**5. Analyses**

Trends can be analyzed in various ways, with applicability depending on the research questions at hand. For our research questions, we did with two easily interpretable methods.

### **5.1 First-last comparison**

We started with a comparison between the first and last observation in each time series and assessed whether and to what extent the difference denoted a decline (−) or gain (+) in happiness. An evident limitation of this method is that it takes only a fraction of the information into account and misses possible ups and down in happiness in between. The method is also vulnerable to outliers in the first and last years. We report this analysis in **Table 1**.




#### *Technical details:*

*1.The years 2020 and 2021 are left out in this comparison because of the COVID-19 pandemic, which lowered average happiness substantially in most nations (up to one point). Since score for these years are not available for all countries, comparison would flaw*

*2.Measure codes refer to a equivalent of survey questions on happiness:* 

#### *Best-Worst possible life (Link 3)*

*Bw11 question on how one rated one's current life on a numerical scale ranging from best possible to worst possible*

#### *Happiness (Link 4)*


#### *Life-satisfaction (Link 5)*


*5.Data were rounded up to three decimal places.*

#### **Table 1.**

*Change average happiness expressed in points on scale 0–10. Difference between first and last assessment.*

#### **5.2 Linear regression**

Using all available data points, we next estimated the best-fitting regression line, applying ordinary least square analysis. This analysis is presented in **Figure 3**. The resulting unstandardized regression coefficient denotes the angle of deviation from the horizontal line of no change. Since we deal with a 0–10 range, a regression coefficient of +0.01 denotes a yearly increase in happiness of 1%, giving a rise of a full point in 10 years. We report this analysis in **Table 2**.

#### **Figure 3.**

*Example of trend analysis using ordinary least squares regression.*










#### *Technical details:*


#### *Best-Worst possible life (Link 3)*

*Bw11 question on how one rated one's current life on a numerical scale ranging from best possible to worst possible*

#### *Happiness (Link 4)*


#### *Life-satisfaction (Link 5)*


*ls10+11question on life-satisfaction answer rated on 10 and 11-step numeral response scale*


#### **Table 2.**

*Change average happiness expressed in average annual increase/decline 1946–2021. Change expressed in linear regression coefficients.*

#### **5.3 Significance of change in separate time-series**

In this analysis, we also considered the statistical significance of observed rise or decline in happiness, which will depend on both the number of observations and the size of deviations from the average trend. We do that using confidence intervals on which the reader can see whether or not the difference falls with a 95% interval above or below zero, but also how big that interval is.

This test for statistical significance involves the debatable assumption that the available data points provide an a-select sample of all years in the period in a particular nation. The test is also quite severe for the time series close to the minimum of 10 data points. A change on only 10 observations with a standard deviation of 0.1 must be at least 0.07 to reach statistical significance.

#### **5.4 Significance of change over all time-series**

In **Table 2**, we also reported the average yearly change of average happiness in all nations in a period and at the bottom of the table, we did that for all periods together. We did that in two ways, (1) we presented the *total change* taking the average of the change coefficient irrespective of the sign. This tells us how much average happiness has changed. In addition, we assess the *net change*, using the difference between change to the positive and change to the negative. This tells whether average happiness has risen more than declined.

In this case, we also assessed statistical significance, while acknowledging that this test is even more debatable now, since the countries at hand cannot be considered to provide a random sample of all nations at that time. In this test, we meet again with the problem of small numbers, now the number of time series in a period. With only three time series over the years 1946–2019, the average change must be at least 0.15 to reach the 5% level of significance. Given these limitations, the reader can also opt to ignore the statistical significance and take the average change scores as they are.

#### **6. Results**

We can now answer the research questions raised in Section 1.4.

#### **6.1 Has average happiness in nations changed over time?**

In **Table 1**, we noticed the presence of a difference between the first and last observed average and found a difference in all nations, ranging from a 1.8-point rise in Poland after the fall of communism to a 1.2-point decline in Egypt. The average rise was 0.65 points and the average decline was 0.58 points, so a change of about 6% in both directions.

In **Table 2**, we considered all the data points and report the coefficient of linear change through these points. In this case, we could assess statistical significance. Of the 200 trends up to 2019, 81 were significant at the 5% level, while 119 were not. So, there was less change than stability in happiness over the years and countries considered here. Still, the 40% cases of significant change are not to be neglected. The inclusion of the COVID years 2020–2021 rises the value to 47%.

#### **6.2 Was there more rise than decline?**

At the bottom of **Table 1**, we see that there were 50 cases of rise and 30 cases of decline in average happiness in nations over the years. The average size of the rise was +0.65 points and the average size of the decline was −.58. So clearly more rise than decline.

At the bottom of **Table 2**, we see that average happiness changed significantly only in 37 nations, of which 26 changed to greater happiness and 11 to less, the average size of the chances being similar. So again, more rise than decline. Remember that this test for significance is quite severe given the many time series around the minimum of 10 data points (cf. Section 5.2), even in this contestable test.

At the bottom of **Table 2**, we can also see that the average *net change* in the level of happiness over all the years and nations was positive, with a significant mean of +0.007. We report in more detail on this finding in another paper [20].

#### **6.3 What was the size of these changes?**

At the bottom of **Table 1**, we see that the average size of the rise was +0.65 points and the average size of the decline was −0.58 points. When expressed as a percentage on the possible 0 to 10 range, this denotes about a 6% change to better or worse. When expressed on the actual range of 4.4 between 8.2 in Denmark and 3.8 in Tanzania [19], the changes are respectively 15% to the better and 13% to the worse.

The size of the changes reflects better in the change coefficients in **Table 2**. Considerable changes to the positive appear again for the post-communist East-European countries after the year 2000, while considerable negative changes appear in the South-European countries that went through an economic crisis in these years. Remember that a coefficient of 0.01 denotes a yearly change of 1%, which will result in a change of a full point on a scale of 0–10 in 10 years. Note that most of the change coefficients are below that level, some just being zero (e.g., hl4 in Norway 1981–2018).

At the bottom of **Table 2**, we presented the average *total change* over all periods and nations, which is +0.016. This mean is based on 200 time series and is statistically significant. This corresponds to a yearly change of 0.16% which denotes a one-point change in average happiness in a nation in 63 years. The *net change* of +0.007 corresponds to an average yearly rise in the happiness of 0.07%. At this rate, a one-point increase in happiness (10%) will take 143 years. This is a factor 10 less than the spectacular rise in longevity in the period considered here2 but also signifies a change for the better.

#### **6.4 Did the COVID epidemic leave average happiness unaffected?**

To date (December 2022), we have trend data on average happiness that include the years 2020–2021 for 117 time series in 46 nations. The change scores at the bottom of **Table 2** show that the inclusion of these years reduces the average rise by 0,003 points and increases the average decline by 0.01 points. An illustrative case is the United Kingdom, where average happiness declined from 7.4 in 2019 to 7.1 in 2020 as can be seen https://worlddatabaseofhappiness.eur.nl/nations/united-kingdom-16/.

<sup>2</sup> Longevity increased by some 10 years since 1950 and denotes a yearly change of about 0.08% [21].
