Here are five ways causation without correlation can occur:

1. Averaging: increasing A sometimes causes increasing B, but other times, it causes B to decrease. The two balance out. Since correlation measures the average relationship, the correlation is zero.

For example, if you drive up a symmetrical hill and then down the other side, there’s no correlation between how many times the wheels have revolved on the hill and the car’s height above sea level, even though the revolving of the wheels causes the altitude to change.

2. Confounders: when A increases, that causes B to increase, but change is coming from C, and increasing C both causes A to increase AND causes B to decrease. The decrease in B from more C is the right amount to counteract the increase in B caused by C causing A to increase.

Example: A is in love with B and best friends with C. When C is happy, that makes A happy. When B compliments someone in front of A, that makes A unhappy. When B complements C, that makes C happy, making A happier, but the complement itself makes A unhappier, balancing it out.

3. Control: a system is designed to stabilize the value of B. Even though increases in A normally cause an increase in B, the system resists this change by exerting the opposite effect on B with the goal of keeping B constant.

For example, opening the vents would normally cool down the house, but when the heating system detects a draft, it causes the heating system to start working harder in order to keep the house at the desired 70 degrees.

4. Multiple causation: while A does cause C, C is also caused by B (so either A or B on its own is sufficient to cause C). Since A and B are both active, deactivating one has no effect on C. A and B never get deactivated at the same time, so the relationship between A and C is 0.

Example: on death row in a certain country, they administer a lethal dose of two different poisons. They have experimented with removing one or the other poison, and this did not affect whether the inmate died.

5. Deactivated causation: an increase in A causes an increase in B normally, but only if C is active. Since C is not active, there is no correlation measured between A and B. For example, force on the gas peddle only causes the car to increase speed when the car is turned on

All of this being said, while causation does not NECESSARILY imply correlation, causation USUALLY DOES imply correlation. Some software that attempts to discover causation in observational data even goes so far as to make this assumption of causation implying correlation.

This piece was first written on March 14, 2022, and first appeared on this site on December 7, 2023.

• If you’re a psychology researcher investigating possible causes of depression (Y), you may have trouble disentangling the effects of poor sleep quality (A) and anxiety (B), both of which tend to be correlated with depression.
• If you’re a health researcher investigating the causes of diabetes (Y), you may have trouble disentangling the effects of high carbohydrate intake (A) and obesity (B).
• If you’re investigating the causes of high life satisfaction (Y), you may have trouble disentangling the effects of friendship quality (A) and mental well-being (B).

In all these examples, we know that at least two of the variables (A and B) are related to the main variable (Y), but the really tricky question is to figure out what all the possible causal relationships are between the three. For instance, does A cause B, which causes Y, does Y cause both A and B, or is there some other explanation? 

In the pdf below, I sketch out 45 possible explanations to consider in situations where there are two variables that both correlate with a third variable of interest.

First of all, there are the types of causal relationships one often expects, where A and B both cause Y in simple ways (either directly or through each other):

Even if A and B really do cause Y, they could be interconnected to each other in complex ways:

It also could be the case that only A or only B causes Y, with the other variable only appearing to cause Y due to a confounding effect:

It’s also possible that Y is actually one of the causes rather than merely being caused by A and B:

Then there are situations where there is a critical other variable (or set of variables – represented as a “?” below) that are integral to the causal structure:

Finally, there are situations where Y is caused by A or B (or both), but Y also causes A or B (or both), resulting in a cyclic relationship:

Here’s a link to my pdf showing most of the possible relationships.

If you want to read about other challenges associated with untangling causality in the real world, you can read another post about this here.

I first created this diagram on April 19, 2021. I made minor edits to the diagram and wrote this piece with assistance from Clare Harris. This piece first appeared on my website on November 22, 2023.

Additionally, many studies have found that SSRIs (and other medications) help people with both depression and anxiety, as do certain therapeutic modalities such as Cognitive Behavioral Therapy, suggesting further linkage.

Findings like these lead some to conclude that the two diseases are just one and the same, or part of the “same thing.” I don’t agree. The main reasons I don’t agree are because:

A. Anxiety and depression feel different internally (i.e., they have different “qualia” for most people). This is a major part of how we can tell which one we’re experiencing at a given moment. For instance, for me, I am more likely to experience anxious feelings in my upper chest, with depressive feelings being more like an “emptiness.”

B. Some events cause anxiety but not depression (e.g., worrying that there is a tiger hiding by the watering hole because you saw a tiger there at another time); others cause depression but without necessarily causing anxiety (e.g., having trouble getting over the death of a beloved friend a year after the event).

C. The behavioral changes they cause tend to be different since anxiety tends to cause avoidance of the things you fear, whereas depression tends to produce a lack of motivation.

D. There are some personal factors that are strongly linked to one but not the other. For instance, in our research, we found that negative self-talk is strongly linked to depression, but it is not linked to anxiety (once you control for depression).

Clearly, though, anxiety and depression ARE very connected.

So, how ARE they linked?

Here’s what I think the main links between anxiety and depression are:

1. Anxiety sometimes causes depression since anxiety at high levels leads people to avoid important things of value out of fear and (in some cases) out of exhaustion. Missing out on the things they value has a tendency to make people depressed. And feeling trapped by your anxiety can also give a sense of hopelessness, leading to depression.

2. Depression sometimes causes anxiety since feeling that “nothing really matters,” or that there is “no point in trying,” or that “I’m worthless” can lead to difficulty with motivation, exhaustion, and giving up, which can cause a snowballing set of anxiety-inducing life problems (e.g., fear of losing one’s job, or fear of losing friendships, or a piling up of life chores that go undone, with increasingly large consequences).

3. There are factors that increase one’s chances of getting both depression AND anxiety, such as early life trauma, negative life events (like losing a job), and poverty.

Therefore I see the links this way:

Depression sometimes causes anxiety.

so: D -> A

Anxiety sometimes causes depression.

so: A -> D

A negative spiral can occur, with anxiety causing depression, which causes anxiety, which causes depression, and so on, in a feedback loop.

so: A -> D -> A -> D -> …

And difficult life situations and events can cause BOTH simultaneously.

so: X, Y, Z -> A & D

So yes, depression and anxiety are highly related, but they don’t, by any means, seem to be “the same thing.”

This piece was first written on January 10, 2021, and first appeared on this site on December 23, 2022.

We conducted a study of 999 people in the United States; recruited through our study platform at Positly.com. We looked for a correlation between 18 different personality traits (each trait being assessed with two questions) and life satisfaction. We examined the association each trait had with scores on the Satisfaction With Life Scale (a 5 question scale by Diener, Emmons, Larsen, Griffin). There are, of course, many personality traits beyond the 18 we measured!

We found that 8 of the 18 personality traits were strongly associated with life satisfaction, in the sense that the relationship held in the same direction whether measured:

(1) as simple correlations between each individual trait and life satisfaction

(2) controlling for all the other personality traits as well as income, age, gender and education (using linear regression), or

(3) controlling only for the other personality traits most strongly associated with life satisfaction (again using linear regression).

We also found a 9th personality trait with a slightly weaker association to life satisfaction; it was statistically significant, at p=0.05, using two of the three methods mentioned above.

The personality traits we found to be most closely associated with life satisfaction are listed below (ordered roughly by strength of association).

While reviewing the results, please keep a few things in mind:

A. The personality traits were reworded (to have the reverse meaning) in cases where there was a negative correlation to life satisfaction, so that all associations are positive.

B. Also, the exact cause of association is somewhat ambiguous so, for each trait, I cited three different speculative theories on why the relationship to life satisfaction may exist. For example, an association between X (e.g. a personality trait) and Y (e.g. life satisfaction) doesn’t necessarily mean that X causes Y (see this for all the meanings a correlation can have).

In the case of any particular association, it could be that:

• (a) the trait CAUSED greater life satisfaction (i.e. X->Y)
• (b) the trait is CAUSED BY greater life satisfaction (i.e. Y->X)
• (c) some other variable or variables increase the value of the trait and SEPARATELY cause greater life satisfaction. In other words, mutual exclusivity (i.e. Z->X and Z->Y).

The 9 personality traits together (in a linear regression without any other variables) explain about 23% of the variance in life satisfaction (i.e. adjusted R^2 = 0.23). Of course, we only studied 18 personality traits in this study, there are many others that exist that we did not investigate in this work.

Personality Traits Most Positively Associated with Life Satisfaction

1. At Ease – Seldom experiencing fear / Seldom worrying

Perhaps because…

• (a) High levels of anxiety cause people to feel unsatisfied with life.
• (b) People become anxious about the fact that they are unsatisfied with life (for instance, worrying because they feel like they “should” feel satisfied and that something must be wrong with them because they don’t)
• (c) Tough life situations (e.g. divorce or job loss) cause both lower life satisfaction and higher anxiety (separately).

Note: Many people learn to reduce their fear and worry. For instance, they may use Cognitive Behavioral Therapy (including Exposure Therapy for specific fears) or Mindfulness Based Stress Reduction. I think it’s likely this really does improve life satisfaction for people who don’t naturally feel “At Ease”. If you feel a lot of anxiety, fear, stress, or worry in your life, I recommend trying out our app Mind Ease.

2. Self-Valuing – Feeling of superiority / Feeling equal to others

Perhaps because…

• (a) Feeling inferior to others makes people feel bad about themselves which makes them feel unsatisfied with their lives.
• (b) Being unsatisfied with life causes people to feel inferior to others (e.g. due to blaming themselves for their unsatisfying situation).
• (c) Some commonly occurring bad life events (e.g. being harshly rejected or being put down a lot by family members) cause people both to become unsatisfied with life and to feel inferior to others.

Note: Some people learn not to view themselves as inferior to others by challenging their feelings of inferiority (e.g. using Cognitive Therapy techniques) or learning self-compassion (some have benefited from related literature like “Self-compassion” by Kristin Neff). I expect that for someone low on the trait of Self Valuing, learning to view yourself as equal to others may improve life satisfaction.

3. Warm – Laughing aloud / Expressing happy feelings

Perhaps because…

• (a) Being warm causes others to be drawn to us, this closeness improves life satisfaction.
• (b) Being satisfied with life causes people to feel more relaxed around others, which causes them to openly share positive emotions.
• (c) Having emotionally supportive caregivers growing up causes people to be both more comfortable showing their positive feelings, and more satisfied with life.

Note: People can get better at expressing their positive feelings (e.g. I have!), for instance by consciously channeling positivity when greeting people, consciously smiling when feeling happy (if it doesn’t happen automatically, which it doesn’t for some people), verbally expressing that something has made you feel good, etc. I suspect that for those low on the Warm trait these efforts might cause at least a minor boost to life satisfaction.

Personality Traits A Bit Positively Associated with Life Satisfaction

4. Unselfish – Putting others before oneself

Perhaps because…

• Being unselfish leads to better interpersonal relationships which makes people more satisfied with life.
• Being more satisfied with your life means you have less need to focus on yourself, hence, increased focus on others.
• When bad interpersonal experiences teach people that they shouldn’t trust others, they become less satisfied with life (due to worse social relationships) and become more selfish (because they don’t expect others to be unselfish toward them).

5. Forgiving – Not wanting or seeking revenge

Perhaps because…

• Harboring anger and dwelling on wrongs makes you feel bad about your life.
• Being more satisfied with your life makes it easier to minimize or forget about ways you were wronged by others.
• Growing up around forgiving people makes you both more satisfied with life as an adult and more forgiving of others.

6. Improvisational – Being adaptable or quick on your feet

Perhaps because…

• Being adaptable is often useful in the workplace, leading to increased effectiveness and work satisfaction; this leads to increased life satisfaction.
• When you are unsatisfied with life, that unhappiness causes a cognitive burden that makes it harder to be improvisational
• Negative thinking makes them less satisfied with life, and it also separately makes it harder for them to be think quickly on their feet because it’s distracting.

7. Self-Defending – Not being overly self-critical when things go wrong

Perhaps because…

• Blaming yourself for a lot of things may cause you to become unhappy about your life.
• Having a life that makes you feel satisfied may give you greater self-esteem (if you attribute that good life to your own character), which could prevent you from blaming yourself for problems.
• Being the sort of person that very rarely upsets other people could cause you to be both more satisfied with life (due to better social relationships) and less likely to attribute negative incidents to your own character.

8. Normal – Acting in a socially acceptable way

Perhaps because…

• Behaving normally may allow people to fit in better with their social groups; making them more satisfied with life.
• Being increasingly unsatisfied with life may cause people to engage in increasingly abnormal seeming behavior.
• Being a social outcast may cause people to be both less satisfied with life and less likely to care about their behaviors conforming to what others view as normal.

Personality Trait Possibly Associated with Life Satisfaction

(this final trait was not as consistently associated with life satisfaction as those above)

1. Unfeeling – being indifferent to the feelings of others

Perhaps because…

• Feeling too intensely when others suffer causes one to suffer; leading to lower life satisfaction.
• Being more satisfied with life makes people feel less need for maintaining existing social relationships causing indifference to the feelings of others
• People with a more positive disposition feel less negative emotions (causing more satisfaction with life) and less negative emotion in response to other people’s feelings (hence greater indifference).This fairly weak association could easily be a statistical fluke.

Note that there is some subjectivity in the rank order above because the strength order varied somewhat based on which method was used to measure the associations, and because there is a limit to the precision with which the associations can be measured using our data (which, naturally, depends on the sample size).

Also, since each personality trait was measured using only two questions (and, as a result, each trait was measured only superficially for each person), one might assume that these results fail to capture the true extent of the correlations. On the other hand, since we tested 18 traits and selected the strongest, a regression to the mean effect will be working in the opposite direction to some extent.

Below are 166 (rather interesting!) size-ordered correlations that I calculated on 870 people in the United States, who were recruited using our study recruitment platform, Positly.

All responses are self-reported by the study participants, mostly measured on a scale of 1-4 or 1-5, except those that suggest a different scale (e.g., number of minutes doing something, age, symptom scores, etc.)

Keep in mind that if A and B are correlated, it could be that A causes B, it could be that B causes A, or it could be that some third thing causes both A and B.

The number shown on each row is the correlation between the thing on the left of the “vs.” and the thing on the right of the “vs.”

—
Huge correlations (~67% of variance explained)

0.82: depression symptom score (PHQ9) vs. anxiety symptom score (GAD7)
0.82: “Taking all things together, I am happy.” (1-5 scale) vs. “In general, I feel confident and positive about myself.” (1-5 scale)
0.75: “How religious do you consider yourself to be?” (0-5 scale) vs. “How spiritual do you consider yourself to be?” (0-5 scale)
0.75: satisfactionWithDatingOrRomanticLife vs. howWellTreatedByRomanticPartner
0.74: socialLiberalness vs. economicLiberalness
0.73: placeOfWorshipAffiliation vs. “How religious do you consider yourself to be?” (0-5 scale)
0.68: “In general, I feel confident and positive about myself.” (1-5 scale) vs. “How optimistic a person are you usually?” (-2 to 2 scale)
0.67: parentsHappyWhenYouWereGrowingUp vs. parentsTreatedWellWhenGrowingUp
0.67: videoGameMinutesPerDayWhenPlays vs. videoGamePlayingDaysPerWeek
0.60: howGoodLifeIsRelativeToExpectations vs. “I feel satisfied with what I am achieving in life.” (1-5 scale)
0.60: enoughMoneyToLiveComfortably vs. moreWealthyThanFriends
0.60: hoursWorkedOnWorkDays vs. daysWorkedPerWeek
0.58: takesAntidepressants vs. hasMentalHealthDiagnosis
0.57: satisfactionWithDatingOrRomanticLife vs. relationshipSeriousness
0.54: takesAntidepressants vs. seeingAMentalHealthProfessional
0.54: “How spiritual do you consider yourself to be?” (0-5 scale) vs. placeOfWorshipAffiliation
0.53: alcoholDaysDrinkingPerWeek vs. drinksPerTimeDrinking

—
Large correlations (~25% of variance explained)

0.50: relationshipSeriousness vs. livesWithOtherPeople
0.49: conscientiousness (2-question big 5 scale) vs. howGoodIsWillpower
0.48: “Taking all things together, I am happy.” (1-5 scale) vs. satisfactionWithDatingOrRomanticLife
0.48: hasDepressiveDisorder vs. takesAntidepressants
0.48: enoughMoneyToLiveComfortably vs. howGoodLifeIsRelativeToExpectations
0.46: relationshipSeriousness vs. hasChildren
0.45: hasDepressiveDisorder vs. hasAnxietyDisorder
0.42: selfReportedHowGoodAtMathComparedToOthers vs. selfReportedIntelligence
0.41: howWellTreatedByRomanticPartner vs. “Taking all things together, I am happy.” (1-5 scale)
0.40: “In general, I feel confident and positive about myself.” (1-5 scale) vs. howGoodIsWillpower
0.40: incomeScore vs. enoughMoneyToLiveComfortably
0.38: age vs. hasBeenDivorced
0.38: howOftenReadsBlogs vs. howOftenReadsTheNews
0.38 : timesSexualActivityWithOtherPersonIn7Days vs. howWellTreatedByRomanticPartner
0.37: moreWealthyThanFriends vs. “I feel satisfied with what I am achieving in life.” (1-5 scale)
0.36: howGoodLifeIsRelativeToExpectations vs. howWellTreatedByRomanticPartner
0.36: hasChildren vs. age
0.36: “Taking all things together, I am happy.” (1-5 scale) vs. enoughMoneyToLiveComfortably
0.36: selfReportedIntelligence vs. selfReportedGoodLookingnessForAge
0.36: selfReportedGoodLookingnessForAge vs. “In general, I feel confident and positive about myself.” (1-5 scale)
0.35 : timesSexualActivityWithOtherPersonIn7Days vs. satisfactionWithDatingOrRomanticLife
0.35: parentsHappyWhenYouWereGrowingUp vs. “In general, I feel confident and positive about myself.” (1-5 scale)
0.34: selfReportedIntelligence vs. considersSelfLifelongLearner
0.34: exerciseDaysPerWeek vs. hoursOutsideWeekly
0.31: homeOwnershipLevel vs. age
0.31: seeingAMentalHealthProfessional vs. depression symptom score (PHQ9)

—
Medium correlations (~9% of variance explained)

0.3: “Taking all things together, I am happy.” (1-5 scale) vs. numberOfCloseFriendsAndFamilyMembers
0.3: homeOwnershipLevel vs. enoughMoneyToLiveComfortably
0.3: depression symptom score (PHQ9) vs. takesAntidepressants
0.3: republican1DemocratNegative1 vs. “How religious do you consider yourself to be?” (0-5 scale)
0.29: earlyTechnologyAdopter vs. appsTheyDownloadedAndUseWeekly
0.28: restednessUponWakingAfterIdealHoursOfSleep vs. “I feel satisfied with what I am achieving in life.” (1-5 scale)
0.28: healthLevel vs. exerciseDaysPerWeek
0.28: healthLevel vs. moreWealthyThanFriends
0.27: educationScore vs. incomeScore
0.27: selfReportedGoodLookingnessForAge vs. moreWealthyThanFriends
0.27 : isChristian vs. republican1DemocratNegative1
0.27: hasAPet vs. isFemale
0.26: selfReportedIntelligence vs. selfReportedGoodnessAndMoralness
0.25: numberOfCloseFriendsAndFamilyMembers vs. “How optimistic a person are you usually?” (-2 to 2 scale)
0.24: “How spiritual do you consider yourself to be?” (0-5 scale) vs. age
0.23: age squared vs. “How spiritual do you consider yourself to be?” (0-5 scale)
0.23: smokeCigarettesFrequency vs. addictedToADrugOtherThanCaffeineOrNicotine
0.23: hoursWorkedOnWorkDays vs. positivenessOfFeelingsAboutJob
0.23: hasAPet vs. isWhite
0.22: selfReportedIntelligence vs. educationScore
0.22: anxiety symptom score (GAD7) vs. takesAntidepressants
0.22: depression symptom score (PHQ9) vs. debtsCannotPayLevel
0.22: “How optimistic a person are you usually?” (-2 to 2 scale) vs. parentsTreatedWellWhenGrowingUp
0.21: hoursPastMidnightGoesToSleep vs. videoGameMinutesPerDayWhenPlays
0.21: hoursOutsideWeekly vs. exerciseMinutesPerExerciseDay
0.21: satisfactionWithDatingOrRomanticLife vs. parentsHappyWhenYouWereGrowingUp
0.21: socialLiberalness vs. homosexuality
0.21 : isChristian vs. hasChildren

—
Small correlations (~4% of variance explained)

0.2: howOftenReadsTheNews vs. considersSelfLifelongLearner
0.2: hoursPastMidnightGoesToSleep vs. depression symptom score (PHQ9)
0.2: earlyTechnologyAdopter vs. internetCapableSmartphone
0.2: howGoodIsWillpower vs. moreWealthyThanFriends
0.2: nightclubAttendance vs. timesSexualActivityWithOtherPersonIn7Days
0.2: daysPerWeekUsesTwitter vs. appsTheyDownloadedAndUseWeekly
0.2: “How spiritual do you consider yourself to be?” (0-5 scale) vs. republican1DemocratNegative1
0.2: enoughMoneyToLiveComfortably vs. positivenessOfFeelingsAboutJob
0.2: bookReadingDaysPerWeek vs. considersSelfLifelongLearner
0.19: daysPerWeekUsesFacebook vs. isFemale
0.19: bodyMassIndex vs. depression symptom score (PHQ9)
0.19: differenceBetweenAverageAndNeededSleepHours vs. “Taking all things together, I am happy.” (1-5 scale)
0.19: selfReportedGoodLookingnessForAge vs. exerciseMinutesPerExerciseDay
0.19: selfReportedIntelligence vs. earlyTechnologyAdopter
0.18: hasAPet vs. daysPerWeekUsesFacebook
0.18: howWellTreatedByRomanticPartner vs. parentsTreatedWellWhenGrowingUp
0.18: “How spiritual do you consider yourself to be?” (0-5 scale) vs. “How optimistic a person are you usually?” (-2 to 2 scale)
0.18: moreWealthyThanFriends vs. timesSexualActivityWithOtherPersonIn7Days
0.18: nightclubAttendance vs. drinksPerTimeDrinking
0.18: incomeScore vs. selfReportedGoodLookingnessForAge
0.17 : firedFromAJobInLast12Months vs. addictedToADrugOtherThanCaffeineOrNicotine
0.17: isFemale vs. “How spiritual do you consider yourself to be?” (0-5 scale)
0.17: numberOfCloseFriendsAndFamilyMembers vs. “How religious do you consider yourself to be?” (0-5 scale)
0.17: selfReportedHowGoodAtMathComparedToOthers vs. selfReportedGoodLookingnessForAge
0.17: educationScore vs. enoughMoneyToLiveComfortably
0.17: selfReportedIntelligence vs. moreWealthyThanFriends
0.17 : timesSexualActivityWithOtherPersonIn7Days vs. healthLevel
0.17: daysPerWeekSpeaksToFriends vs. numberOfCloseFriendsAndFamilyMembers
0.17: “How religious do you consider yourself to be?” (0-5 scale) vs. takingAllThingsTogetherIAmHAPPY
0.16: minutesOnComputerTypicalDay vs. hoursPastMidnightGoesToSleep
0.16: hasBeenDivorced vs. “How spiritual do you consider yourself to be?” (0-5 scale)
0.16 : timesSexualActivityWithOtherPersonIn7Days vs. selfReportedGoodLookingnessForAge
0.16: hoursOutsideWeekly vs. “How optimistic a person are you usually?” (-2 to 2 scale)
0.16: “How spiritual do you consider yourself to be?” (0-5 scale) vs. numberOfCloseFriendsAndFamilyMembers
0.16: educationScore vs. bookReadingDaysPerWeek
0.16: howGoodIsWillpower vs. positivenessOfFeelingsAboutJob
0.16: gotDivorcedInLastTwoYears vs. addictedToADrugOtherThanCaffeineOrNicotine
0.16: howOftenReadsTheNews vs. educationScore
0.16: hasChildren vs. hasAPet
0.16: differenceBetweenAverageAndNeededSleepHours vs. exerciseDaysPerWeek
0.16: bodyMassIndex vs. chronicMedicalConditionSeriousness

—
Tiny correlation (~2% of variance explained)

0.15: anxiety symptom score (GAD7) vs. socialLiberalness
0.15: restednessUponWakingAfterIdealHoursOfSleep vs. positivenessOfFeelingsAboutJob
0.15: relationshipSeriousness vs. republican1DemocratNegative1
0.15: daysPerWeekSpeaksToFriends vs. howOftenReadsTheNews
0.15: alcoholDaysDrinkingPerWeek vs. smokeCigarettesFrequency
0.15: gotDivorcedInLastTwoYears vs. firedFromAJobInLast12Months
0.15: selfReportedGoodLookingnessForAge vs. satisfactionWithDatingOrRomanticLife
0.15: videoGameMinutesPerDayWhenPlays vs. bookReadingMinutesPerDayWhenRead
0.14: parentsHappyWhenYouWereGrowingUp vs. selfReportedGoodLookingnessForAge
0.14: isChristian vs. daysPerWeekUsesFacebook
0.14: considersSelfLifelongLearner vs. howOftenReadsBlogs
0.14: healthLevel vs. differenceBetweenAverageAndNeededSleepHours
0.14 : republican1DemocratNegative1 vs. homeOwnershipLevel
0.13: hasAPet vs. mentalIllnessInFamilyLevel
0.13: economicLiberalness vs. daysPerWeekUsesTwitter
0.13: economicLiberalness vs. hoursPastMidnightGoesToSleep
0.13: seeingAMentalHealthProfessional vs. gotDivorcedInLastTwoYears
0.13: videoGamePlayingDaysPerWeek vs. bodyMassIndex
0.13: “How spiritual do you consider yourself to be?” (0-5 scale) vs. physicalDisabilityLevel
0.12: bornInUS vs. hasAPet
0.12: howGoodIsWillpower vs. numberOfCloseFriendsAndFamilyMembers
0.12: howOftenReadsBlogs vs. educationScore
0.12: “How optimistic a person are you usually?” (-2 to 2 scale) vs. hasBeenDivorced
0.12: parentsTreatedWellWhenGrowingUp vs. “How religious do you consider yourself to be?” (0-5 scale)
0.12: urbannessOfLocation vs. economicLiberalness
0.12: isFemale vs. depression symptom score (PHQ9)
0.11: nightclubAttendance vs. selfReportedGoodLookingnessForAge
0.11: howOftenReadsTheNews vs. daysPerWeekUsesTwitter
0.11: worksMoreThanWouldLike vs. depression symptom score (PHQ9)
0.11: incomeScore vs. hasAPet
0.11: parentsHappyWhenYouWereGrowingUp vs. howGoodIsWillpower
0.11: isFemale vs. hasMentalHealthDiagnosis
0.11: hasAnxietyDisorder vs. hasAPet
0.11: usCitizen vs. isWhite
0.11: howOftenReadsBlogs vs. socialLiberalness
0.11 : firedFromAJobInLast12Months vs. nightclubAttendance
0.11: educationScore vs. appsTheyDownloadedAndUseWeekly

—
Negligible correlations (~1% of variance explained)

0.10: videoGameMinutesPerDayWhenPlays vs. hasMentalHealthDiagnosis
0.09: Points (gad7) vs. smokeCigarettesFrequency
0.09: healthLevel vs. alcoholDaysDrinkingPerWeek
0.09: howOftenReadsTheNews vs. incomeScore
0.08: selfReportedHowGoodAtMathComparedToOthers vs. howOftenReadsTheNews
0.07: physicalDisabilityLevel vs. lookingForWork
0.07: isMidwestUSRegion vs. hasChildren
0.07: gotDivorcedInLastTwoY

This piece was first written on January 13, 2018, and first appeared on my website on July 30, 2025.

What are the possible explanations for (or causes of) this?

• A Causes B – Increasing A is a cause of increasing B but not the reverse. [e.g., more happiness causes more willpower]
• (2) B Causes A – Increasing B is a cause of increasing A but not the reverse. [e.g., more willpower causes more happiness]
• (3) A Causes B Causes A – Increasing A and B are both causes of increases of the other, leading to a positive feedback loop between them. [e.g., more willpower causes more happiness which causes more willpower which causes more happiness, etc.]
• (4) X Causes A and B – There exists at least one other variable X (potentially many more than one) such that increases (or decreases) in X lead simultaneously to increases in both A and B. [e.g., living in a stable environment and having a supportive romantic partner are both situations that increase happiness and are also both situations that increase willpower]
• (5) Non-linearity – A and B actually have a much stronger relationship than it appears (in fact they could be fully deterministically related) because correlation only captures the average extent to which A exceeding its mean coincides with B exceeding its mean, and can understate the strength of relationships that go both up and down or that go up in an inconsistent fashion (that is, it captures linear relationships, but can sometimes mask non-linear ones). [e.g., as willpower goes up happiness tends to go up as people become increasingly good at making good longer-term effective choices, but as willpower gets to extremely high levels, people start experiencing less happiness again because extreme levels of willpower are linked to reduced emotional responses of all kinds]
• (6a) Noise – The correlation is actually much larger or smaller than it seems as a result of sampling error or noise (e.g., the sample size is too low to measure it with reliability, and so it is really more like 0.32 plus or minus 0.3 and could realistically be near zero) [e.g., with a sample size of n=30, a measured correlation of 0.32 has an insanely wide 95th percentile confidence interval of -0.045 to 0.609]
• (6b) Too Many Tries – You found this correlation by looking at a long list of correlations that you calculated (and it stood out to you because it was one of the highest correlations), but there is actually not a significant correlation at all, it just looks that way because you tested so many hypotheses and each one had some chance of looking significant due to random fluctuations (so it’s unsurprising that one ended up being moderately large, and that’s the one you honed in on) [e.g., if you look at all pairs of correlations for 15 variables that leads to 105 distinct correlations, and with a sample size of 50 data points used to calculate each correlation, it is quite likely that you’d get a correlation of 0.32 or higher even if the true correlation between all pairs of variables was 0]
• (7) Outliers – There is an extreme outlier in the data (e.g., a transcription error or data corruption or disgruntled survey respondent), and without it, the calculated correlation would decrease or increase dramatically. [e.g., with n=100 data points, a crazy outlier pair of 30 for A and 1.35 for B when the rest of your values are between 0 and 1 can make the calculated correlation come out to 0.32 when the correlation calculated without that one outlier is actually -0.12]
• (8a) Selection Bias – Your data is a biased sample of the population that you actually care about due to unintentional selection effects in your sampling procedure, and so the 0.32 correlation, which you assumed applies to the broader population from which your data was drawn, is not actually representative of the population you are attempting to draw conclusions about. [e.g., you inadvertently surveyed only younger people, and in younger people, the correlation between willpower and happiness is positive, whereas in older people it is a negligible correlation, yet you’re trying to draw conclusions about the entire population which includes both young and old]
• (8b) Correlation From Conditioning – The variables A and B are actually uncorrelated if you had looked at them in the full population of interest, but you only sampled them in some subpopulation out of convenience, and A and B are both correlated with how likely you are to end up in that subpopulation, creating an observed correlation in the subpopulation that doesn’t exist in the full population [e.g., happiness and willpower are actually uncorrelated, but you only collected data on people at camp, and whether or not a person decides to go to camp is strongly positively predicted by happiness and strongly negatively predicted by willpower; therefore campers are likely to have high happiness or low willpower (though not both) creating a correlation between happiness and willpower among campers that doesn’t exist among non-campers]
• (9) The World Is Too Complex For Mere Mortals – Some mixture of (1), (2), (3), (4), (5) and (6a), (6b), (7), (8a), and (8b) are true.
• (10) Wrong Problem – Of the literally infinite variety of formulas that capture the extent to which A and B vary together, the correlation (i.e., the average of the product of standard deviations from the mean) is not the formula you are truly interested in, what you actually care about is, say, the median of the product of absolute deviations from the median, but you calculated the ordinary correlation because that’s all that you could think of to do, or that’s the only relevant function the software you used had available.
• (11) Undefined – A and B were generated from Cauchy distributions, and the true correlation between these two variables is mathematically undefined (much like how the Cauchy distribution has an undefined expected value), so your calculated value of 0.32 is a meaningless estimate of an undefined quantity.
• (12) Bug – there was a bug in the correlation calculation or data loading code, or data cleaning code and your software just happened to output 0.32, but that’s not actually the correlation value or a value of interest at all.
• (13) Wrong Calculation – You only thought you had run your correlation coefficient code, but you accidentally ran the wrong program (the one you wrote as a teen), and the number 0.32 was the fraction of baseball cards you had at that time that were in mint condition.
• (14) Memory Mistake – Your faulty memory only makes you think the correlation between A and B is 0.32, when in fact, the correlation number you saw on your computer screen (a mere 60 seconds ago) was 0.23 (thanks be to the unreliable three pounds of jello between your ears).
• (15) Dreaming – You are actually asleep right now (with your head slumped down on your keyword, and your knocked-over cup of tea dripping Earl Grey on the carpet), and you only dreamed that you calculated a 0.32 correlation, but when you wake up the correlation will turn out to be, say, -0.134 (or maybe you never collected the data in the first place and will get an F on your assignment).
• (16) God – God, it turns out, predetermined everything, and is, therefore, the one and only cause, so is the true (and only) explanation for this correlation of 0.32.
• (17) Solipsism – Metaphysical Solipsism turns out to be true, and the world has no independent existence outside of your mind, so in effect, you are the only cause, and therefore you are the cause of this experience of observation of 0.32 correlation (but what does it say about you that you would create this experience?)
• (18) Many Worlds – The Many World’s hypothesis is true, and the laws of physics don’t forbid any possible values of this particular correlation, hence for any number r within the range -1 to 1, there is a you who witnessed that correlation r, but most you’s most likely witnessed a correlation close to 0.32 (as evidenced by the fact that you witnessed it and that you are unlikely to have witnessed an unlikely event).
• (19) Simulation – The Simulation Hypothesis is true, you are part of a simulation, and the (simulated) world you live in was designed by conscious beings to have a 0.32 correlation between variables A and B (the true reason for which you will surely never understand, perhaps it has to do with getting published in a 5th dimension outer-reality academic journal on the niche topic of civilizational development in 4d space-time universes).
• (20) Relativism – Truth and meaning are relative and culturally determined, and the definition and usage of correlation, as well as the ritualistic “scientific” process of calculating it, and the belief that it should be calculated at all, are merely an artifact of your time and place, which props up the power of the current ruling elite, yet is so deeply rooted in your culture that you fail to see any other possibility.
• (21) Evil Demon – Descartes’ Evil Demon, as “clever and deceitful as he is powerful,” has been tricking you for the entirety of what you call your life, and all that you think you know of the external world is merely an illusion designed by this demon, including this godforsaken correlation.
• (22) Boltzmann Brains – The universe is infinite (in space, or time) and hence contains an infinite number of brains produced by the brief chance alignment of particles into structures capable of consciousness, and given that only a finite number of brains could evolve on planets, you have a 100% chance of being one of these randomly coalescing “Boltzmann brains,” and you just happen to be one that momentarily believes there is such a thing as correlation and that you measured a 0.32 correlation between A and B (in a moment you will pop back out of existence – bye!)
• (23) Contradiction – There is an as of yet undiscovered (but as the Incompleteness Theorem shows, impossible to rule out) contradiction in the axioms of mathematics as we know it, and a valid mathematical proof exists to show that A and B have any correlation including -1, Pi or 0.32.
• Or perhaps I’m overthinking this, and just: “as A goes up, B tends to go up a bit, on average.”

What causes journalistic distortion?

1. Equal time to each side. There are many issues for which there are two or more reasonable positions that a person can hold. Then there are those issues where one side is supported by nearly everyone who has relevant expertise, and only a few fringe people oppose that view. The trouble is that stories about highly unbalanced issues can lead to a false impression of balance, either because the journalist feels compelled to spend equal time discussing each view-point, or because the journalist is himself unaware of which side is more trustworthy. And a person with highly unrepresentative but highly quotable opinions may be quoted in the article more than is warranted. It may seem less biased to present both sides, but when one side is almost certainly right, an equal presentation may distort more than it informs.

2. Selective reporting. Since news organizations are in the business of selling the news (or, at least, driving traffic to their websites) they have a monetary incentive to produce news that people will be eager to read. Feel-good stories about a dog saving someone’s life can beat out information that might be more important or relevant to most people. What’s problematic from a reality distortion perspective though is that the rate at which events occur and the rate at which they are reported are massively out of sync. For each story about someone coming home from work only to be murdered by their ex-boyfriend, we never hear the millions of tales of people coming home to work only to sit down and eat dinner. This is problematic because the way the human brain tries to estimate how likely something is to occur involves an attempt to retrieve instances of that thing in memory. The more easily you can retrieve those instances, the more frequent you will tend to assume that thing is. If you’ve recently read about a few murder cases, you may have the impression that murder has become more common than it used to be, even if this is merely an artifact of journalists choosing (for whatever reason) to report on more murders. If you can easily think of an example of a shark attack, you may overestimate the frequency of sharks killing people.

The vividness of the accounts we hear can also alter our perception. A vivid retelling not only increases the chance that we remember an account, but also tends to increase our emotional response to it. If you’ve recently read an article that described a gruesome murder in horrid detail, you may subsequently be more afraid when walking alone on an empty street. Through this mechanism, news reading can cause people to have excessive fear of things that aren’t very likely to harm them, and fail to fear far more dangerous things that are rarely reported on. You’re much more likely to die in a car crash than be killed by terrorism, yet in a world where terrorism is reported on constantly, you will likely fear terrorism more.

3. Mix-ups of correlation and causation. Just because X tends to occur together with Y doesn’t mean that X causes Y. In fact, it could be that Y causes X instead, or that both X and Y are caused by some third thing. Unfortunately, reporters frequently get this wrong (or at least fail to make the distinction clear to the reader), especially when reporting on scientific findings. Articles will insinuate that since the latest study found higher wine/broccoli/nicotine consumption was associated with greater longevity/health/focus, that means that wine/broccoli/nicotine must actually cause those benefits. A related problem that you’ll sometimes see (especially in articles about finance) is the implication that since Y came after X, that means that Y was caused by X. It may be true that many stock market investors reacted negatively to a new bill that was just signed into law, but that doesn’t mean that’s a causal explanation of why the stock market fell 1% today. There surely were many factors influencing the change in the market’s price, some tending to push it up, others tending to push it down. Even if it were true that the signing of the bill had a strong effect (which it might be difficult to confirm), that event certainly cannot take all the credit for determining the change in the market’s price.

4. Use of low quality studies. Just because a study “proves” something, doesn’t make it so. In fact, most studies that are conducted are of poor quality for one reason or another. This could be due to a small number of study participants, lack of a control group, lack of randomization, the wrong choice of statistical test, flawed experimental protocol, poor choice of outcome measures, selective reporting of study results, or a variety of other reasons. Unfortunately, journalists rarely make it clear whether a study was of high quality, being mainly interested in what the study claimed to have found. Even the reporting of high quality studies can be problematic, if the journalist fails to mention other high quality studies that found different results. Given all the things that can go wrong in the design and execution of a study, we should be hesitant to accept the results even of those studies that look to be of high quality, until we have seen replication of the study by a different research team.

5. Lack of understanding. Many journalists write about a wide range of subjects. It is rare that they are true experts in the subject of a particular article. But as non-experts writing about what are sometimes very complicated subjects, there is the danger that journalists misunderstand the underlying subject matter. This problem occurs especially often in articles about highly technical research. The issue is compounded further by the fact that journalists are often working under tight deadlines, and so may lack the ability to do extensive background research.

6. Selective use of the facts. Even within a single story, the problem of selective reporting can be substantial. Not all facts in a case are equally entertaining or fit the narrative equally well. There is some incentive to favor those facts that improve the story over drier, though perhaps important material. Of course a political or other agenda on the part of the reporter can also determine which facts he chooses to report on. Since there is a tendency for liberals to read liberal news sources while conservatives read conservative sources, both groups may have their pre-existing views bolstered by selectively reported evidence.

7. Exaggeration of importance. News sells better if it sounds important, so news organizations have an incentive to make their news fit this criteria. One way to do this is to report on stories that actually matter to a lot of people, but sometimes it is better for the organization to just make whatever they’re reporting on sound more important than it is. The next big scientific breakthrough reported on turns out to be completely forgotten a few years or months later (but who remembers?) One of the most common forms of exaggeration in journalism is when a trend is constructed from a few data points. If a handful of celebrities are eating a lot of coconut, or museums have recently become a little more popular among people in their twenties, that doesn’t mean there’s a new fad that the world should hear about.

Choose your news sources carefully, because the information you consume determines what you believe about the world. And as incredibly valuable as journalism is, it can distort reality.