# The common-is-moral association is stronger among less religious people

### Participants

We use data on 37,154 participants from 31 countries in the 1999 wave of the European Values ​​Study, 54% women, mean age 45.1 with SD 17.0.

### measurements

#### Perceptions of how common certain questionable behaviors are

The survey included the question “According to you, how many of your compatriots do the following?”, which was asked for eight questionable behaviours: cheating on taxes, claiming government benefits to which you are not entitled, having casual sex, paying cash to avoid taxes, speeding over the limit in built-up areas, taking soft drugs, and throwing away litter in public place. Our criterion for including items in our study was that the item had been asked in all countries. (Three additional items that were only asked in 13 out of 31 countries are therefore excluded.) Responses were given on a five-step scale: “almost none” (1), “some” (2), “many” (3) , “almost all” (4).

#### Moral judgments of the same questionable behaviors

In another section of the survey, respondents were asked: “Please tell me for each of the following statements whether you think it can always be justified, never be justified, or something in between”. A list of questionable behaviors followed which included the eight behaviors used in the previous question. Responses for each behavior were given on a ten-step response scale with endpoints labeled “never justifiable” (coded 1) and “always justifiable” (10).

#### religiosity

As a proxy for the extent to which religion plays an important part in shaping the participant’s moral judgments, we use an item on how important religion is in the participant’s life. Responses were given on a four-step scale: not at all important (coded 1), not important (2), quite important (3), very important (4). As a reviewer pointed out, this is not the only variable in the European Values ​​Study that could be used for our purpose. An alternative possibility would have been an item on how often the participant attends religious services. Unsurprisingly, this alternative variable is correlated with the variable we used and the results we present are qualitatively similar if we use the alternative variable instead (see results in Supplementary Table 1).

### Analytic strategy

To examine the universality of the common-is-moral association and how it depends on people’s religiosity, we conduct a series of analyses. The data are complex and best analyzed by mixed-effects models. However, such models are non-trivial to understand and readers may wonder what raw correlations look like. For this reason, we adopt a strategy in which we first examine raw correlations between frequency perceptions and moral judgments in various samples. We will examine the common-is-moral association both within individuals across behaviors and between individuals for a fixed behaviour.

1. 1.

Correlations within each individual are used to examine (a) whether most participants exhibit a positive within-individual common-is-moral association, (b) whether this holds in every country, and (c) whether the association tends to be weaker among more religious individuals.

2. two.

Correlations between individuals for each fixed behavior are used to examine (a) whether a positive common-is-moral association between individuals is present for every questionable behaviour, (b) whether this holds in every country, and (c) whether the association tends to be weaker within more religious subsamples.

The raw correlations approach is easy to understand but has two major drawbacks that mixed-effect models can address. One drawback is that analyzing each subsample separately yields small sample sizes, which makes individual results less reliable. By contrast, the mixed-effects model uses the full dataset. Another drawback with raw correlations is that they may be confounded by other variables. In the mixed-effects models below we include controls for standard demographic variables: age (in 10 years), sex, and education (with “primary or lower” as baseline and with dummy variables for secondary and tertiary education); we do not include income, as it was missing for up to 20% of cases in some countries. We analyze the common-is-moral association within individuals by estimating a three-level model with 277,341 individual ratings of eight different behaviors nested in 37,154 individuals nested in 31 countries. The model has the form

$$begin{array}{l}{mathrm{{Mo}}}_{kij} =( {beta _1 + u_{1j} + v_{1ij}} ) + ( {beta _2 + u_{ 2j} + v_{2ij}} ){mathrm{{Co}}}_{kij} \ qquadqquad +,beta _3{mathrm{{Relig}}}_{ij} + beta _4{mathrm{{Co}}}_{ij} times {mathrm{{Relig}}}_{ij} + X_{kij}end{array}$$

(M0)

Here, Mokij and Cokij denote the ratings of moral justifiability and commonness, respectively, of behavior kas rated by individual Yo country j. religionij is the same individual’s religiosity score. Xkij is shorthand for terms representing the effects of individual-level controls, their cross-level interactions with Cokij, and an error term. CoYojk is centered at the individual mean so that βtwo represents the within-individual common-is-moral association, while β4 represents how this association is moderated by individual religiosity, which is centered at country means (the same as control variables). Random effects at the individual level (v1jk, vtwojk) and the country level (or1k, ortwok) follow a multivariate normal distribution with mean zero. Consistent with M1, we only include random slope for commonness ratings to check that additional random effects for religiosity and the interaction term would not affect the fixed effect estimates in a substantial way.

We analyze the common-is-moral association between individuals by estimating, for each of the eight behaviours, a two-level mixed-effects model with individuals nested in countries. The exact number of individuals varied between 32,799 and 36,242 depending on missing values. The model has the form

$${mathrm{{Mo}}}_{ij} = ( {beta _1 + u_{1j}} ) + ( {beta _2 + u_{2j}} ){mathrm{{Co}}} ij + beta _3{mathrm{{Relig}}}_{ij} + beta _4{mathrm{{Co}}}_{ij} times {mathrm{{Relig}}}_ {ij} + X_{ij}$$

(M1)

Here, Moij and Coij denote the ratings of moral justifiability and commonness, respectively, of individual Yo country j. All predictors are centered at the country mean. notice that βtwo now represents the between-individual common-is-moral association for the fixed behaviour, while β4 represents how this between-individual association is moderated by individual religiosity. Random effects at the country level (or1j, ortwoj) follow a multivariate normal distribution with means zero. We do not include random slopes for religiosity as that would reduce the model fit in three out of eight models; the effect on coefficient estimates is negligible anyway.

A potential problem with these model specifications is that the outcome variable (Mo) has a right-skewed distribution; specifically, the mode is at the lower end of the scale, “never justifiable”. This skew leads to a violation of the assumption of normality of residuals. However, it is unlikely to bias results. A recent simulation study found that linear mixed-effect models are robust to non-normality and yield unbiased, though less precise, estimates of fixed effects and group variance (Schielzeth et al., 2020). However, we checked robustness by estimating additional models. To address the skew, we used a two-part model: part 1 models the probability that Moij> 1 (ie, above “never justifiable”) with logistic regression, and part 2 is the same as M0 or M1 but estimated on the subsample of moral justifiability ratings above 1 and with Moij log transformed before standardization. We also check the moderation effect of religiosity using an alternative item.

Analyzes were conducted in the R programming language. Mixed models were estimated by maximum likelihood in the lme4 package (Bates et al., 2015). Restricted maximum likelihood was used in all linear mixed effect models except M2.1.