As control variables, I include year born, education and income (expressed as relative ranks within each country) and the year the data were gathered (between 2002 and 2010).

Some of the findings so far:

- In almost every country, younger people are less religious.
- In most countries, people with more education are less religious.
- In about half of the 34 countries, people with lower income are less religious. In the rest, the effect (if any) is too small to be distinguished from noise with this sample size.
- In most countries, people who watch more television are less religious.
- In a fewer than half of the countries, people who listen to more radio are less religious.
- The results for newspapers are similar: only a few countries show a negative effect, and in some countries the effect is positive.
- In almost every country, people who use the Internet are less religious.
- There is a weak relationship between the strength of the effect and the average degree of religiosity: the negative effect of Internet use on religion tends to be stronger in more religious countries.

In the previous article, I measured effect size using the parameters of the regression models: for logistic regression, the parameter is a log odds ratio, for linear regression it is a linear weight. These parameters are not useful for comparing the effects of different factors, because they are not on the same scale, and they are not the best choice for comparing effect size between countries, because they don't take into account variation in each factor in each country.

For example, in one country the parameter associated with Internet use might be small, but if there is large variation in Internet use within the country, the net effect size might be greater than in another country with a larger parameter, but little variation.

#### Effect size

So my next step is to define effect size in terms that are comparable between factors and between countries. To explain the methodology, I'll use the logistic model, which predicts the probability of religious affiliation. I start by fitting the model to the data, then use the model to predict the probability of affiliation for a hypothetical respondent whose values for all factors are the national mean. Then I vary one factor at a time, generating predictions for hypothetical respondents whose value for one factor is at the 25th percentile (within country) and at the 75th percentile. Finally, I compute the difference in predicted values in percentage points.

As an example, suppose a hypothetically average respondent has a 45% chance of reporting a religious affiliation, as predicted by the model. And suppose the 25th and 75th percentiles of Internet use are 2 and 7, on a 7 point scale. A person who is average in every way, but with Internet use only 2 might have a 47% chance of affiliation. The same person with Internet use 7 might have a 42% chance. In that case I would report that the effect size is a difference of 5 percentage points.

As in the previous article, I run this analysis on about 200 iterations of resampled data, then compute a median and 95% confidence interval for each value.

#### Quadratic age model

Before I get to the results, there is one other change from the previous installment: I added a quadratic term for year born. The reason is that in preliminary results, I noticed that Internet had the strongest negative association with religiosity, followed by television, then radio and newspapers. I wondered whether this pattern might be the result of correlation with age; that is, whether younger people are more likely to consume new media and be less religious. I was already controlling for age using yrborn60 (year born minus 1960) but I worried that if the relationship with age is nonlinear, I might not be controlling for it effectively.

So I added a quadratic term to the model. Here are the estimated parameters for the linear term and quadratic term:

In many countries, both parameters are statistically significant, so I am inclined to keep them in the model. The sign of the quadratic term is usually positive, so the curves are convex up, which suggests that the age effect might be slowing down.

Anyway, including the quadratic term has almost no effect on the other results: the relative strengths of the associations are the same.

#### Model 1 results

Again, the first model uses logistic regression with dependent variable hasrelig, which indicates whether the respondent reports a religious affiliation.In the following figures, the x-axis is the percentage point difference in hasrelig between people at the 25th and 75th percentile for each explanatory variable.

In most countries, people with more education are less religious.

In most countries, the effect of income is small and not statistically significant.

The effect of television is negative in most countries.

The effect of radio is usually small.

The effect of newspapers is usually small.

In most countries, Internet use is associated with substantial decreases in religious affiliation.

Overall, the effect size for Internet use is the largest, followed by education and television. The effect sizes for income, radio, and newspaper are all small, and centered around zero.

#### Model 2 results

The second model uses linear regression with dependent variable rlgdgr, which indicates degree of religiosity on a 0-10 scale.In the following figures, the x-axis shows the difference in rlgdgr between people at the 25th and 75th percentile for each explanatory variable.

In most countries, people with more education are less religious.

The effect size for income is smaller.

People who watch more television are less religious.

The effect size for radio is small.

The effect size for newspapers is small.

In most countries, people who use the Internet more are less religious.

Comparing the effect size for different explanatory variable, again, Internet use has the biggest effect, followed by education and television. Effect sizes for income, radio, and newspaper are smaller and centered around zero.

That's all for now. I have a few things to check out, and then I should probably wrap things up.