statistical significance levels. This is particularly important if you have large sample sizes in which often minute differences can become significant. SPSS gives you partial eta-squared values routinely (if you click on ‘effect sizes’ under the ‘options’). Cohen (1988) differentiated between small  (0.01), medium (0.06), and large effect size (0.14) for eta-squared. Please note that SPSS gives you partial eta-squared values (which is the variance due to the effect, independent of the effect of other effects), whereas eta-squared does not take the other effects take into account. Partial eta-squared values are often larger than the traditional eta-squared values (overestimating the effect), but at the same time there is much to be recommended for using partial instead of traditional eta-squared values (see Pierce, Block & Aguinis, 2004, in Educational and Psychological Measurement).

Step 3:  Run your ANOVA for each item separately. The IV’s are country/sample and score level (the variable created using ranking procedures). Transfer your IV’s into the ‘Fixed Factor’ boxes. As described above, the important stuff to look out for is the significant main effect of country/sample (indicating uniform DIF) and/or the significant interaction between country/sample x score level (indicating non-uniform DIF). You can use plots produced by SPSS to identify that nature and direction of the bias (under plots, transfer your score level to the ‘horizontal axis’ and the country/sample to ‘separate lines’, click ‘add’ and then ‘continue’). Van de Vijver and Leung (box 4.3) describe a different way of plotting the results. However, the results are the same, only different way of visualising the main effect and/or interaction.
This little figure for example shows evidence of both uniform and nonuniform bias. The item is overall easier for the East German sample and it does not discriminate equally well across all score levels. Among higher score levels, it does not differentiate well for the UK sample. 



Step 4: Ideally, you would not like to have DIF. However, it is likely that you will encounter some biased items. I would run all analyses first and identify the most biased items. If all items are biased, you are in trouble (well, unless you are a cultural psychologist, in which case you rejoice and party). In this case, there is probably little you can do at this point except trying to understand the mechanisms underlying the processes (how do people understand these questions, what does this say about the culture of both groups, etc.).
If you have only a few biased items, remove them (you can either remove the item with the strongest partial eta-square or all of the DIF items in a single swoop – I would recommend the former procedure though) and recompute the sum score (step 1). Go through step 2 and 3 again to see whether your scale is working better now. You may need to repeat this analysis various times, since different items may show up as biased at each iteration of your analysis.

Problems:

My factor analysis showed that one factor is not working in at least one sample: In this case, there is no point in running the conditional ANOVA with that sample included. You are interested in identifying those items that are problematic in measuring the latent score. You therefore assume that the factor is working in all groups included in the analysis.

My overall latent scores do not overlap: This will lead to situations where the latent scores are so dramatically different that you can not find score levels with at least 50 participants in each sample. In this case, your attempt to identify Differential ITEM functioning is problematic, since something else is happening. One option is to increase score levels (make the groups larger – obviously this involves a loss of sensitivity and power to detect effects). Sometimes, even this might not be possible.
At a theoretical level, it could be that you have a situation where you have generalized uniform item bias in at least one sample (for example because one group gives acquiescent answers that are consistently higher or lower). It also might indicate method bias (for example, translation problems that make all items significantly easier in one group compared to the others) or construct bias (for example, you might have tapped into some religious or cultural practices that are more common in one group than in another – in this case your items might load on the intended factor but conceptually the factor is measuring something different across cultural groups). Of course, it can also indicate a true differences. Any number of explanations (construct or method bias or substantive effects that lead to different cultural scores) could be possible.

What happens if most items are biased and only a few unbiased items remain? In this situation you run into the paradox that you can not actually determine whether your biased items are actually unbiased or unbiased items are biased. This type of analysis only functions properly if you have a small number of biased items, up to probably half the number of items in your latent variable. Once you move beyond this, it means that there is a problem with your construct. If you mainly find uniform bias, but no interactions, you can still compare correlations or patterns of scores (since your instrument most likely satisfies metric equivalence). If you have interactions, you do not satisfy metric equivalence and you may need to investigate the structure and function of your theoretical and/or operationalized construct (functional and structural equivalence). 

Any questions? Email me ;)