A meta-analysis of the minimal group paradigm with liking and resource allocation as dependent measures

0.1 Introduction

Our meta-analysis focused on the minimal group paradigm based on liking and resource allocation, with the research goals of examining the possibility and extent of publication bias in studies involving the minimal group paradigm, estimating the meta-analytic effect size, and exploring possible moderators. This meta-analysis stemmed from interest and an intense amount of curiosity in Tajfel’s minimal paradigm paper in 1970, “Experiments in Intergroup Discrimination.”

The paper’s general question investigates discrimination between groups of people based on an individual’s association with one group over another. Stereotypes stem from assumptions and thoughts from groups not associated personally with an individual and can lead to choosing to harm other groups of people even without any perceived benefit to doing so. Finding out whether discrimination is based on association with certain groups is essential in discovering the roots of major social issues such as racism and sexism. These issues can lead to wars, and feelings of hatred towards certain groups of people that must co-exist with one another. Finding the critical cause for these issues can result in a solution towards lessening tensions between different groups of people, ultimately helping to create peace and resolve conflicts.

Specifically, the paper investigates the question of whether two groups, an ‘in-group’ (an individual is a part of this group) and ‘out-group’ (an individual is not part of this group) to determine whether teenage boys would favor their group (the in-group) or be fair overall to both groups. Some moderators that could have affected performance in this paper’s task are that the group of boys selected already knew each other beforehand, as they came from the same school. Therefore, they could have had preconceived notions of certain members in the two groups, affecting their decisions on what to do. Additionally, the only people tested were teenage boys aged 15-17; including other factors, such as including females or a larger age range, could have resulted in different results or added more robust evidence for adolescents altogether, rather than only selecting males within a two-year age range.

The paradigm of experiment one focused on the minimal group paradigm. It was analyzed whether group bias was based on being a member of a certain group. Sixty-four boys aged 15 to 17 years from the same background (i.e., school, state) were put into two sets of two randomized groups (eight boys in each group and two sets of tests), but told categorization was based on their results from a visual judgment test. Then, they were each separately told to allocate rewards and punishments to people within their group (the in-group) and those not in their group (the out-group) on a given booklet. Depending on the number of rewards and punishments, each boy was told they would be given a certain amount of money as a cash prize.

Results from this paper found a pattern from both sets of tests that individuals gave more money to members of their own group (in-group) versus the other group (out-group). Statistically, these skewed results ranked above what is considered to be fair for all groups and showed that individuals greatly favored their own group. Within the groups themselves, the money seemed to be distributed equally and almost precisely to the point of fairness. These results display that when allowed to fairly distribute points to two groups of similar backgrounds in addition to being categorized randomly, individuals will always favor their own group more over the out-group.

Within our own meta-analysis, we used Tajfel’s seminal paper to find and research an additional 31 papers regarding the minimal group paradigm’s effects. These discovered minimal group paradigm papers, including authors such as Sachdev, Gardham, and Nesdale, broadened the results found in Tajfel’s paper by experimenting with a broader age range and both genders on an international scale. These papers also tested a similar hypothesis of whether an individual would favor their own group (in-group) vs. one they are not associated with (out-group). However, they also included collectively children as young as four years old to adults (around the age of 30 years old). Additionally, females were also included in nearly all of these studies to explore the paradigm’s effects. This inclusion removes the factor of gender, disregarding the possibility the results were affected by any neurological differences between males and females Countries such as Australia, Italy, Denmark, and Japan were included in our meta-analysis in addition to the United States (where Tajfel’s study was conducted) to diversify results internationally across all types of people. These papers also cumulatively ranged the years of 1962 to 2020, removing any notions that present/past culture, mindsets, and trends could influence one’s decision to favor the in-group opposed to the out-group. Together, these papers removed certain unaccounted for moderators from Tajfel’s paper: gender, race, age, and cultural influences (including geographical and historical times).

0.2 Method

In order to select these certain papers over others for our meta-analysis, we included any journals, books, theses, and conference proceedings that had the following criteria: ages ranging from children to adults, a categorization that is both novel and arbitrary (i.e., randomized groups, no history of experiences with experiments regarding in-group vs. out-group), anonymous categorization (i.e., no face-to-face interaction between any group members), the dependent measures of liking or resource allocation, and no utilitarian self-interests that could be directly served from intergroup evaluations or allocations.

Ultimately, out of the original 186 papers we screened based on their titles and abstracts from sources such as Google Scholar and JSTOR, we excluded 49 papers due to either not being randomized, containing self benefits within the study, or were not anonymous based grouping. From the remaining 137 papers, 106 were excluded due to missing standard deviations (information needed to calculate an effect size) or inability to access these texts (i.e., they were in a different language, the texts were not available on an online platform) to gain the remaining 31 papers included in our meta-analysis as seen in the PRISMA flow diagram, Figure 1. From these papers, we coded the following variables: short citations, the source for our data within the paper, the paper’s experiment number, the experiment’s condition (i.e., explicit attitude, positive/negative traits, linguistic abstraction), the study’s dependent measure (either liking, a numerical rating of preference for in-group vs. out-group members, or resource allocation, assigning points/money to certain members of each group), the necessary data to calculate effect size(s) (such as standard deviation), the mean age of participants in days, the participants’ perceived grouping categorization (while in reality, categorization was random), the proportion of female participants, the study’s specific population characteristics (i.e., age, geographical location, university name), and whether the study was conducted with Non-US or US participants.

From the data coded, our effect sizes were calculated using R’s metafor package for each study based on Cohen’s d, an effect size based on the comparison between two means. This was found by taking the difference between the in-group versus out-group and dividing the number by the population’s resulting standard deviation containing both groups. The scale for Cohen’s d is as follows: an estimated 0.2 Cohen’s d is considered to be a ‘small’ effect size, a 0.5 is a ‘medium’ effect size, and a 0.8 is valued as a ‘large’ effect size. Specifically, the effect size determines how big of a difference there is between resource allocation or liking between the in-group and out-group to display whether there is favoritism for one’s own group.

Figure 1: This figure shows the search protocol we went through to gain the remaining papers for our meta-analysis

0.3 Results

Figure 2: This figure shows a forest plot of all effects sizes for our meta-analysis

Our forest plot, as seen above in Figure 2, has all 31 papers and 57 effect sizes from these papers (due to some papers contained multiple effect sizes). The left portion of the plot identifies the principal author of each study, along with what year the experiment was conducted, while the right signifies the estimated Cohen’s d for each effect size. Each point on the plot is one effect size, with the size of each point explicitly corresponding to the sample size of the individual study. The red diamond displays the overall analytic mean for all 31 of the papers. The plot’s vertical, dotted line displays the effect size of 0 throughout all of the studies as a reference. The overall analytic mean was calculated to be about 0.36, with a confidence interval ranging from a value of 0.21 to 0.51.

Figure 3: This figure shows a funnel plot percision of the study and effect sizes

The funnel plot shown in Figure 3 displays the precision of the study on the y-axis and effect size on the x-axis. The triangular funnel shape presents the 95% confidence interval surrounding the overall effect size mean. Since this plot is mostly symmetrical, there is no indication of any publication bias regarding effect sizes. If one side were more skewed than the other, then there would be an extreme angle for the triangle resulting in the possibility that publication bias could have occurred. There are points outside of the funnel plot due to not considering moderators, such as resource allocation vs. liking.

Figure 4: This figure displays a violin plot of effect sizes based on whether the study was non-US and US

The violin plot, as seen in Figure 4, displays the difference in effect size distribution based on whether the study’s participants were from the US or non-US. As seen, the red plot shows all studies done outside of the United States, and the blue plot represents all data from the United States. The horizontal, dashed line signifies the effect size of zero. As seen in the plot, the non-US populations have a stronger preference for those within their own group versus the out-group in comparison to studies done in the United States.

Figure 5: This figure presents the effect size based on proportion of females in the studies

Figure 5 examines effect size distribution based on what proportion of the studies’ participants were female. Each point on the plot is larger or smaller, based on the number of participants in each study. The x-axis displays the percentage of females in each study, while the y-axis shows the effect size for that given study. The plot’s blue line displays the average effect size based on the proportion of females in a given study. The gray hourglass-like shape shows the confidence interval for the given data. As shown, there is a slight upward trend in the effect size as the number of females in a study increases. However, this could be affected based on the fact that most of the studies had around half females and half males, as seen by the majority of the effect size dots plotted along with the 0.5 proportion of females, while only one study consisted of strictly females.

Figure 6: This figure displays the effect sizes of each study based on each study’s average age (in days)

The data in Figure 6 shows the various effect sizes based on the average age of an individual in each study calculated in days. The x-axis displays the average participant’s age in each study, while the y-axis shows the effect size for the study. Similar to Figure 5, the dot’s size displays the sample size of each study. The blue line displays the average effect size based on the average age based on days in a given study. The gray hourglass-like shape presents the confidence interval for the given data. As shown, there is a slight upward trend (less than Figure 5) in the effect size as the average age in each study increases. However, this could have been affected by the fact that we were not always given an age range or average age for every study, and were able to include only 19 of these studies for our age moderator plot.

0.4 Discussion

Based on the results given from our meta-analysis consisting of 31 papers, we determined that there was a somewhat significant robust effect in the minimal group paradigm, where individuals would prefer their own group instead of those outside that group.

Since the Cohen’s d value of around 0.2 is considered ‘small,’ and we discovered an overall analytic mean of 0.36 in our forest plot (as seen in Figure 2), we determined that there is evidence for favoritism for the in-group opposed to the out-group, however, not a drastic, significantly large one. Although the confidence interval determined that the range was 0.21 to 0.51, we only had a few papers that reached these ranges from ‘small’ to ‘medium’ effect, and none reach a ‘large’ effect.

The funnel plot in Figure 3 indicates that there was no publication bias, meaning that these effect sizes calculated for each study were not influenced by the motive of results finding hypotheses as true. Given that the overall hypothesis across all of these studies was that the in-group an individual was in favored the out-group, it can be determined that these collective results display a diverse, accurate analysis of the minimal group paradigm altogether.

Figure 4 indicated that those within the United States tend to be fairer/more neutral as opposed to those residing outside of the US. This supports the preconceived notions that cultural factors in the United States, such as ideas of individualism, influence their decision making of favoritism for those within their own group. On the other hand, this could have also been impacted by the fact that we had more studies from the United States versus other countries since it was challenging to find foreign studies, not in their own native languages.

Both the proportion of gender and age showed a slight upward trend, with more females creating a larger effect size over an increase in age, as seen in both Figure 5 and Figure 6. The distribution of females in Figure 5 shows a relatively upward trend based on the increasing amount of women in the study. This trend is perhaps due to neurological or cultural differences in women as opposed to men internationally. Since the trend for age was only minuscule, there is not necessarily a correlation between age changing the favoritism for in-group versus the out-group.

The mean effect sizes overall in comparison to psychology literature is between a ‘small’ and ‘medium’ effect size (between 0.2 and 0.5). While an effect size depends on the study’s design, various variables, and other factors, the mean effect size of 0.36 determines that there is statistically somewhat of a significance in preferences for those within their own group versus those in the out-group.

However, there are some limitations of our meta-analysis. Given that we were only able to find 31 papers for the minimal group paradigm that met our search protocol criteria, less than 50 papers is not a vast amount to conclude results that range such a vast amount of factors such as race, geographical location, year conducted, age, and gender. Additionally, many of the papers did not specify certain moderators, such as average age, or the number of females versus males within each study. These papers had to be removed from our moderator plots and reduced our 31 paper’s results to even fewer points of data. We also found more papers published within the United States, and consequently, had more participants in the studies from the United States opposed to internationally. This was mostly due to publications being in different languages and unable to be interpreted, which could have impacted our violin plot in Figure 4. Having more or equal amounts from both the United States and internationally would have supported our seminal paper considerably.

Collectively, this data from our meta-analysis signifies that there is favoritism for the in-group one is a part of toward those outside of their own group. With more time given, it would have been beneficial to find more papers that met our criteria, specifically those that could have diversified our results in our moderator plots, to have found more evidence that supported or disproved the general notion or in-group preference.

0.5 References

Tajfel, H. (1970). Experiments in Intergroup Discrimination. Scientific American, 223(5), 96-103. Retrieved May 8, 2020, from www.jstor.org/stable/24927662