Your Happiness is like Your Height

September 22, 2019

This article shows that happiness is a random variable that is normally distributed just like height. Height follows a bell-curve, which is broad and dense in the middle and shallow at the tails. The typical normal distribution for height looks like Figure 1, below. The question is: Can happiness be inherited as well as environmental just like height?

Figure 1. Normal Distribution of Height (cm)

(Source: http://www.restore.ac.uk/srme/www/fac/soc/wie/research-new/srme/modules/mod1/8/index.html )

This article does not solve this question, but rather, shows that happiness is a random variable that is normally distributed–a first step. The idea is that if happiness were heritable, it would likely be random, just like height. If it were environmental, it would mirror the distribution of environmental characteristics–including economic, social, and political environments. According to this analysis, environmental factors such as economy, family, freedom, generosity, and trust in government are all not normally distributed.

Turning to the World Happiness Report data for 2017, I first produce a histogram of the Happiness Score overlaid with the normal density curve. A histogram plots a frequency distribution of happiness and looks like Figure 2, below.

Figure 2. Histogram of Happiness Score

(Source: https://www.kaggle.com/unsdsn/world-happiness#2017.csv )

The bell-shaped normal curve in Figure 2 shows that happiness is approximately normally distributed. To formally test the normality of the Happiness Score, I use the Shapiro-Francia Normality Test. This procedure tests whether the Happiness Score is statistically different from normal. The p-value of 0.13 reveals that the Happiness Score is not statistically different from normal. In other words, the Happiness Score is likely to be normally distributed.

Figure 3.  Shapiro-Francia Test for Normality of the Happiness Score
Happiness Score1550.986631.7361.1470.12572

This analysis shows that happiness is a random variable with a normal distribution. It does not test whether happiness is inherited, but raises the question of whether it might be. Like height, weight, and other normally distributed traits, happiness might partially be genetic and partially environmentally-affected.

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