Intelligence 68 (2018) 48–57
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Intelligence and religious disbelief in the United States a,*
Tatiene C. Souza , Francisco Cribari–Neto a b
Departamento de Estatística, Universidade Federal da Paraíba, Cidade Universitária, João Pessoa/PB, 58051–900, Brazil Departamento de Estatística, Universidade Federal de Pernambuco, Cidade Universitária, Recife/PE, 50740–540, Brazil
A R T I C LE I N FO
A B S T R A C T
Keywords: Atheism Beta regression Intelligence Quantile regression
We estimate the net eﬀect of intelligence on the prevalence of atheists in the United States. We evaluate such an eﬀect both at the mean and at diﬀerent quantiles of the conditional distribution of the proportion of atheists using data on all ﬁfty U.S. states. The results show that the net eﬀect of intelligence on religious disbelief is strictly increasing. This pattern is diﬀerent from that found elsewhere (Cribari-Neto and Souza, 2013) using data from over 100 countries in which the eﬀect peaks and then weakens. We show that in the U.S. the eﬀect is also stronger outside what we call the ‘Extended Bible Belt’. Our results also point to the existence of a ‘hurdle eﬀect’ that only takes place the U.S. most religious area. In that area, the eﬀect of average intelligence on the prevalence of religious disbelievers, albeit positive, loses strength above the conditional median, i.e., where there already are more atheists. Such a loss in strength above the conditional median does not happen in the rest of the country.
1. Introduction General intelligence relates to the ability to reason deductively or inductively, think abstractly, use analogies, synthesize information, and apply it to new domains (Kanazawa, 2010). It is usually measured by the intelligence quotient (IQ) which is a score obtained from several standardized tests designed to assess human intelligence. Average IQ scores have been computed for a large number of countries (Lynn & Meisenberg, 2010; Lynn & Vanhanen, 2002). Similar measures are available for the ﬁfty United States (U.S.) states: Kanazawa (2006) estimated average IQ based of scores on the Scholastic Achievement Test (SAT), McDaniel (2006b) based estimates on scores of the ACT test, McDaniel (2006b) estimated average state IQ based on a composite of the SAT and ACT scores, and McDaniel (2006a) used scores on the National Assessment of Educational Progress test (NAEP), which, like the SAT and ACT, tests abilities in reading and mathematics. Both nationwide and U.S. state IQs predict many of the things that individual IQ scores do, including socio-economic status (Pesta, McDaniel, & Bertsch, 2010) and education (Lynn & Meisenberg, 2010). The evidence suggests that intelligence correlates negatively with religious beliefs (Bertscha & Pesta, 2009; Ganzach, Ellis, & Gotlibovski, 2013; Lynn, Harvey, & Nyborg, 2009; Nyborg, 2009; Zuckerman, Silberman, & Hall, 2013); see, in particular, the meta-analysis in Zuckerman et al. (2013). Using 137 nation-level estimates of both intelligence and religiosity, Lynn et al. (2009) noted a substantial positive correlation between general intelligence and atheism. Higher levels of
IQ and education are associated with lower levels of religiosity at the national level (Ganzach et al., 2013; Lynn et al., 2009). Religiosity has also been consistently negatively associated with cognitive ability (Zuckerman et al., 2013). That is, individuals who are more religious tend to be less intelligent, albeit by only a small degree. Using data on the U.S., Pesta et al. (2010) report that state level estimates of intelligence are negatively correlated (r = −0.55) with a latent factor of religious belief (derived from seven items, including ‘I am certain God exists' and ‘Religion is very important to me’). Finley, Tang, and Schmeichel (2015) argued that the negative correlation between analytic thinking and religious belief arises when participants are put in an analytic thinking mindset prior to reporting their level of religious belief. However, Pennycook, Ross, Koehler, and Fugelsang (2016) showed that this is not the case. The authors showed that the negative association between performance on analytic thinking measures and religious belief holds even when the two measures are administered in separate surveys and concluded that there is a genuine association between analytic thinking and religious disbelief. Webster and Duﬀy (2016) re-analyzed data from Zuckerman et al. (2013) and Lynn et al. (2009) to test whether the intelligence-religiosity link is moderated and mediated, and the extent to which it generalizes across time, samples, measures, and levels of analysis. The authors reanalyzed Zuckerman et al.’s meta-analysis, and showed that the negative intelligence-religiosity link declined over time. The intelligencereligiosity link was found to be non-signiﬁcant among samples using men, pre-college participants, grade point average, and those collected
Corresponding author. E-mail addresses: [email protected]
(T.C. Souza), [email protected]
https://doi.org/10.1016/j.intell.2018.02.004 Received 2 July 2017; Received in revised form 15 February 2018; Accepted 15 February 2018 0160-2896/ © 2018 Elsevier Inc. All rights reserved.
Intelligence 68 (2018) 48–57
T.C. Souza, F. Cribari–Neto
of the impact of intelligence on religious disbelief after other conditioning eﬀects have been taken into account. Such studies thus aim at measuring the net impact of intelligence on the lack of religious beliefs. Using data on a large cross-section of nations, Cribari-Neto and Souza (2013) performed a beta regression analysis to estimate the functional form of such a net impact. They showed that the impact is positive, statistically signiﬁcant, gains strength up to a certain level and then weakens. In that analysis, nonetheless, the U.S. appears as an outlying observation, being much more religious than predicted by the statistical models on the basis of its per capita income and average IQ. For instance, according to the data used by Cribari-Neto and Souza (2013), 10.5% (34%) of the U.S. population is made of atheists (people who do not value religion in their daily lives) which contrasts with the model prediction for that country: 26.2% (60.8%). Even though the two regression models used by Cribari-Neto and Souza (2013) provide good overall ﬁts to the data, it is clear that the U.S. behaves substantially diﬀerently from what the empirical analysis predicted, displaying much lower prevalence of religious disbelief than it would be expected on the basis of the existing international evidence. We used the ﬁtted beta regression model of Cribari-Neto and Souza (2013) to obtain predictions for the prevalence of atheists in the U.S. varying IQ and ﬁxing all other covariates at their observed values. The results showed that the predicted and observed values roughly coincide when IQ is set at 90. Since the average intelligence quotient in the U.S. equals 98, it can be asserted that in what concerns religious beliefs Americans behave as if their IQ were 8 points lower than it really is. As noted by Berggren and Bjørnskov (2011), the least religious U.S. state (Vermont) is roughly on par with Spain and Switzerland whereas the most religious state (Mississippi) is placed along countries such as India, El Salvador and Malaysia. Hence, religion is, on average, substantially more important in the U.S. than in most other countries in the Western hemisphere. We thus believe that the U.S. deserves a separate analysis, and this is the motivation for this paper. In this paper, we use data on the 50 U.S. states to perform a beta regression analysis and estimate the net impact of average intelligence on the prevalence of religious disbelievers. Our results show that the functional form of that net impact is quite diﬀerent from the one found using data on many diﬀerent countries: it is strictly increasing, i.e., it does not weaken after peaking. The results also how that it is stronger outside the U.S. most religious area. We call that area ‘the Extended Bible Belt’, an area of the country that contains a large population of fundamentalist Christians who tend to interpret the Bible literally. The Bible Belt generally refers to a handful of states in the southeastern U.S. in which Evangelical Protestants are relatively more numerous than in other areas of the country. Additionally, there also exists in the Western United States a region called the Mormon Corridor, where the predominant religious denomination is The Church of Jesus Christ of Latter-day Saints. It includes the state of Utah. By Extended Bible Belt we mean the states whose entire territory (5 states) or most of it (8 states) belong to the Bible Belt plus Utah, more exactly: Arkansas, Texas, Oklahoma, Louisiana, Kentucky, Tennessee, Mississippi, Alabama, North Carolina, South Carolina, Virginia, Georgia, Missouri and Utah. We also perform a quantile regression analysis, which allows us to measure the impact of religious disbelief over the entire conditional distribution of the prevalence of religious disbelievers, and not only at its mean. The results we report show the impact of intelligence on religious disbelief becomes stronger as we move from the conditional distribution lower tail up to the median. Interestingly, from that point on the intensity of the impact of intelligence on religious disbelief slows down inside but not outside the Extended Bible Belt. We thus say that there is a ‘hurdle eﬀect’ that takes place in the U.S. most religious area. The paper unfolds as follows. Section 2 describes the data. In Section 3, we brieﬂy present the beta and quantile regression models, on which our results are based. Section 4 contains the results of our empirical analysis. In particular, we present impact curves that describe
after 2010. Education also partially mediated the intelligence-religiosity link. The authors also re-analyzed Lynn et al.’s data from 137 countries and found that quality of human conditions positively moderated and partially mediated the positive relation between IQ and disbelief in God; this link becomes non-signiﬁcant when one controls for spatial dependence. Based on a large cohort of adolescents (data from the National Longitudinal Study of Youth — NLSY97), Nyborg (2009) noted that atheists scored on average 1.95 IQ point higher than agnostics, 3.82 points higher than liberal persuasions, and 5.89 points higher than dogmatic persuasions. Religiosity declines between ages 12 to 17, but intelligence still modestly predicts central components of religiosity such as a sense of religious identiﬁcation and private religious practice. Using the NLSY97 data, Ganzach et al. (2013) modeled intelligence as a function of changes in religiosity and in intelligence over time and also of family characteristics. Their results suggest that even though education has an overall negative impact religiosity, the eﬀect does not hold for individuals with strong religious backgrounds; for such individuals education has a positive impact on religiosity. In contrast, education has a clear negative eﬀect on religiosity for those who come from secular backgrounds. Reeve and Basalik (2011) suggested that more intelligent individuals are more likely beneﬁt more from higher levels of education, which strengthen rational thinking and enable individuals to develop ways to understand the world without reference to supernatural forces. Stoet and Geary (2017) reported that higher levels of religiosity at the national level are associated with lower educational performance in mathematics and science. Kanazawa (2010) used large samples from the National Longitudinal Study of Adolescent Health and from the General Social Survey to show that there is a signiﬁcant negative association between intelligence and religiosity. Lewis, Ritchie, and Bates (2011) considered a large sample of U.S. adults and measured six dimensions of religiosity along with a multi-scale instrument to assess general intelligence. The results indicate that lower intelligence is most strongly associated with higher levels of fundamentalism. Yang and Lester (2016) investigated whether, at the aggregate level, the average IQ of residents of the U.S. states was associated with the states' economic performances (growth in per capita gross state product) and with negative economic indicators (foreclosure rates and credit card debt). The results showed that states with higher average IQs tend to display superior economic performance. Kanazawa (2006) found that his estimates of state IQs are moderately associated with gross state product per capita (r = 0.32). Using a sample of 81,000 adolescents, Damian, Su, Shanahan, Trautwein, and Roberts (2015) found a correlation of 0.18 between intelligence and later income. Additionally, U.S. states with higher average IQs are on average wealthier (Kanazawa, 2006; Strenze, 2007). The negative (positive) relationship between intelligence and religiosity (religious disbelief) is well established at both the individual and group level. i.e., it is robust to data aggregation. For instance, using U.S. data Reeve and Basalik (2011) found that the correlation between state IQ and state religiosity is − 0.55. Their state religiosity data came Pew U.S. Religious Landscapes Survey. Lynn et al. (2009) used worldwide data (country-level, 137 nations) and found that the correlation between IQ and religious disbelief (proportion of atheists) equals 0.60. At the individual level, Ganzach and Gotlibovski (2013) used data from the 1997 cohort of the National Longitudinal Survey of Youth (NLSY97), measured religiosity at diﬀerent ages based on ﬁve dichotomous items and found correlations between intelligence and religiosity that ranged from − 0.23 to − 0.30. It is also noteworthy that several diﬀerent measures of religiosity have been used in the literature. Even though the way one deﬁnes and measures religiosity may impact the magnitude of the correlation, the direction of such an association seems to be robust to how religiosity (or the lack of it) is measured. Regression analyses have been carried out to estimate the strength 49
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groups populate the region, as well as a range of religious denominations. The geographic area of the Bible Belt overlaps with the West South Central (Arkansas, Texas, Oklahoma and Louisiana), East South Central (Kentucky, Tennessee, Mississippi, and Alabama), South Atlantic (North Carolina, South Carolina, Virginia and Georgia) and West North Central (Missouri) Census Regions of the U.S. There also exists in the Western U.S. a region called the Mormon Corridor, where the predominant religious denomination is The Church of Jesus Christ of Latter-day Saints. It includes the state of Utah. Our deﬁnition of the Extended Bible Belt includes the Bible Belt plus the state of Utah. According to the Pew Center's Religious Landscape Study (2017),the percentage of adults in the U.S. who identify themselves as Evangelical Protestants is 25.4% whereas in North and South Carolina the ﬁgure is 35%, 46% in Arkansas, 49% in Kentucky, 52% in Tennessee (highest concentration of Evangelical Protestants), 41% in Mississippi, 49% in Alabama, 31% in Texas, 27% in Louisiana, 47% in Oklahoma, 36% in Missouri, and 38% in Georgia. Additionally, only 1.6% of the U.S. adult population are Mormons, the ﬁgure for Utah being 55%. As noted earlier, we chose to group together the states that are in the Bible Belt and Utah when deﬁning the Extended Bible Belt. Utah belongs to what is known as the Mormon Corridor, which also covers some areas of other states, such as Arizona, California, Idaho, Nevada and Wyoming. The only two states that are entirely or mostly covered by the Mormon Corridor are Utah and Arizona. Over 60% of all Utah residents are of members of The Church of Jesus Christ of Latter-day Saints whose world headquarter is located in Salt Lake City. Even though both literalist and somewhat non-literalist interpretations of the Bible are accepted in The Church of Jesus Christ of Latter-day Saints, the literalist view is dominant. In contrast, most Arizona residents are members of The Catholic Church, which is not known of widespreading literal interpretations of the Bible. For the purposes of our analysis, we thus decided to deﬁne a new religious belt, namely: The Extended Bible Belt. It includes the states that belong to the Bible Belt and Utah. A 2016 Gallup survey showed that Mississippi remains the most religious state in the U.S., with 59% of its residents classiﬁed as “very religious,” followed by Alabama (56%) and Utah (54%). Vermont is the least religious state: only 21% of its residents are very religious. Two other New England states, Maine and Massachusetts, are the secondand third-least religious states. There is no clear-cut answer as to why state-by-state diﬀerences in religiosity persist. Part of such diﬀerences relates to each state's culture, which in turn derives from many years of religious history. A state's religious culture also reﬂects its most dominant religion. Utah's majority-Mormon population and Southern states' strongly Protestant population, for example, are more likely to be more religious than the population of states where such religions are less dominant. One of the covariates we use is the percentage of Hispanic or Latino population. As noted by Jung, Schieman, and Ellison (2016), the Latino population has been growing rapidly, surpassing African Americans as the largest minority group. Latinos now make up over 16% of the U.S. population, their numbers being projected to increase up to 20% by 2030. The authors note that such trends give birth to Latino-oriented churches, hence transforming the religious landscape. Income is also expected to impact the prevalence of religious disbelief. For instance, Alam, Amin, and McCormick (in press) found that as income increases, people are less likely to be religious. The evidence presented by the authors also showed that religious people spend less time performing religious activities as their incomes rise. We consider the percentage of the total population living in urban areas as a possible conditioning variable to account for the fact that some states with high average intelligence such as Vermont and Maine have a relatively small fraction of their population living in urban areas. Since such a conditioning eﬀect may prove important we shall consider it. Table 2 contains some descriptive statistics on the variables used in
how average intelligence impacts the prevalence of religious disbelievers. Finally, Section 5 oﬀers some concluding remarks. 2. The data The Pew Research Center (www.pewforum.org) is a nonpartisan fact tank that informs the public about the issues, attitudes and trends shaping America and the world. It conducts the U.S. Religious Landscape Survey which is a benchmark for understanding religion in the U.S. The 2014 U.S. Religious Landscape Study was based on telephone interviews with more than 35,000 Americans from all ﬁfty states. It was the second time the Pew Research Center has conducted such a survey. The ﬁrst survey took place in 2007. Both surveys have margins of error of less than one percentage point for the full sample, making it possible to identify even relatively small changes in religious groups' share of the U.S. population. The Christian share of the U.S. population is in decline whereas the number of adults who do not identify themselves with any organized religion is on the rise. The 2014 Pew Religious Landscape Study found that the percentage of adults (ages 18 and older) who describe themselves as Christians dropped by nearly eight percentage points in just seven years, from 78.4% to 70.6% between 2007 and 2014. Over the same period, the percentage of Americans who are religiously unaﬃliated and describe themselves as atheist, agnostic or nothing in particular increased by more than six points, going from 16.1% to 22.8%. Our chief interest in this article lies in modeling the prevalence of atheists in the ﬁfty U.S. states. We measure it as the proportion of people who answered ‘no’ to the following question of the U.S. Religious Landscape Survey: “Do you believe in God or a universal spirit?” (NOGOD). As a measure of average intelligence, we use the state IQ scores computed by McDaniel (2006a). Such scores were obtained using the reading and math scores from the 4th and 8th grades National Assessment of Progress between 1991 and 2005. Since our interest lies in estimating the net impact of intelligence on religious disbelief, we have also collected data on other conditioning variables: median personal earnings (wages and salaries) for all workers, full- and part-time, age 16 and above (INCOME); percentage of the total population in urban areas (URB); percentage of Hispanic or Latino population (HISP); and a dummy variable that equals 1 if the state belongs to the Extended Bible Belt, and 0 otherwise (EXTBELT). We note that INCOME assumes values between 0 and 10. We considered several other covariates in our regression analysis, but IQ, URB, HISP, INCOME and EXTBELT were the variables that proved useful in explaining the behavior of NOGOD. Table 1 provides a brief description of the variables used in our empirical analysis. As explained hereinbefore, the Extended Bible Belt is deﬁned as containing 13 states in the Bible Belt plus Utah. The Bible Belt generally refers to a group of states in the southeastern U.S. in which Evangelical Protestants make up a larger portion of the population relative to other areas of the country (McClure, 2017). A variety of racial and ethnic Table 1 Variables used in the empirical analysis and their descriptions. Variable
NOGOD IQ URB
Proportion of atheist in USA in 2014 (http://www.pewforum.org) Average intelligence quotient (McDaniel, 2006a) Percentage of the total population living in urban areas on 2010 (http://www.icip.iastate.edu/tables/population/urban-pct-states) Percentage of Hispanic or Latino population in 2015 (https://www. census.gov) Income Index based personal earnings (wages and salaries) for all workers, full- and part-time, age 16 and above in 2010; assumes values in [0,10] (http://www.measureofamerica.org) Indicator variable that equals 1 if the state belongs to the Extended Bible Belt and 0 otherwise
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3.1. Beta regression
Table 2 Descriptive statistics on the continuous variables used in the empirical analysis.
NOGOD IQ INCOME URB HISP
0.02 94.20 3.22 38.70 1.60
0.07 98.48 4.02 65.10 4.83
0.09 100.80 4.32 73.75 9.20
0.09 100.30 4.60 73.59 11.36
0.11 102.70 5.16 86.95 13.45
0.21 104.30 6.71 95.00 48.00
0.40 0.03 0.18 0.20 0.87
Our variable of interest assumes values in the standard unit interval, i.e., in (0,1). The standard linear regression model is not appropriate for dependent variables of that nature. First, because the ﬁtted model may yield predicted values that are negative and/or greater than one. Second, because such variables are usually asymmetrically distributed and several inferences that are carried out in linear regression modeling are based on the assumption that the response is normally distributed. Third, because responses that assume values in the standard unit interval typically display non-constant variances. Fourth, because the marginal eﬀects (i.e., the individual impacts of the diﬀerent independent variables on the mean response) are typically not constant, but dependent on the values of the other regressors. Transforming the dependent variable so that it assumes values in the real line prior to using it in a linear regression analysis is also not appropriate since the regression coeﬃcients would need to be interpreted in terms of the mean of the transformed (artiﬁcial) variable, and not in terms of the mean of the original response, which is the variable that matters to the practitioner. A regression model speciﬁcally designed for dependent variables that assume values in (0,1) was introduced by Ferrari and Cribari-Neto (2004) and further generalized by Simas (2010). The main underlying idea is that the response (y) follows the beta law, i.e., that it is betadistributed. The two parameters that index the distribution, in the parameterization proposed by Ferrari and Cribari-Neto (2004), are the mean (μ) and the precision (ϕ); for a given mean value, the larger ϕ the smaller the response variance. Let y1,…,yn be independent random variables, each yt, t = 1,…,n, being beta-distributed with mean μt and precision parameter ϕt. The mean response is related to a set independent variables (covariates, regressors) as follows:
our analysis: minimum, ﬁrst quartile (Q1/4), median, mean, third quartile (Q3/4), maximum and coeﬃcient of variation (CV). In 75% of the states, the proportion of atheists does not exceed 0.11. The largest prevalence of atheists is 0.21. In half of the states, the average IQ does not exceed 100.80. The mean percentage of people who live in urban areas is approximately 74%, the smallest being 39%. The largest income index is 6.710, which is nearly twice the smallest value. The standard deviation of HISP equals 87% of the average. Vermont has the largest proportion of disbelievers (0.21). Other states with large prevalence of disbelievers are Massachusetts, Maine and New Hampshire. The states with the highest average IQs are Massachusetts, New Hampshire, North Dakota and Vermont. In contrast, Mississippi, Louisiana, California and Hawaii have the smallest average IQs. The states with the lowest prevalence of atheists belong to the Bible Belt: Alabama, Tennessee, Arkansas and Mississippi. The state with the highest income index is Maryland. The states with the largest percentage of Hispanics/Latinos are New Mexico, California and Texas. Table 3 contains the sample correlations between all pairs of continuous variables. Notice that NOGOD is positively correlated with all variables. The highest correlations of NOGOD are with IQ and INCOME (0.40). The correlation between NOGOD and IQ is highly statistically signiﬁcant as well as that between NOGOD and INCOME. IQ and INCOME are also positively correlated (0.24). It is noteworthy that the correlation between religious disbelief and IQ in the U.S. (0.44) is weaker than that found by Lynn et al. (2009) using data on 137 countries (0.60).
g (μt ) =
∑ βi xti , i=1
where the βi’s are unknown parameters and g(⋅) is a link function that maps the standard unit interval onto the real line, e.g., g(μt) = log(μt/ (1 − μt)), the logit link. The precision parameter ϕt is also related to a set of independent variables:
3. Regression models
h (ϕt ) =
Our interest lies in modeling the proportion of atheists in the ﬁfty U.S. states. In particular, we seek to determine whether the eﬀect of IQ on religious disbelief in the U.S. is statistically signiﬁcant after the impacts that other conditioning variables exert on religious disbelief have been accounted for. For instance, average intelligence and income are positively correlated, and they both negatively correlate with religious disbelief. Is the net impact of average intelligence on religious disbelief (i.e., after conditioning on income and other relevant variables) statistically signiﬁcant? If so, is it strong or weak? In order to provide such questions with answers we shall perform a regression analysis. Two diﬀerent regression modeling strategies will be used, namely: (i) beta regression, and (ii) quantile regression.
∑ γi z ti. i=1
Here, the γi’s are unknown parameters and h(⋅) is a link function that maps the set of positive real numbers onto the real line, e.g., h (ϕt) = log(ϕt), the log link. It is noteworthy that the response distribution can be symmetric or asymmetric (to the left or to the right). There is thus no symmetry assumption. It should also be noted that all regression parameters can be interpreted in terms of the mean response, μt. Parameter estimation is typically performed by maximum likelihood. For further details on beta regression, see Cribari-Neto and Zeileis (2010). 3.2. Quantile regression The beta regression model, like the standard linear regression model, focuses on modeling the mean of the variable of interest, i.e., the interest lies in measuring the impacts of a set of independent variables on the mean response. In other words, one models mean eﬀects. A diﬀerent and somewhat more general approach was introduced by Koenker and Bassett (1978): the quantile regression model. It allows practitioners to model a given quantile of the distribution of variable of interest as a function of a set of covariates. It is noteworthy that by carrying out the analysis at diﬀerent quantiles (e.g., from 0.1 to 0.9) one can estimate the impacts of the covariates at diﬀerent regions of the conditional distribution of y. For instance, it is possible to evaluate such impacts in the distribution lower tail, around the median (the central
Table 3 Pairwise sample correlations between proportion of atheists in USA (NOGOD), average intelligence (IQ), Income Index (INCOME), percentage of the population in urban areas (URB) and percentage of Hispanic or Latino population (HISP).
NOGOD IQ INCOME URB HISP
– 0.44* 0.40* 0.11 0.11
– – 0.24* − 0.14 − 0.33*
– – – 0.56* 0.18
– – – – 0.57*
* Signiﬁcantly diﬀerent from zero at the 10% signiﬁcance level.
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average intelligence impacts religious disbelief obtained using data on 124 countries (Cribari-Neto & Souza, 2013) hold for the ﬁfty U.S. states. Our previous analysis was based on beta regression modeling. In this subsection we shall pursue the same approach. In our previous paper we answered the following question: Is there a statistically signiﬁcant relationship between intelligence and religious disbelief after accounting for the impacts of other relevant conditioning variables? The results showed that such an impact is always positive, being weaker at low intelligence levels and much stronger around a peak that takes place when the average intelligence quotient equals 105. In that article, we noted that although the average IQ in the United States is high, the proportion of people who do not consider religion important in their daily lives is low relative to countries with similar average intelligence quotients. The U.S. thus deserves a separate analysis. Our interest lies in modeling the proportion of atheists in the U.S. The dependent variable (y) in our analysis is the proportion of atheists in each of the ﬁfty U.S. states. It assumes values in the standard unit interval, i.e., in (0,1). We use several conditioning variables, such as average intelligence (IQ), a measure of income (INCOME), percentage of the total population in urban areas (URB), percentage of Hispanic or Latino population (HISP) and a dummy variable that equals 1 if the state belongs to the Extended Bible Belt, and 0 otherwise (EXTBELT). We shall use the class of beta regressions, which, as noted earlier, is tailored to handling data that assume values in the standard unit interval. All estimations were carried out using the betareg package developed for the R statistical computing environment (R Core Team, 2014); see Cribari-Neto and Zeileis (2010). For details on the R statistical computing environment, see https://www.r-project.org. Model selection was performed using sequential testing and residual analyses. At the outset, we use the likelihood ratio test to test the null hypothesis of ﬁxed precision, i.e., ℋ0 : ϕ1 = ϕ2 = ⋯ = ϕn = ϕ, which is rejected at the usual signiﬁcance levels. We thus conclude that precision is variable, i.e., that the precision parameter varies across observations. After an exhaustive process of model selection, we arrived at the following beta regression model:
region of the distribution) and also in the distribution upper tail. By doing so, the practitioner is oftentimes able to gain more complete knowledge on how each independent variable impacts the variable of interest. The linear quantile regression model is deﬁned as k
Q yt (τ ) =
∑ βτ ,i xti , i=1
where the βτ,i’s are unknown parameters and Q yt (τ ) denotes the τth conditional quantile of yt (0 < τ < 1), i.e., the τth quantile of yt given xt. Notice that Q yt (0.5) is the distribution median. The regression coeﬃcients are estimated using an asymmetric absolute loss function. For details, see Koenker and Bassett (1978). The coeﬃcient estimates are frequently viewed as being analogous to standard linear regression estimates, albeit for diﬀerent points of the dependent variable conditional distribution. It is less commonly recognized, however, that quantile regression can produce estimates of changes in the entire dependent variable distribution in response to changes in the explanatory variables' values (McMillen, 2012). As noted hereinbefore, the analysis is not restricted to the distribution mean, but can be carried out at diﬀerent quantiles of the response distribution, from the lower tail to the upper tail. Quantile regression can be easily used with responses that assume values in the standard unit interval, which is our interest in this paper. One can transform the variable so that it assumes values in the real line, carry out the regression analysis, and then use the inverse transformation to obtain coeﬃcients that measure the impacts of the changes in the covariates on the quantiles of the variable of interest. This is possible because, unlike the mean, quantiles enjoy what is known as the invariance property. Such a property can be formally stated as follows. For any random variable Z and for any monotone real function g, Qg(Z)(τ) = g(QZ(τ)). As an illustration, suppose that yt assumes values in (0,1) and let g(⋅) be the logistic function, i.e., g(a) = log(a/(1 − a)). Notice that g(yt) assumes values in the real line. The τth quantile regression of g(yt) is Qg (yt ) (τ ) = βτ ,1 + βτ ,2 x t 2 + ⋯+βτ , k x tk . It follows from the equivariance property of quantiles that
Q yt (τ ) =
exp(βτ ,1 + βτ ,2 x t 2 +⋯+βτ , k x tk ) 1 + exp(βτ ,1 + βτ ,2 x t1+⋯+βτ , k x tk )
cloglog (μt ) = β1 + β2 IQt + β3 EXTBELTt + β4 HISPt + β5 INCOMEt +β6 URBt + β7 INCURBt log(ϕt ) = γ1 + γ2 IQt ,
t = 1,…,50, where INCURBt is the interaction between INCOMEt and URBt. Parameter estimates and the corresponding z-tests p-values are presented in Table 4. The covariates IQ, HISP, INCOME and URB positively impact the mean proportion of atheists, i.e., we conclude that the prevalence of atheists tends to be higher in states where average intelligence is higher, salaries are higher, more people live in urban areas and also where there are more Hispanics/Latinos. In contrast, the covariate EXTBELT exerts a negative eﬀect on the mean response, i.e., all else being equal there tends to be fewer atheists in the Extended Bible Belt (Bible Belt states plus Utah). The estimated precision submodel also leads to an interesting conclusion. We note that precision is inversely related to average intelligence, i.e., dispersion increases with IQ. The
Once parameter estimates are obtained, inference on Q yt (τ ) can be performed by applying the inverse transform in given in Eq. (1). For further details on quantile regression, see Koenker (2005). 4. Empirical modeling In what follows, we shall present the results of two empirical analyses, one that uses the beta regression model (Section 4.1) and another that makes use of the logistic quantile regression model (Section 4.2). The variable of interest (response) is the proportion of atheists in the ﬁfty U.S. states. We consider several conditioning variables, such as average intelligence, percentage of the population living in urban areas, percentage of Hispanics or Latinos in the population, a measure of income and an indicator as to whether the state is in the Extended Bible Belt. In Section 4.3, we show that the results of our two empirical analyses are not sensitive to the dependent variable we use. Similar inferences are obtained when we model the proportion of people who do not perceive religion as important in their lives instead of the proportion of atheists. The impact measures we compute are conditional on there existing a causal relationship involving intelligence and religious disbelief.
Table 4 Parameter estimates and z-tests p-values for the ﬁtted beta regression model (mean and precision submodels); response: proportion of atheists in the U.S. states.
Intercept IQ EXTBELT HISP INCOME URB INCURB
4.1. Beta regression modeling In this paper, we examine whether our previous ﬁndings on how 52
−9.0960 0.0362 −0.4990 0.0077 0.6698 0.0353 −0.0074
< 1 × 10−6 0.0321 < 3 × 10−6 0.0524 0.0607 0.0634 0.0824
24.6476 −0.1960 – – – – –
1 × 10−4 0.0086 – – – – –
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0.008 0.006 0.004 0.000
We then pose the following question: How would the prevalence of religious disbelievers be impacted if average intelligence in all ﬁfty U.S. were equal to 104.30, the maximal value? Using the ﬁtted beta regression model and contingent on a causal relationship between intelligence and religious disbelief, we computed the predicted values ( μt̂ ) for all states by setting IQ = 104.30 and the remaining covariates at their observed values. We then multiplied the predicted proportions of atheists by the corresponding total populations and added such values to get an estimate of the total number of atheists in the country. The results indicate that if average intelligence in all ﬁfty U.S. states were equal to the maximal value (104.30), all else being equal, the total number of religious disbelievers in the country would jump from 29,335,134 (observed value) to 34,912,828, an increase of 19%. It is worth noting that in our analysis we considered several alternative models. In particular, we considered the inclusion in the model of a conditioning variable related to education. Schwadel (2016) used four waves of longitudinal data for the U.S., with respondents ranging in age from 13 to 29, to model the within- and between-person eﬀects of higher education on several measures of religiosity. The author showed that earning a bachelor's degree is associated with withinperson declines in some but not all measured aspects of religiosity, which partially supports the argument that higher education causes religious decline. Arias-Vazquez (2012) found evidence of a negative impact of education on religiosity. Alam et al. (2017) used American Time Use Survey data and a two-part econometric model to investigate the relationship of income and education to religiosity in the U.S. They found that people with an associate's, bachelor's, or master's degree are more likely to be religious than people with no high school degree. However, among religious people, additional education is associated with less time devoted to religious activities. Their results, albeit mixed, contradict those of Arias-Vazquez (2012). In our analysis, we tried to include a covariate (EDUC) related to education in the candidate models, more speciﬁcally the Education Index (http://www.measureofamerica.org), which is based on two subindices: an Educational Attainment Index and an Enrollment Index. The Educational Attainment Index measures the overall level of educational attainment achieved by the adult population. It takes into account the percentage of the population age 25 years and older with at least a high school diploma or equivalent, the percentage with at least a bachelor's degree, and the percentage with an advanced degree. The Enrollment Index is based on a net enrollment calculation that takes into account the total number of students enrolled in school divided by the total school-aged population of 3 to 24-year-olds. These two components are combined into the Education Index. We note that the correlation between IQ and EDUC is positive and large: r = 0.66. It is also noteworthy that North Dakota has high average IQ (103.8) but relatively low Education Index (4.71, smaller than the median value). We selected the best ﬁtting model that includes EDUC as a regressor (MEDUCIQ). Its mean regressors are EDUC, EDUC2, IQ, HISP, URB and HISPIQ, and the precision regressor is IQ, where EDUC2 is the square of EDUC and HISPIQ denotes the interaction between IQ and HISP. The link functions for the mean and precision submodels are, respectively, log-log and log. Interestingly, EDUC loses statistical signiﬁcance when EXTBELT, the Extended Bible Belt indicator, is included in the model. Let MIQ denote the model used in our beta regression analysis. It has larger pseudo-R2 (0.55 v. 0.49), i.e., it explains better the variations in the dependent variable than the alternative model. Our model is also favored by the AIC (−217.88 v. −212.35) and BIC (−200.67 v. −195.15). The two models (MEDUCIQ and MIQ) are non-nested, i.e., no model can be obtained by imposing restrictions on the parameters that index the other model. In order to select the best ﬁtting model on the basis of a hypothesis test, we use the J and MJ tests as described in Cribari-Neto and Lucena (2015, 2017). Since the sample size is small, we use bootstrap resampling with 1000 bootstrap replications; for details on the bootstrap method, see Davison and Hinkley (1997). Model MIQ is not rejected in favor of model MEDICIQ at the 5% signiﬁcance level (p-
outside the Extended Bible Belt inside the Extended Bible Belt
Fig. 1. Net impact of intelligence on the mean prevalence of atheists; the curves are the estimates of the impact measure presented in Eq. (2) computed by setting the continuous covariates at their median values, EXTBELT = 0 (outside the Extended Bible Belt) and EXTBELT = 1 (inside the Extended Bible Belt).
ratio between the largest and smallest estimated precisions equals 7.24 and the pseudo-R2 (as deﬁned by Ferrari and Cribari-Neto, 2004), which is an overall measure of goodness-of-ﬁt, equals 0.55. Thus, our model explains 55% of the variation in the prevalence of atheists across diﬀerent states. Our chief interest lies in measuring the impact of average intelligence on the prevalence of atheists. More speciﬁcally, we wish to assess how changes in average intelligence impact the mean prevalence of atheists when all other relevant conditioning variables are held constant. Following Cribari-Neto and Souza (2013), we use the following measure of impact: ∂μt/∂IQt, where μt = (NOGODt ) . Here,
∂ (NOGODt ) = − exp(−exp(β1 + β2 IQt + β3 EXTBELTt + β4 HISPt ∂IQt + β5 INCOMEt + β6 URBt + β7 INCURBt )) × (−exp(β1 + β2 IQt + β3 EXTBELTt + β4 HISPt + β5 INCOMEt + β6 URBt + β7 INCURBt )) × β2. (2) Fig. 1 shows the estimated impacts of intelligence on the mean prevalence of atheists for states that belong (EXTBELT = 1) and do not belong (EXTBELT = 0) to the Extended Bible Belt. The values of the remaining covariates are ﬁxed at their medians. Notice that the impact varies with IQ, i.e., it is not constant. The estimated impact is always positive for both groups of states (EXTBELT = 0 and EXTBELT = 1): the larger the average intelligence quotient the larger the predicted mean proportion of atheists. That is, religious disbelief tends to increase with IQ. We note that the estimated impact is stronger in states that do not belong to the Extended Bible Belt. For instance, when IQ = 95,100,105 and EXTBELT = 0, the estimated impacts of intelligence on the prevalence of atheists are 0.00285, 0.00337 and 0.00394, respectively; for EXTBELT = 1, the corresponding ﬁgures are 0.00179 0.00213 and 0.00251. Additionally, the distance between the two impact curves increases with IQ. It is also noteworthy that the two impact curves for the U.S. are quite distinct from that computed using data on 124 countries (Cribari-Neto & Souza, 2013) which increases up to a certain point and then decreases, i.e., the eﬀect peaks (around IQ = 105) and then weakens. In contrast, the impact of average intelligence on the prevalence of atheists in the U.S. is strictly increasing. As noted earlier, the largest average IQ equals 104.30; see Table 2. 53
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The previous analysis focused on mean eﬀects, i.e., on the impact of average intelligence on the prevalence of atheists at the mean of the conditional distribution of the proportion of atheists. We shall now evaluate how such an impact varies over the entire conditional distribution. To that end, we shall use quantile regression modeling. Since the dependent variable assumes values in the standard unit interval, we shall use its logistic transform in the regression analysis and then use the inverse transformation to obtain estimated impacts on the original scale. Recall that such an approach is valid because of the equivariance property enjoyed by quantiles. The dependent variable we use in the quantile regression speciﬁcation is
conditional response quantile when all other conditioning variables are held constant. For instance, when IQ increases by one unit, the 0.30th quantile of the logit of the proportion of atheists is estimated to increase by 0.0406 whereas for the 0.70th quantile the increase amounts to 0.0560. In the middle region of the conditional distribution (median) a unit increase in IQ leads to an increase in the logit of proportion of atheist of 0.0415. When URB increases by one unit (i.e., one percentage point) the 0.10th (0.90th) conditional quantile of the response is expected to increase by 0.0091 (decrease by 0.0002). It is interesting to note that such a regressor has most impact on the prevalence of atheists in the lower half of the conditional distribution, i.e., up until the median. It is possible to graphically display a given covariate net impact along the entire response conditional distribution. A typical graphical representation of quantile regression coeﬃcients shows how each regression coeﬃcient changes as we move from lower to upper conditional quantiles. This is what we present in Fig. 2 for two regressors: IQ and EXTBELT. The shaded gray area depicts a 90 % pointwise conﬁdence interval for the quantile regression parameter. Notice that, overall, the strength of the IQ eﬀect slopes upward as we move from lower to upper quantiles. It is also interesting to note that the negative impact of EXTBELT is more pronounced at the lower and upper tails of the response conditional distribution. Our chief goal, as noted earlier, is to estimate the net impact of intelligence on the prevalence of atheists in the U.S. In the previous subsection, we estimated such an impact at the mean of the response conditional distribution. We shall now evaluate it at the diﬀerent quantiles. We wish to estimate
NOGODt ⎞ logit (NOGODt ) = log ⎛ . − NOGODt ⎠ 1 ⎝
∂η (τ ) ∂Qτ (yt ) ∂Qτ (yt ) = × t , ∂IQt ∂IQt ∂ηt (τ )
All estimations were carried out using the quantreg package (https:// cran.r-project.org/web/packages/quantreg) developed for the R statistical computing environment. The following quantile regression model was selected for the τth conditional quantile:
where ηt (τ ) = ∑i = 1 βτ , i x ti . It follows from the estimated model and from the equivariance property of quantiles that
value = 0.0883) whereas model MEDUCIQ is rejected in favor of model MIQ at the 5% signiﬁcance level (p-value = 0.0309). We have also carried out the MJ test. The null hypothesis that one of the models is the correct model is not rejected at the 5% signiﬁcance level (pvalue = 0.0819). The MJ model selection strategy picks Model MIQ, i.e., the model used in our empirical analysis. Our results are in line with the evidence reported in the meta-analysis of Zuckerman et al. (2013). They report that the prevailing evidence is that controlling for education does not have much of an eﬀect in the intelligence–religiosity relation whereas controlling for intelligence leads to a somewhat greater change in the education religiosity relation. On page 338 of their paper, they conclude in favor of the view that intelligence accounts for the education–religiosity relation. 4.2. Logistic quantile regression modeling
(NOGODt ) (τ )
∂Qτ (NOGODt ) = β2, τ × exp(β1, τ + β2, τ IQt + β3, τ EXTBELTt + β4, τ HISPt ∂IQt + β5, τ URBt )/[1 + exp(β1, τ + β2, τ IQt + β3, τ EXTBELTt
= β1, τ + β2, τ IQt + β3, τ EXTBELTt + β4, τ HISPt + β5, τ URBt ,
+ β4, τ HISPt + β5, τ URBt )]2 ,
t = 1,…,50. We consider ﬁve diﬀerent quantiles, namely: τ = 0.10, 0.30, 0.50, 0.70, and 0.90. The estimated regression coeﬃcients for diﬀerent quantiles are reported in Table 5 along with the corresponding p-values. The latter were obtained using standard errors computed via the wild bootstrap as proposed by Feng, He, and Hu (2011). Such pvalues were computed using 1000 bootstrap samples. The quantile regression coeﬃcients are all signiﬁcantly diﬀerent from zero at the 10% signiﬁcance level at nearly all considered quantiles. The model intercept is signiﬁcantly diﬀerent from zero for all quantiles. The estimated coeﬃcient of each continuous regressor can be interpreted as the impact of a unit increase in that regressor on the τth
(3) t = 1,…,50. Fig. 3 shows the estimated net impact of intelligence on the τth quantile of the proportion of atheists for states that belong (EXTBELT = 1) and do not belong (EXTBELT = 0) to the Extended Bible Belt. The values of the remaining covariates (URB and HISP) are ﬁxed at their medians. It is noteworthy that: (i) All estimated impacts are strictly increasing, i.e., they become stronger as average intelligence increases; (ii) The estimated impacts are stronger outside the Extended Bible Belt, which is in agreement with the results presented in the previous subsection; (iii) The estimated impacts become stronger as we move from the lower to the upper tail of the conditional distribution; (iv) Unlike what happens outside the Extended Bible Belt, in that region the impact slows down after the conditional median, more so at low average intelligence levels. Table 6 contains the estimated net impacts of intelligence at the τth quantile of the response (prevalence of atheists) conditional distribution. We present results for IQ = 95, 100, and 105 and for EXTBELT = 0, 1 (i.e., outside and inside the Extended Bible Belt — EBB). The remaining covariates were ﬁxed at their median values. We note again that the impact of intelligence on the proportion of atheists is stronger outside the Extended Bible Belt. For instance, when IQ = 105 and τ = 0.10 or τ = 0.90, the impact of intelligence on prevalence of atheists is approximately 1.7 times stronger outside the Extended Bible Belt. The ﬁgures in Table 6 also show that the impact of intelligence on the prevalence of atheists slows down as we move above the conditional
Table 5 Parameter estimates for τ-regression quantiles, τ being the selected quantile of the response conditional distribution; p-values presented below the estimates; response: proportion of atheists in the U.S. states.
Intercept IQ EXTBELT HISP URB
τ = 0.10
τ = 0.30
τ = 0.50
τ = 0.70
τ = 0.90
−5.6115 0.0998* 0.0217 0.5330 −0.6136 0.0026* 0.0152 0.0411* 0.0091 0.0944*
−7.6557 0.0017* 0.0406 0.0742* −0.3328 0.0012* 0.0012 0.8943 0.0158 0.0054*
−7.2261 0.0027* 0.0415 0.0580* −0.3573 0.0021* 0.0098 0.0537* 0.0089 0.0640*
−7.9532 0.0056* 0.0560 0.0408* −0.4748 0.0043* 0.0070 0.2797 0.0021 0.7849
−6.9019 0.0002* 0.0507 0.0029* −0.6833 < 0.0001* 0.0021 0.6955 −0.0002 0.9624
* Signiﬁcantly diﬀerent from zero at the 10% signiﬁcance level.
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Fig. 2. Estimates (dash dot) and the 90% conﬁdence bands (shaded gray areas) for the regression coeﬃcients associated with IQ (left panel) and EXTBELT (right panel) for τ = 0.10,0.15, …,0.90.
median in the Extended Bible Belt, but not outside that region, i.e., they point to the existence of a ‘hurdle eﬀect’ that only takes place in the most religious area of the country. Consider, for instance, the ratio between (i) the diﬀerence between the impacts at τ = 0.90 and τ = 0.50 and (ii) the diﬀerence between the impacts at τ = 0.50 and τ = 0.10. Inside (outside) the Extended Bible Belt that ratio equals 0.55, 0.60 and 0.64 (1.30, 1.29 and 1.26) for IQ = 95, 100, and 105, respectively. The results from our quantile regression analysis thus reveal an important and clear diﬀerence between the impact of intelligence on the prevalence of atheists inside and outside the U.S. most religious area: inside that area the impact, at any given level of average intelligence, albeit positive, loses strength above the conditional median (i.e., where the prevalence of atheists is already above the conditional median); outside that deeply religious area, in contrast, the impact keeps gaining strength beyond the median. A natural question that arises is: What is the driving force behind the identiﬁed hurdle eﬀect? Diﬀerent driving forces may be at work. The ﬁrst explanation for identiﬁed hurdle eﬀect relates to the idea of preference falsiﬁcation as outlined by Kuran (1987, 1995). Assume that describing oneself as religious is more socially desirable in the Extended Bible Belt than outside it. It follows that those who are intent on appearing socially desirable and live in the Extended Bible Belt (but not those living elsewhere) will over-report religious beliefs. Such individuals will more likely be the more intelligent because intelligent
Table 6 Estimated net impacts of intelligence on the proportion of atheists for τ = 0.10, 0.50, 0.90; IQ is ﬁxed at 95, 100 and 105, EXTBELT = 1 (inside the EBB) and EXTBELT = 0 (outside the EBB). τ
Inside the EBB
Outside the EBB
95 100 105 95 100 105 95 100 105
0.00066 0.00073 0.00080 0.00207 0.00250 0.00297 0.00284 0.00356 0.00436
0.00115 0.00127 0.00138 0.00283 0.00338 0.00397 0.00502 0.00611 0.00723
people are more likely than others to work in careers that require the pretense of socially desirable beliefs (e.g., those in managerial positions). A noteworthy implication is that as IQ keeps rising and true religious belief keeps falling, sooner or later a threshold will be reached beyond which bright people will realize that everyone else is a disbeliever as well, hence being acceptable to be an atheist. A second driving force behind the hurdle eﬀect involves the extent to which religion percolates through other institutions in the U.S. most religious area. Barton (2010) notes that in the Bible Belt, “Christian
outside the Extended Bible Belt
0.10 0.50 0.90
0.10 0.50 0.90
inside the Extended Bible Belt
Fig. 3. Net impact of intelligence (IQ) on the τth quantile of the prevalence of atheists (NOGOD), τ = 0.10, 0.50, and 0.90; the curves are the estimates of the impact measure presented in Eq. (3) computed by setting the continuous covariates at their median values, EXTBELT = 0 (outside the Extended Bible Belt) and EXTBELT = 1 (inside the Extended Bible Belt).
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signiﬁcant in the U.S.? If so, is it strong or weak? Does it vary with average intelligence, i.e., is it stronger for certain levels of average intelligence? Is it constant along the diﬀerent quantiles of the prevalence of atheism conditional distribution? Is such an impact similar to that documented in the literature for a large cross section of countries? In this paper we answer such questions. We used data on all ﬁfty U.S. states and performed two separate regression analyses. They were based on a model that is tailored to dependent variables that assume values in the standard unit interval (beta regression model) and on a model in which each quantile of the response distribution is aﬀected by a set of independent variables (quantile regression). In both analyses, we sought to measure the impact of average intelligence on religious disbelief. The evidence we reported shows that the net impact of average intelligence on the prevalence of atheism (proportion of atheists in the U.S. states) is statistically signiﬁcant, strictly increasing with IQ, and stronger outside the Extended Bible Belt (Bible Belt states plus Utah). It is noteworthy that previous results obtained using data on over 100 countries found that the impact of average intelligence on the prevalence of atheism peaks and then weakens; see Cribari-Neto and Souza (2013) who have also used beta regression modeling. That does not happen in the U.S., where such an impact was shown to be strictly increasing. Unlike previous studies, we used quantile regression to estimate the net impact of average intelligence on the prevalence of atheism at diﬀerent quantiles of the response conditional distribution. Most regression analyses only evaluate the impacts of a set of auxiliary variables at the response distribution mean, that is, they focus on a single point of the variable of interest conditional distribution. By using the quantile regression model, we sought to overcome that shortcoming, i.e., we sought to measure the impact of each independent variable at diﬀerent points of the response conditional distribution, ranging from its lower tail to its upper tail. Our ﬁndings showed that the impact of average intelligence on the prevalence of atheists is weaker at low quantiles and more intense at higher quantiles. Interestingly, the results point to the existence of a hurdle eﬀect that only takes place in the Extended Bible Belt: the impact of intelligence on the prevalence of religious disbelief slows down above the conditional median of the latter (i.e., where the prevalence of atheists is already higher for a given level of average intelligence) inside but not outside the Extended Bible Belt. The causes of the hurdle eﬀect we identiﬁed should be better studied. An explanation we oﬀered relates preference falsiﬁcation. Individuals who are intent on appearing socially desirable and live in the Extended Bible Belt will over-report religious beliefs. Such individuals will more likely be the more intelligent because intelligent people are more likely than others to work in careers that require the pretense of socially desirable beliefs (e.g., those in managerial positions). A second driving force behind the hurdle eﬀect lies in the fact that Christian fundamentalism percolates through nonreligious institutions considerably more inside than outside the U.S. most religious area. As a result of such driving forces, beyond the conditional median of the distribution of religious disbelievers (where the prevalence of such individuals is already high), the net effect of intelligence on religious disbelief looses strength inside but not outside the Extended Bible Belt. A third driving force is that the conﬂict between science/reason and religion is more intense in the Extended Bible Belt, thus making people more immune to evidence and logical arguments, hence exerting a negative impact on the prevalence of religious disbelievers. It is also noteworthy that our results indicate that, all else being equal and contingent on there existing a causal relationship between the relevant variables, if average intelligence in all ﬁfty U.S. states were equal to the maximal value (i.e., to the maximal average intelligence, 104.30), the total number of religious disbelievers in the country would be expected to increase by approximately 20%. Finally, our empirical analysis is not without limitations. Since we use state level data the results are based on a sample of only ﬁfty
fundamentalism exerts a powerful inﬂuence on a wide range of local nonreligious institutions like schools and workplaces. Social norms about religious practices and the public presentation of one's Christian identity diﬀer in the Bible Belt relative to other parts of the United States.” In the Extended Bible Belt, nonreligious arenas of public life are much more impacted by religious fundamentalism than in other areas of the country which may be yet another cause for the hurdle eﬀect we identiﬁed. A third and ﬁnal driving force relates to the conﬂict between science and religion. Science and reason are based on facts whereas religion is, at least in part, based on revelation and Scripture. Such a conﬂict is more evident and also more intense when a sacred text such as the Bible is interpreted rather literally. Take, e.g., public acceptance of Darwin's evolution theory. Several Protestant denominations endorse some form of creationism, hence not accepting evolution by natural selection. It is thus expected that the conﬂict between religion and science be more dominant where a literalist interpretation of the Bible prevails. Consider, for instance, data from the 2014 Religious Landscape Study on views about human evolution, more speciﬁcally the percentage of adults that accept evolution as a natural process. Inside the Extended Bible Belt the mean ﬁgure is 23.8% whereas outside that region the mean acceptance rate of evolution by natural selection equals 35.7%. That is, outside the Extended Bible Belt public acceptance of evolution as a natural process is 50% higher than inside the U.S. most religious area. The more intense the conﬂict between science/reason and religion/faith the more immune people tend to be to evidence and logical arguments. To a lesser degree relative to the general population, that probably also holds for more intelligent individuals, thus exerting a negative impact on the prevalence of religious disbelievers. Finally, the ﬁtted quantile regression model with τ = 0.50 (median) implies, contingent on a causal relationship between intelligence and religious disbelief, that if average intelligence in all ﬁfty U.S. states were equal to the maximal average intelligence (104.30), the total number of atheists in the country would be expected to increase from 29,335,134 to 35,575,357, a variation of 21%. This result is similar to that obtained using the ﬁtted beta regression model (19%). Notice that the latter is based on the mean predictions whereas the former is based on median predictions. 4.3. A diﬀerent dependent variable In the empirical analyses presented the previous subsections, we modeled the proportion of atheists in the ﬁfty U.S. states. It is noteworthy that similar results are obtained when a diﬀerent response is used, namely: the proportion of people that do not consider religion important in their lives (NORELIG). The two dependent variables are highly correlated: the correlation coeﬃcient between them equals 0.91. The correlation between NORELIG and IQ equals 0.40, i.e., it is slightly smaller than that of NOGOD and IQ (0.44). The total number of people who do not value religion is approximately 19% larger than the total number of atheists. For brevity, we shall not report the results obtained with the new response. We note, nonetheless, that the ﬁtted beta regression now predicts that if average intelligence in all ﬁfty states were equal to the maximal value (104.30) and accepting a causal relationship between intelligence and religious disbelief, there should be an increase in the number of people who do not value religion of nearly 23%. (Recall that the corresponding ﬁgure obtained in Section 4.1 was 19%.) The ﬁtted quantile regression with τ = 0.50 (median) predicts that such an increase would be of 22%. (Recall that the corresponding ﬁgure in the previous subsection was 21%.) The impact of intelligence on religious disbelief is now slightly stronger. 5. Concluding remarks Is the net impact (i.e., after accounting for other conditioning effects) of average intelligence on the prevalence of atheism statistically 56
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observations. Future research should try to obtain results using less aggregated data.
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