age period cohort analysis – Probably Overthinking It

The Remarkable Decline of Homophobia

July 2, 2023 AllenDowney

This article is an excerpt from the manuscript of Probably Overthinking It, available from the University of Chicago Press and from Amazon and, if you want to support independent bookstores, from Bookshop.org.

[This excerpt is from a chapter on moral progress. Previous examples explored responses to survey questions related to race and gender.]

The General Social Survey includes four questions related to sexual orientation.

What about sexual relations between two adults of the same sex – do you think it is always wrong, almost always wrong, wrong only sometimes, or not wrong at all?

And what about a man who admits that he is a homosexual? Should such a person be allowed to teach in a college or university, or not?

If some people in your community suggested that a book he wrote in favor of homosexuality should be taken out of your public library, would you favor removing this book, or not?

Suppose this admitted homosexual wanted to make a speech in your community. Should he be allowed to speak, or not?

If the wording of these questions seems dated, remember that they were written around 1970, when one might “admit” to homosexuality, and a large majority thought it was wrong, wrong, or wrong. In general, the GSS avoids changing the wording of questions, because subtle word choices can influence the results. But the price of this consistency is that a phrasing that might have been neutral in 1970 seems loaded today.

Nevertheless, let’s look at the results. The following figure shows the percentage of people who chose a homophobic response to these questions as a function of age.

It comes as no surprise that older people are more likely to hold homophobic beliefs. But that doesn’t mean people adopt these attitudes as they age. In fact, within every birth cohort, they become less homophobic with age.

The following figure show the results from the first question, showing the percentage of respondents who said homosexuality was wrong (with or without an adverb).

There is clearly a cohort effect: each generation is substantially less homophobic than the one before. And in almost every cohort, homophobia declines with age. But that doesn’t mean there is an age effect; if there were, we would expect to see a change in all cohorts at about the same age. And there’s no sign of that.

So let’s see if it might be a period effect. The following figure shows the same results plotted over time rather than age.

If there is a period effect, we expect to see an inflection point in all cohorts at the same point in time. And there is some evidence of that. Reading from top to bottom:

More than 90% of people born in the nineteen-oughts and the teens thought homosexuality was wrong, and they went to their graves without changing their minds.
People born in the 1920s and 1930s might have softened their views, slightly, starting around 1990.
Among people born in the 1940s and 1950s, there is a notable inflection point: before 1990, they were almost unchanged; after 1990, they became more tolerant over time.
In the last four cohorts, there is a clear trend over time, but we did not observe these groups sufficiently before 1990 to identify an inflection point.

On the whole, this looks like a period effect. Also, looking at the overall trend, it declined slowly before 1990 and much more quickly thereafter. So we might wonder what happened in 1990.

What happened in 1990?

In general, questions like this are hard to answer. Societal changes are the result of interactions between many causes and effects. But in this case, I think there is an explanation that is at least plausible: advocacy for acceptance of homosexuality has been successful at changing people’s minds.

In 1989, Marshall Kirk and Hunter Madsen published a book called After the Ball with the prophetic subtitle How America Will Conquer Its Fear and Hatred of Gays in the ’90s. The authors, with backgrounds in psychology and advertising, outlined a strategy for changing beliefs about homosexuality, which I will paraphrase in two parts: make homosexuality visible, and make it boring. Toward the first goal, they encouraged people to come out and acknowledge their sexual orientation publicly. Toward the second, they proposed a media campaign to depict homosexuality as ordinary.

Some conservative opponents of gay rights latched onto this book as a textbook of propaganda and the written form of the “gay agenda”. Of course reality was more complicated than that: social change is the result of many people in many places, not a centrally-organized conspiracy.

It’s not clear whether Kirk and Madsen’s book caused America to conquer its fear in the 1990s, but what they proposed turned out to be a remarkable prediction of what happened. Among many milestones, the first National Coming Out Day was celebrated in 1988; the first Gay Pride Day Parade was in 1994 (although previous similar events had used different names); and in 1999, President Bill Clinton proclaimed June as Gay and Lesbian Pride month.

During this time, the number of people who came out to their friends and family grew exponentially, along with the number of openly gay public figures and the representation of gay characters on television and in movies.

And as surveys by the Pew Research Center have shown repeatedly, “familiarity is closely linked to tolerance”. People who have a gay friend or family member – and know it – are substantially more likely to hold positive attitudes about homosexuality and to support gay rights.

All of this adds up to a large period effect that has changed hearts and minds, especially among the most recent birth cohorts.

Cohort or period effect?

Since 1990, attitudes about homosexuality have changed due to

A cohort effect: As old homophobes die, they are replaced by a more tolerant generation.
A period effect: Within most cohorts, people became more tolerant over time.

These effects are additive, so the overall trend is steeper than the trend within the cohorts – like Simpson’s paradox in reverse. But that raises a question: how much of the overall trend is due to the cohort effect, and how much to the period effect?

To answer that, I used a model that estimates the contributions of the two effects separately (a logistic regression model, if you want the details). Then I used the model to generate predictions for two counterfactual scenarios: what if there had been no cohort effect, and what if there had been no period effect? The following figure shows the results.

The circles show the actual data. The solid line shows the results from the model from 1987 to 2018, including both effects. The model plots a smooth course through the data, which confirms that it captures the overall trend during this interval. The total change is about 46 percentage points.

The dotted line shows what would have happened, according to the model, if there had been no period effect; the total change due to the cohort effect alone would have been about 12 percentage points.

The dashed line shows what would have happened if there had been no cohort effect; the total change due to the period effect alone would have been about 29 percentage points.

You might notice that the sum of 12 and 29 is only 41, not 46. That’s not an error; in a model like this, we don’t expect percentage points to add up (because it’s linear on a logistic scale, not a percentage scale).

Nevertheless, we can conclude that the magnitude of the period effect is about twice the magnitude of the cohort effect. In other words, most of the change we’ve seen since 1987 has been due to changed minds, with the smaller part due to generational replacement.

No one knows that better than the San Francisco Gay Men’s Chorus. In July 2021, they performed a song by Tim Rosser and Charlie Sohne with the title, “A Message From the Gay Community”. It begins:

To those of you out there who are still working against equal rights, we have a message for you […]
You think that we’ll corrupt your kids, if our agenda goes unchecked.
Funny, just this once, you’re correct.
We’ll convert your children, happens bit by bit;
Quietly and subtly, and you will barely notice it.

Of course, the reference to the “gay agenda” is tongue-in-cheek, and the threat to “convert your children” is only scary to someone who thinks (wrongly) that gay people can convert straight people to homosexuality, and believes (wrongly) that having a gay child is bad. For everyone else, it is clearly a joke.

Then the refrain delivers the punchline:

We’ll convert your children; we’ll make them tolerant and fair.

For anyone who still doesn’t get it, later verses explain:

Turning your children into accepting, caring people;
We’ll convert your children; someone’s gotta teach them not to hate.
Your children will care about fairness and justice for others.

And finally,

Your kids will start converting you; the gay agenda is coming home.
We’ll convert your children; and make an ally of you yet.

The thesis of the song is that advocacy can change minds, especially among young people. Those changed minds create an environment where the next generation is more likely to be “tolerant and fair”, and where some older people change their minds, too.

The data show that this thesis is, “just this once, correct”.

Sources

The General Social Survey (GSS) is a project of the independent research organization NORC at the University of Chicago, with principal funding from the National Science Foundation. The data is available from the GSS website.

The Pew Research study showing that familiarity breeds acceptance is “Four-in-Ten Americans Have Close Friends or Relatives Who are Gay”.

You can see a performance of “A Message From the Gay Community” on YouTube.

Young Christians are more sex-positive than the previous generation

January 18, 2020 AllenDowney

This is the fifth and probably final in a series of articles where I use data from the General Social Survey (GSS) to explore

Differences in beliefs and attitudes between Christians and people with no religious affiliation (“Nones”),
Generational differences between younger and older Christians, and
Generational differences between younger and older Nones.

In the first article, I looked at changes in religious beliefs and found that younger Christians are more secular in many ways than the previous generation.

In the second article, I looked at views related to law and public policy and found that young Christians are more progressive on most issues than the previous generation.

In the third article, I found that generational differences on most questions related to abortion are small and probably not practically or statistically significant.

In the fourth article, I looked at responses to questions related to priorities and public spending. On many dimensions, younger Christians are moving toward the beliefs of their secular peers, but there are notable exceptions.

In this article, I use the same dataset to explore changes in attitudes related to sex. For details of the methodology, see the first article.

When is sex wrong?

GSS respondents were asked several questions related to their attitudes about sex:

There’s been a lot of discussion about the way morals and attitudes about sex are changing in this country.

If a man and woman have sex relations before marriage, do you think it is always wrong, almost always wrong, wrong only sometimes, or not wrong at all?
What if they are in their early teens, say 14 to 16 years old? In that case, do you think sex relations before marriage are always wrong, almost always wrong, wrong only sometimes, or not wrong at all?
What about sexual relations between two adults of the same sex–do you think it is always wrong, almost always wrong, wrong only sometimes, or not wrong at all?
What is your opinion about a married person having sexual relations with someone other than the marriage partner–is it always wrong, almost always wrong, wrong only sometimes, or not wrong at all?

For each of these questions, I count the fraction of respondents who reply “always wrong”.

And I looked at responses to one other sex-related question:

Would you be for or against sex education in the public schools?

Here are the results:

Generational changes in attitudes related to sex.

The blue markers are for people whose religious preference is Catholic, Protestant, or Christian; the orange markers are for people with no religious affiliation.

For each group, the circles show estimated percentages for people born in 1968; the arrowheads show percentages for people born in 1993.

For both groups, the estimates are for 2018, when the younger group was 25 and the older group was 50. The brackets show 90% confidence intervals.

In almost every scenario, young Christians are less likely than the previous generation to say that sex is “always wrong”, and in the cases of homosexual and teen sex, the changes are substantial.

Opposition to premarital sex was already low and did not change as much. Support for sex education was already high and is now an overwhelming majority.

The exception is extramarital sex, where there is practically no generational change: more than 80% of both generations think it is always wrong.

Compared to their Christian peers, the non-religious are more sex-positive by 15-30 percentage points. And their generational changes go in the same direction, with young Nones less likely to think sex in these scenarios is wrong.

But again, extramarital sex is the exception; among the Nones, the small generational change is within the margin of error.

This exception suggests that both groups distinguish between actions that harm people and transgressions of divine law.

Summary

In 2007, when I started writing about religious trends, I thought the increasing number of people with no religious affiliation was hugely underreported. Now, the “rise of the Nones” is well known.

Then, for a while, the story was that people were leaving organized religion, but they were still religious or at least spiritual; that is, they were “believing without belonging”.

More recently, it has become clear that beliefs and attitudes among the Nones are getting more secular.

In this series of articles, I have looked at changes among the ones who are left behind; that is, the decreasing fraction who identify as Christian. On many dimensions, the pattern is the same: young Christians are more secular than the previous generation.

Responses that follow this pattern include:

Almost all religious beliefs and activities, except belief in the afterlife.
Opposition to sex and sex education, except extramarital sex.
Matters of public policy including the legalization of marijuana, pornography, and euthanasia; support for affirmative action; and opposition to the death penalty and school prayer.

Many questions related to public spending follow the same pattern, with younger Christians generally moving toward positions held by their secular peers; the only substantial exception is mass transportation, which has less support among young people in both groups [although this result is so surprising to me that I need more evidence to be confident it is correct].

The most notable exceptions are opposition to gun control and abortion, which show almost no generational changes. Maybe not coincidentally, these exceptions are probably the most politicized topics among the questions I explored.

In summary, we can describe secularization in the U.S. as the sum of two trends, changes in affiliation and changes in belief. Both trends are moving fast, and they are moving in the same direction, away from religion.

Generational changes in public spending priorities

January 10, 2020 AllenDowney

This is the fourth in a series of articles where I use data from the General Social Survey (GSS) to explore

Differences in beliefs and attitudes between Christians and people with no religious affiliation (“Nones”),
Generational differences between younger and older Christians, and
Generational differences between younger and older Nones.

In the first article, I looked at changes in religious beliefs and found that younger Christians are more secular in many ways than the previous generation.

In the second article, I looked at views related to law and public policy and found that young Christians are more progressive on most issues than the previous generation.

In the third article, I found that generational differences on most questions related to abortion are small and probably not practically or statistically significant.

In this article, I use the same dataset to explore changes in opinions about public spending and national priorities. For details of the methodology, see the previous article.

Public spending priorities

GSS respondents were asked, “We are faced with many problems in this country, none of which can be solved easily or inexpensively. I’m going to name some of these problems, and for each one I’d like you to tell me whether you think we’re spending too much money on it, too little money, or about the right amount.”

Since they asked about 18 areas of public spending, I’ve put them in three categories:

Areas where young people are more inclined to increase spending,
Areas where young people are less inclined to increase spending, and
Areas where generational differences are inconsistent or small.

The following figure shows the first group, areas where young people are more likely to say we spend too little:

Generational changes in views on public spending

The blue markers are for people whose religious preference is Catholic, Protestant, or Christian; the orange markers are for people with no religious affiliation.

For each group, the circles show estimated percentages for people born in 1968; the arrowheads show percentages for people born in 1993.

For both groups, the estimates are for 2018, when the younger group was 25 and the older group was 50. The brackets show 90% confidence intervals.

The way these questions were posed, I suspect that most respondents can’t answer them literally. Few people know how much we spend in each area, what we spend it on, or what effect it would have if we spent more.

So their answers reflect some combination of how important they consider each issue, how much they think we are spending, and how effective they imagine more government spending would be.

With those caveats, we can draw a few conclusions:

On these issues, the priorities of Christians and Nones are generally aligned. The biggest difference between the groups is on spending to protect the environment, but a majority of both groups think we are spending too little.
The biggest generational changes are in foreign aid and protecting the environment; on both issues, young people are substantially more inclined to increase spending. But with respect to foreign aid, it is still a small minority.

The following figure shows areas of public spending where the generational change is generally negative:

Compared to their parents’ generation, young people are substantially less likely to increase spending on the military, transportation infrastructure and Social Security. To me, the direction of those changes is not surprising, but the magnitude is.

The other change I find surprising is in support for mass transportation, which decreased in both groups. I double-checked the data and this result seems to be correct, but it might warrant more investigation.

Finally, the following figure shows areas of public spending where generational changes are small and unlikely to be practically or statistically significant.

On these issues, the spending priorities of Christians and Nones are generally aligned, although Nones are more inclined to increase spending on space exploration, alternative energy, and education.

In the next article, I’ll look at generational changes related to confidence in various government and private institutions.

A large majority of Americans support legal abortion, at least in some circumstances

January 7, 2020 AllenDowney

This is the third in a series of articles where I use data from the General Social Survey (GSS) to explore

Differences in beliefs and attitudes between Christians and people with no religious affiliation (“Nones”),
Generational differences between younger and older Christians, and
Generational differences between younger and older Nones.

In the first article, I looked at changes in religious beliefs and found that younger Christians are more secular in many ways than the previous generation.

In the second article, I looked at views related to law and public policy and found that young Christians are more progressive on most issues than the previous generation.

In this article, I use the same dataset to explore changes in opinions about abortion. For details of the methodology, see the previous article.

GSS respondents were asked, “Please tell me whether or not you think it should be possible for a pregnant woman to obtain a legal abortion” under different circumstances.

The following figure shows the results.

Generational changes in beliefs about legal abortion

The blue markers are for people whose religious preference is Catholic, Protestant, or Christian; the orange markers are for people with no religious affiliation.

For each group, the circles show estimated percentages for people born in 1968; the arrowheads show percentages for people born in 1993.

For both groups, the estimates are for 2018, when the younger group was 25 and the older group was 50. The brackets show 90% confidence intervals.

Before we look for generational changes, we should notice the starting point: a large majority of Americans support legal abortion, at least in some circumstances.

In cases of severe birth defects and pregnancy due to rape, the majority is about 70% of Christians and 90% of the nonreligious.
In cases of serious danger to the woman’s health, it’s almost 90% of Christians and nearly all of the nonreligious.

Under other circumstances, opinions are more divided, with support near 40% among Christians and 70% among the Nones.

Looking now at the generational changes, I see only one that is likely to be practically and statistically significant: younger people in both groups are less likely than the previous generation to support legal abortion if there is a chance of serious birth defect.

Even so, there is majority support in both groups, more than 60% among Christians and 80% among Nones at age 25.

In summary:

Beliefs about abortion depend substantially on the circumstances;
In many circumstances, a large majority of Christians and the non-religious support legal abortion;
Even where there is disagreement between the groups, there is substantial diversity of opinion within both groups;
Generational changes in these opinions are generally small and within the statistical margin of error.

Generational changes in religious belief and public policy

January 6, 2020 AllenDowney

This is the second in a series of articles where I use data from the General Social Survey (GSS) to explore

Differences in beliefs and attitudes between Christians and people with no religious affiliation (“Nones”),
Generational differences between younger and older Christians, and
Generational differences between younger and older Nones.

In the first article I looked at changes in religious beliefs; in this article, we’ll see how those beliefs relate to public policy.

I picked nine questions that were included in the GSS during the period from 1998 to 2018, and selected respondents born during or after 1940. For details of the methodology, see the previous article.

Here are results for five propositions with relatively high support:

Generational changes in support for issues related to law and public policy

The blue markers are for people whose religious preference is Catholic, Protestant, or Christian; the orange markers are for people with no religious affiliation.

For each group, the circles show estimated percentages for people born in 1968; the arrowheads show percentages for people born in 1993.

For both groups, the estimates are for 2018, when the younger group was 25 and the older group was 50. The brackets show 90% confidence intervals.

The first row shows the percentage of respondents who answered “Yes” to the question “Do you think the use of marijuana should be made legal or not?”

Young Christians are substantially more likely to support legalization than their parents’ generation. Among the Nones, support might also be increasing, but the change is within the statistical margin of error.

Young Christians also support legal pornography. When asked, “Which of these statements comes closest to your feelings about pornography laws?”, more than 75% of them indicated that it should be legal, or legal for adults, rather than illegal. That’s more than 10 percentage points higher than in the previous generation.

Support for legal pornography has also increase among the unaffiliated, from 85% to almost 90%.

Young Christians are more likely to support legal euthanasia; when asked “When a person has a disease that cannot be cured, do you think Doctors should be allowed by law to end the patient’s life by some painless means if the patient and his family request it?”, more than 75% say “Yes”.

On these three questions, Christians are moving toward the position of their secular peers. On the other two questions, there are no clear patterns:

Support for gun control might have decreased among Christians, which is consistent with patterns I observed in a previous project.
Support for fair housing policy is high in both groups and might be increasing.

Here are results for four propositions with somewhat lower support:

These results shows that younger Christians are more likely than the previous generation to:

Support affirmative action,
Oppose legal obstactles to divorce,
Oppose the death penalty, and
Approve the prohibition of prayer in public schools.

In each case, Christians are moving toward the position held by the nonreligious, and in one case they have overtaken them: Christians are now more likely to oppose the death penalty than Nones of the current or previous generation.

Regarding school prayer, they were asked “The United States Supreme Court has ruled that no state or local government may require the reading of the Lord’s Prayer or Bible verses in public schools. What are your views on this–do you approve or disapprove of the court ruling?” More than 50% of young Christians answered that they approve, 20 percentage points higher than the previous generation.

Summary

These results suggest that people who identify as Christians are more politically progressive than previous generations. On most issues of law and public policy, a 25-year old Christian is more aligned with a 50-year old None than a 50-year old Christian.

In the next article, I’ll explore generational changes in other opinions and attitudes.

Related reading: In this article about an evangelical Christian activist, The Washington Post Magazine asks “Can Shane Claiborne’s progressive version of evangelical Christianity catch on with a new generation?” The article emphasizes Claiborne’s progressive views on reducing gun violence. My analysis of data from the GSS suggests that young Christians are more progressive than previous generations on many issues, but gun control is not one of them.

Young Christians are less religious than the previous generation

January 5, 2020 AllenDowney

This is the first in a series of articles where I use data from the General Social Survey (GSS) to explore

Differences in beliefs and attitudes between Christians and people with no religious affiliation (“Nones”),
Generational differences between younger and older Christians, and
Generational differences between younger and older Nones.

On several dimensions of religious belief, young Christians are less religious than their parents’ generation. I’ll explain the methodology below, but here are the results:

Generational changes in religious belief, comparing people born in 1968 and 1993

The blue markers are for Christians (people whose religious preference is Catholic, Protestant, or Christian); the orange markers are for people with no religious affiliation.

For each group, the circles show estimated percentages for people born in 1968; the arrowheads show percentages for people born in 1993.

For both groups, the estimates are for 2018, when the younger group was 25 and the older group was 50. The brackets show 90% confidence intervals for the estimates, computed by random resampling.

The top row shows the fraction of respondents who interpret the Christian bible literally; more specifically, when asked “Which of these statements comes closest to describing your feelings about the Bible?”, they chose the first of these options:

“The Bible is the actual word of God and is to be taken literally, word for word”
“The Bible is the inspired word of God but not everything in it should be taken literally, word for word.
“The Bible is an ancient book of fables, legends, history, and moral precepts recorded by men.”

Not surprisingly, people who consider themselves Christian are more likely to interpret the Bible literally, compared to people with no religious affiliation.

But younger Christians are less likely to be literalists than the previous generation. Most of the other variables show the same pattern; younger Christians are less likely to answer yes to these questions:

“Would you say you have been ‘born again’ or have had a ‘born again’ experience — that is, a turning point in your life when you committed yourself to Christ?”
“Have you ever tried to encourage someone to believe in Jesus Christ or to accept Jesus Christ as his or her savior?”

And they are less likely to report that they know God really exists; specifically, they were asked “Which statement comes closest to expressing what you believe about God?” and given these options:

I don’t believe in God
I don’t know whether there is a God and I don’t believe there is any way to find out.
I don’t believe in a personal God, but I do believe in a Higher Power of some kind.
I find myself believing in God some of the time, but not at others.
While I have doubts, I feel that I do believe in God.
I know God really exists and I have no doubts about it.

Younger Christians are less likely to say they know God exists and have no doubts.

Despite all that, younger Christians are more likely to believe in an afterlife. When asked “Do you believe there is a life after death?”, more than 90% say yes.

Among the unaffiliated, the trends are the same. Younger Nones are less likely to believe that the Bible is the literal word of God, less likely to have proselytized or been born again, and less likely to be sure God exists. But they are a little more likely to believe in an afterlife.

Methodology

My goal is to estimate generational changes, that is, cohort effects as distinguished from age and period effects. In general, it is not possible to distinguish between age, period, and cohort effects without making some assumptions. So this analysis is based on the assumption that age effects in this dataset are negligible compared to period and cohort effects.

Data from the General Social Survey goes back to 1972; it includes data from almost 65,000 respondents.

To measure current differences between people born in 1968 and 1993, I could select only respondents born in those years and interviewed in 2018. But there are not very many of them.

Alternatively, I could use data from all respondents, going back to 1972, fit a model, and use the model to estimate generational differences. That might work, but it would probably give too much weight to older, less relevant data.

As a compromise, I use data from 1998 to 2018, from respondents born in 1940 or later. This subset includes about 25,000 respondents. But not every respondent was asked every question, so the number of valid responses for most questions is smaller.

For most questions, I discard a small number of respondents who gave no response or said they did not know.

To model the responses, I use logistic regression with year of birth (cohort) and year of interview as independent variables. For questions with more than two responses, I choose one of the responses to study, usually the most popular; in a few cases, I grouped a subset of responses (for example “agree” and “strongly agree”).

I use a quadratic model for the period effect and a cubic model of the cohort effect, using visual tests to check whether the models do an acceptable job of describing the trends in the data.

I fit separate models for Christians and Nones, to allow for the possibility that trends might look different in the two groups (as it turns out they often do).

Then I use the models to generate predictions for four groups: Christians born in 1968 and 1993, and Nones born in the same years. These are “predictions” in the statistical sense of the word, but they are deliberately not extrapolations into cohorts or periods that are not in the dataset; it might be more correct to call them “interpolations”.

To show how this method works, let’s consider the fraction of Christians who answer that they know God exists, with no doubts. The following figure shows this fraction as a function of birth year (cohort):

Fraction of Christians who says they know God exists, plotted over year of birth

The red dots show the fraction of respondents in each birth cohort. The red line shows a smooth curve through the data, computed by local regression (LOWESS). The gray line shows the predictions of the model for year 2008.

This figure shows that the logistic regression model of birth year does an acceptable job of describing the trends in the data, while also controlling for year of interview.

To see whether the model also describes trends over time, we can plot the fraction of respondents in each year of interview:

Fraction of Christians who says they know God exists, plotted over year of inteview

The green dots show the fraction of respondents during each year of interview and the green line shows a local regression through the data. The purple line shows the model’s predictions for someone born in 1968; the pink line shows predictions for someone born in 1993.

The gap between the purple and pink curves is the estimated generational change; in this example, it’s about 3 percentage points.

In summary, the model uses data from a range of birth years and interview years to fit a model, then uses the model to estimate the difference in response between people born in different years, both interviewed in 2018.

The results are based on the assumption that the model adequately describes the period and cohort effects, and that any age effects are negligible by comparison.

You can see all of the details in this Jupyter notebook, and you can click here to run it on Colab.

Probably Overthinking It

Data science, Bayesian Statistics, and other ideas

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Young Christians are more sex-positive than the previous generation

January 18, 2020 AllenDowney

When is sex wrong?

Summary

A large majority of Americans support legal abortion, at least in some circumstances

January 7, 2020 AllenDowney

Young Christians are less religious than the previous generation

January 5, 2020 AllenDowney

More questions, less religion

Methodology