Introduction
(Slide 1 of 36)

Chapter 10. Global Happiness: Everything Up to the Paired-Samples t Test

Which Test Is Best?
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You must read each slide, and complete any questions on the slide, in sequence.

By Susan A. Nolan, Seton Hall University

Helliwell, J., Layard, R., & Sachs, J. (2016). World Happiness Report 2016, Update (Vol. I). New York: Sustainable Development Solutions Network. Opens in new window https://worldhappiness.report/ed/2016/

Helliwell, J., Layard, R., & Sachs, J. (2012). World Happiness Report 2012. New York: Sustainable Development Solutions Network. Opens in new window https://worldhappiness.report/ed/2012/

In this activity, we’ll describe several findings from the World Happiness Report, which can be found here: https://worldhappiness.report/ed/2016/. Then you’ll identify the statistical analysis that could have been used to draw a conclusion.

Guidelines for choosing the appropriate hypothesis test

Do you celebrate World Happiness Day every March? Probably not. It’s not really that kind of holiday. But evidence suggests that it might help the world if we all took that day to examine happiness research and consider how we might make strides in increasing happiness around the world. With some support from the United Nations, the Gallup Organization, and other organizations, a group of independent researchers has regularly published a World Happiness Report since 2012, offering recommendations for policy makers based on their findings.

A smiling elderly lady watering flowers.
Nika Art/Shutterstock
A smiling young woman outdoors.
Tyler Olson/Shutterstock
A smiling little boy using his tablet.
Singkham/Shutterstock

The 2016 report highlights patterns of self-reported happiness across countries, and within individual countries (Helliwell, Layard, & Sachs, 2016). Understanding well-being around the world has historically focused on economic measures, and sometimes health measures and education measures as well. But these measures may just be proxies for human happiness. In fact, subjective ratings of happiness depend on a range of factors like these – both those in our environment such as the economy and the government and those that are more specific to us as individuals, including health, education, and gender (Helliwell, Layard, & Sachs, 2012). The global happiness researchers suggest that we may be wiser to focus directly on increasing happiness. The next screen will describe one of the findings after which you will be asked to identify the statistical analysis that could have been used to draw a conclusion.

The World Happiness Report described the relatively normal distribution of happiness across countries. Here is a graph with those findings:

The global relatively normal distribution of happiness across countries on a scale of 0-10.
Source: https://worldhappiness.report/ed/2016/ (p. 14)

The relatively normal distribution of happiness across countries, Image Long Description

The global relatively normal distribution of happiness across countries on a scale of 0-10. The left column of the table below represents each of the 10 ladders. The second column represents the actual average happiness value.

The relatively normal distribution of happiness across countries
Ladder World
0 0,024
1 0,028
2 0,049
3 0,091
4 0,114
5 0,249
6 0,133
7 0,119
8 0,102
9 0,035
10 0,041

On a scale of 0-10, the researchers estimated a global mean of 5.353 and a standard deviation of 2.243. For the purposes of this example, let’s treat these as the actual population mean and standard deviation. The researchers also broke down countries into regions, one of which comprised Latin America and the Caribbean. Imagine that you randomly selected 10 countries from this region and found a mean happiness of 6.578 (which is, by the way, the actual mean for this region).

What statistical analysis could be used to determine whether this region has a statistically significantly different mean from the global population mean?
Great! The researchers could have used a z test. There is one nominal independent variable – region of the world. There are two levels/groups, the Latin America/Caribbean region and the entire world. The former is represented by a sample and the latter by a population. There is a scale dependent variable, happiness scores, and we know both the population mean and the population standard deviation for this measure.

Now skip ahead to the next example by clicking here. Or, for more practice walking through the flowchart questions, simply click the Next button in the bottom right corner of the screen.
That’s not the correct statistical analysis. Let’s walk through the questions on the flow chart in Appendix E to help you determine what analysis could be used in this case.

In which of the following four categories does this situation fall? Click if you’d like to see the data again. And click on the flowchart button if you’d like to see the overview for choosing the best test.

On a scale of 0-10, the researchers estimated a global mean of 5.353 and a standard deviation of 2.243. For the purposes of this example, let’s treat these as the actual population mean and standard deviation. The researchers also broke down countries into regions, one of which comprised Latin America and the Caribbean. Imagine that you randomly selected 10 countries from this region and found a mean happiness of 6.578 (which is, by the way, the actual mean for this region).
Correct! There is at least one nominal independent variable and a scale dependent variable.
Actually, there is at least one nominal independent variable and a scale dependent variable.

How many nominal independent variables are there?



Correct! There is one nominal independent variable – region of the world. (The dependent variable, happiness score, is scale.)
Actually, there is one nominal independent variable – region of the world. (The dependent variable, happiness score, is scale.)

How many levels does this independent variable have?
Correct! There are two levels/groups, the Latin America/Caribbean region and the entire world.
Actually, there are two levels/groups, the Latin America/Caribbean region and the entire world.

How many samples are there?
Correct! There are two levels/groups, the Latin America/Caribbean region and the entire world. The former is represented by a sample and the latter by a population.
Actually, there are two levels/groups, the Latin America/Caribbean region and the entire world. The former is represented by a sample and the latter by a population.

For the level represented by a population, what parameters are known with respect to the scale dependent variable?
Correct! For the scale dependent variable, happiness scores, we know both the population mean and the population standard deviation.
Actually, for the scale dependent variable, happiness scores, we know both the population mean and the population standard deviation.

Based on the answers to these questions, what test could be used?
Great! The researchers could have used a z test. There is one nominal independent variable – region of the world. There are two levels/groups, the Latin America/Caribbean region and the entire world. The former is represented by a sample and the latter by a population. There is a scale dependent variable, happiness scores, and we know both the population mean and the population standard deviation for this measure.
Actually, the researchers could have used a z test. There is one nominal independent variable – region of the world. There are two levels/groups, the Latin America/Caribbean region and the entire world. The former is represented by a sample and the latter by a population. There is a scale dependent variable, happiness scores, and we know both the population mean and the population standard deviation for this measure.

Now let’s take a look at another finding from The World Happiness Report, which provides a graph that displays the amount of change in happiness levels experienced by countries around the world. Below is an excerpt from that graph showing the countries with the biggest gains. Other countries saw little change in happiness levels, and still others saw decreases. The researchers used two data points – one between 2005 and 2007 and a second between 2013 and 2015 – to create this graph.

The amount of change in happiness levels experienced by countries around the world.
Source: https://worldhappiness.report/ed/2016/ (p. 25)

The amount of change in happiness levels experienced by countries around the world, Image Long Description

The amount of change in happiness levels experienced by countries around the world. The first column of the table below represents the country, and the second column represents the change in happiness.

The amount of change in happiness levels experienced by countries around the world
Country Change in happiness
Macedonia 0,627
Thailand 0,631
Zimbabwe 0,639
Azerbaijan 0,642
Peru 0,730
Russia 0,738
Uzbekistan 0,755
Uruguay 0,804
Slovakia 0,814
Chile 0,826
Latvia 0,872
Moldova 0,959
Ecuador 0,966
Sierra Leone 1,028
Nicaragua 1,285

If we randomly selected 20 countries from the entire data set, not just the countries on the graph, we could analyze these data to determine if there were an overall shift in happiness levels around the world. For each of the 20 countries, we would have a happiness score from both time points. What statistical analysis could be used to answer this question?
Great! The researchers could have used a paired-samples t test. There is one nominal independent variable – time point. There are two levels/groups, 2005-2007 and 2013-2015. All participants – the countries selected for this study – are in both groups. And there is a scale dependent variable, happiness scores.

Now skip ahead to the next example by clicking here. Or, for more practice walking through the flowchart questions, simply click the Next button in the bottom right corner of the screen.
That’s not the correct statistical analysis. Let’s walk through the questions on the flowchart in Appendix E to help you determine what analysis could be used in this case.

In which of the following four categories does this situation fall? Click if you’d like to see the findings again. And click on the flowchart button if you’d like to see the overview for choosing the best test.

The amount of change in happiness levels experienced by countries around the world, Image Long Description

The amount of change in happiness levels experienced by countries around the world. The first column of the table below represents the country, and the second column represents the change in happiness.

The amount of change in happiness levels experienced by countries around the world
Country Change in happiness
Macedonia 0,627
Thailand 0,631
Zimbabwe 0,639
Azerbaijan 0,642
Peru 0,730
Russia 0,738
Uzbekistan 0,755
Uruguay 0,804
Slovakia 0,814
Chile 0,826
Latvia 0,872
Moldova 0,959
Ecuador 0,966
Sierra Leone 1,028
Nicaragua 1,285

The graph displays the amount of change in happiness levels experienced by countries around the world. The researchers used two data points – one between 2005 and 2007 and a second between 2013 and 2015 – to create this graph. If we randomly selected 20 countries from the entire data set, not just the countries on the graph, we could analyze these data to determine if there were an overall shift in happiness levels around the world. For each of the 20 countries, we would have a happiness score from both time points. What statistical analysis would you use to answer this question?
Correct! There is at least one nominal independent variable and a scale dependent variable.
Actually, there is at least one nominal independent variable and a scale dependent variable.

How many nominal independent variables are there?
Correct! There is one nominal independent variable – time point. (The dependent variable, happiness score, is scale.)
Actually, there is one nominal independent variable – time point. (The dependent variable, happiness score, is scale.)

How many levels does this independent variable have?
Correct! There are two levels/groups, 2005-2007 and 2013-2015.
Actually, there are two levels/groups, 2005-2007 and 2013-2015.

How many samples are there?
Correct! There are two samples, countries assessed at the first time point and countries assessed at the second time point.
Actually, there are two samples, countries assessed at the first time point and countries assessed at the second time point.

What type of design is this?
Correct! This is a within-groups design. All countries in the study were assessed at both time points.
Actually, this is a within-groups design. All countries in the study were assessed at both time points.

Based on the answers to these questions, what test could be used?
Great! The researchers could have used a paired-samples t test. There is one nominal independent variable – time point. There are two levels/groups, 2005-2007 and 2013-2015. All participants – the countries selected for this study – are in both groups. And there is a scale dependent variable, happiness scores.
Actually, the researchers could have used a paired-samples t test. There is one nominal independent variable – time point. There are two levels/groups, 2005-2007 and 2013-2015. All participants – the countries selected for this study – are in both groups. And there is a scale dependent variable, happiness scores.

Let’s take a look at yet another finding from the World Happiness Report. The graph shows the top-fifteen ranked countries in the world for happiness level, according to the 2016 World Happiness Report. The mean happiness scores for each country are represented by the bars. For the purposes of this exercise, we’ll treat these as population means for these countries.

The graph showing the top-fifteen ranked countries in the world for happiness level.
Source: https://worldhappiness.report/ed/2016/ (p. 20)

The top-fifteen ranked countries in the world for happiness level, Image Long Description

The graph showing the top-fifteen ranked countries in the world for happiness level. The first column of the table below represents the country, and the second column represents the happiness level.

The top-fifteen ranked countries in the world for happiness level
Country Happiness
Puerto Rico 7,039
Costa Rica 7,087
United States 7,104
Austria 7,119
Israel 7,267
Sweden 7,291
Australia 7,313
New Zealand 7,334
Netherlands 7,339
Canada 7,404
Finland 7,413
Norway 7,498
Iceland 7,501
Switzerland 7,509
Denmark 7,526

We might use these means to ask questions about specific groups of people. For example, we might ask if university students in Canada have different average happiness levels than the general population of Canada. What statistical test could be used to explore this question?
Great! The researchers could have used a single-sample t test. There is one nominal independent variable – category of Canadian. There are two levels/groups, Canadian university students and all Canadians. The former is represented by a sample and the latter by a population. There is a scale dependent variable, happiness scores, and we know the population mean, but not the population standard deviation, for this measure.

Now skip ahead to the next example by clicking here. Or, for more practice walking through the flowchart questions, simply click the Next button in the bottom right corner of the screen.
That’s not the correct statistical analysis. Let’s walk through the questions on the flowchart in Appendix E to help you determine what analysis could be used in this case.

In which of the following four categories does this situation fall? Click if you’d like to see the findings again. And click on the flowchart button if you’d like to see the overview for choosing the best test.

The top-fifteen ranked countries in the world for happiness level, Image Long Description

The graph showing the top-fifteen ranked countries in the world for happiness level. The first column of the table below represents the country, and the second column represents the happiness level.

The top-fifteen ranked countries in the world for happiness level
Country Happiness
Puerto Rico 7,039
Costa Rica 7,087
United States 7,104
Austria 7,119
Israel 7,267
Sweden 7,291
Australia 7,313
New Zealand 7,334
Netherlands 7,339
Canada 7,404
Finland 7,413
Norway 7,498
Iceland 7,501
Switzerland 7,509
Denmark 7,526

The graph shows the top-fifteen ranked countries in the world for happiness level, according to the 2016 World Happiness Report. The mean happiness scores for each country are represented by the bars. For the purposes of this exercise, we’ll treat these as population means for these countries. We might use these means to ask questions about specific groups of people. For example, we might ask if university students in Canada have different average happiness levels than the general population of Canada. What statistical test would we use to explore this question?
Correct! There is at least one nominal independent variable and a scale dependent variable.
Actually, there is at least one nominal independent variable and a scale dependent variable.

How many nominal independent variables are there?
Correct! There is one nominal independent variable – category of Canadian. (The dependent variable, happiness score, is scale.)
Actually, there is one nominal independent variable – category of Canadian. (The dependent variable, happiness score, is scale.)

How many levels does this independent variable have?
Correct! There are two levels/groups, Canadian university students and all Canadians.
Actually, there are two levels/groups, Canadian university students and all Canadians.

How many samples are there?
Correct! There are two levels/groups, Canadian university students and all Canadians. The former is represented by a sample and the latter by a population.
Actually, there are two levels/groups, Canadian university students and all Canadians. The former is represented by a sample and the latter by a population.

For the level represented by a population, what parameters are known with respect to the scale dependent variable?
Correct! For the scale dependent variable, happiness scores, we know just the population mean – not the population standard deviation.
Actually, for the scale dependent variable, happiness scores, we know just the population mean – not the population standard deviation.

Based on the answers to these questions, what test could be used?
Great! The researchers could have used a single-sample t test. There is one nominal independent variable – category of person. There are two levels/groups, Canadian university students and all Canadians. The former is represented by a sample and the latter by a population. There is a scale dependent variable, happiness scores, and we know the population mean, but not the population standard deviation, for this measure.
Actually, the researchers could have used a single-sample t test. There is one nominal independent variable – category of person. There are two levels/groups, Canadian university students and all Canadians. The former is represented by a sample and the latter by a population. There is a scale dependent variable, happiness scores, and we know the population mean, but not the population standard deviation, for this measure.

Let’s look at one last finding from the World Happiness Report, which monitored changes in happiness between 2005-2007 and 2013-2015. Based on these data, they reported that “the 10 countries with the largest declines in average life evaluations typically suffered some combination of economic, political and social stresses" (p. 28). For example, if you were following world news during those years, you wouldn’t be surprised that Greece, Venezuela, and Ukraine are among these countries.

Below is an excerpt from a graph that shows changes in all countries; this excerpt just shows the decline for the bottom 10. To create this graph, the researchers subtracted the happiness level from between 2005 and 2007 from the happiness level from between 2013 and 2015.

The graph showing the bottom 10 countries with the largest declines in happiness.
Source: https://worldhappiness.report/ed/2016/ (p. 27)

The bottom 10 countries with the largest declines in happiness, Image Long Description

Graph showing the bottom 10 countries with the largest declines in happiness. The first column of the table below represents the country, and the second column represents the negative change in the happiness level.

The bottom 10 countries with the largest declines in happiness
Country Happiness change
Greece -1,294
Egypt -0,996
Saudi Arabia -0,794
Botswana -0,765
Venezuela -0,762
Yemen -0,754
India -0,750
Italy -0,735
Spain -0,711
Ukraine -0,701

If we randomly selected 4 countries from among these 10, we could analyze these data to determine if there were a statistically significant shift in happiness levels among the worst-off countries. For each of the 4 countries, we would have a happiness score from both time points. What statistical analysis could be used to answer this question?
Great! The researchers could have used a paired-samples t test. There is one nominal independent variable – time point. There are two levels/groups, 2005-2007 and 2013-2015. All participants – the countries selected for this study – are in both groups. And there is a scale dependent variable, happiness scores.

Now skip ahead to the end of the activity by clicking here. Or, for more practice walking through the flowchart questions, simply click the Next button in the bottom right corner of the screen.
That’s not the correct statistical analysis. Let’s walk through the questions on the flow chart in Appendix E to help you determine what analysis could be used in this case.

In which of the following four categories does this situation fall? Click if you’d like to see the findings again. And click on the flowchart button if you’d like to see the overview for choosing the best test.

The bottom 10 countries with the largest declines in happiness, Image Long Description

graph showing the bottom 10 countries with the largest declines in happiness. The first column of the table below represents the country, and the second column represents the negative change in the happiness level.

The bottom 10 countries with the largest declines in happiness
Country Happiness change
Greece -1,294
Egypt -0,996
Saudi Arabia -0,794
Botswana -0,765
Venezuela -0,762
Yemen -0,754
India -0,750
Italy -0,735
Spain -0,711
Ukraine -0,701

Let’s look at one last finding from the World Happiness Report, which monitored changes in happiness between 2005-2007 and 2013-2015. Based on these data, they reported that “the 10 countries with the largest declines in average life evaluations typically suffered some combination of economic, political and social stresses" (p. 28). For example, if you were following world news during those years, you wouldn’t be surprised that Greece, Venezuela, and Ukraine are among these countries. This graph shows the decline for the bottom 10. To create this graph, the researchers subtracted the happiness level from between 2005 and 2007 from the happiness level from between 2013 and 2015. If we randomly selected 4 countries from among these 10, we could analyze these data to determine if there were a statistically significant shift in happiness levels among the 10 worst-off countries. What statistical analysis would you use to answer this question?
Correct! There is at least one nominal independent variable and a scale dependent variable.
Actually, there is at least one nominal independent variable and a scale dependent variable.

How many nominal independent variables are there?
Correct! There is one nominal independent variable – time point. (The dependent variable, happiness score, is scale.)
Actually, there is one nominal independent variable – time point. (The dependent variable, happiness score, is scale.)

How many levels does this independent variable have?
Correct! There are two levels/groups, 2005-2007 and 2013-2015.
Actually, there are two levels/groups, 2005-2007 and 2013-2015.

How many samples are there?
Correct! There are two samples, countries assessed at the first time point and countries assessed at the second time point.
Actually, there are two samples, countries assessed at the first time point and countries assessed at the second time point.

What type of design is this?
Correct! This is a within-groups design. All countries in the study were assessed at both time points.
Actually, this is a within-groups design. All countries in the study were assessed at both time points.

Based on the answers to these questions, what test could be used?
Great! The researchers could have used a paired-samples t test. There is one nominal independent variable – time point. There are two levels/groups, 2005-2007 and 2013-2015. All participants – the countries selected for this study – are in both groups. And there is a scale dependent variable, happiness scores.
Actually, the researchers could have used a paired-samples t test. There is one nominal independent variable – time point. There are two levels/groups, 2005-2007 and 2013-2015. All participants – the countries selected for this study – are in both groups. And there is a scale dependent variable, happiness scores.

Congratulations! You have completed the activity and gained some good experience in choosing the best hypothesis test.