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

Introduction

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

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

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. https://worldhappiness.report/ed/2016/

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

Introduction

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

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

Choosing the Appropriate Hypothesis Test, Image Long Description

By asking the right questions about our variables and research design, we can choose the appropriate hypothesis test for our research.

Four Categories of Hypothesis Tests (IV = Independent variable; DV = dependent variable)

  • 1. Only scale variables
  • 1.1. Question about association
  • 1.1.1. Pearson correlation coefficient
  • 1.2. Question about prediction
  • 1.2.1. Regression
  • 2. Nominal IV; Scale DV
  • 2.1. One IV
  • 2.1.1. Two groups (levels)
  • 2.1.1.1. One represented by a sample, one by the population
  • 2.1.1.1.1. Mu and sigma known
  • 2.1.1.1.1.1. z test
  • 2.1.1.1.2. Only mu known
  • 2.1.1.1.2.1. Single-sample t-test
  • 2.1.1.2. Two samples
  • 2.1.1.2.1. Within-groups design
  • 2.1.1.2.1.1. Paired-samples t test
  • 2.1.1.2.2. Between-groups design
  • 2.1.1.2.2.1. Independent-samples t test
  • 2.1.2. Three or more groups (levels)
  • 2.1.2.1. Within-groups design
  • 2.1.2.1.1. One-way within-groups ANOVA
  • 2.1.2.2. Between-groups design
  • 2.1.2.2.1. One-way between groups ANOVA
  • 2.2. One-way between groups ANOVA
  • 2.2.1. Factorial ANOVA (e.g., two-way between-groups ANOVA)
  • 3. Only nominal variables
  • 3.1. One nominal variable
  • 3.1.1. Chi-square test for goodness of fit
  • 3.2. Two nominal variables
  • 3.2.1. Chi-square test for independence
  • 4. Any ordinal variables
  • 4.1. Two ordinal variables; question about association
  • 4.1.1. Spearman rank-order correlation coefficient
  • 4.2. Nominal IV and ordinal DV
  • 4.2.1. Within-groups design; two groups
  • 4.2.1.1. Wilcoxon signed-rank test
  • 4.2.2. Between-groups design
  • 4.2.2.1. Two groups
  • 4.2.2.1.1. Mann-Whitney U test
  • 4.2.2.2. Three or more groups
  • 4.2.2.2.1. Kruskal-Wallis H test

    • Example 1 of 4

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

    Example 1 of 4

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

    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).

    Example 1 of 4

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

    What statistical analysis could be used to determine whether this region has a statistically significantly different mean from the global population mean?

    Question

    +j2VpUbzMzJfoYmV3iKjIlUCw/8+FFzyckI6OiIkX/pD6q7sf3Id1d5Llj7aAIwu3YoGZRdBbP5OAdNWyhCCU4v3vxdWLMHKtCQVWTP9YJIQO2KMl7Hc087VVxkYE4ENjYqN7tHIuaeIVmWlPw7Px7O4Y/c=
    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.

    Example 1 of 4

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

    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).

    Question

    sk97pNhgnDdS8cMuwHIcNGkOQu8zhZMruu2u88fM0qGdW97cS4aHwZRZbj0MaoIISfOaTTPjzGWg1FzVajDZage/lPkk+YotrDyrM4QRuYSjUH7OQ2HACIQv/DswADhdI5A+huzRe13qreW2Z1Br7AMENdjNksgE7me7mwahmFhtkzVYuVwBFlOiJ9OZW5vUlsPBQYcLL3jLqBfNxdCDJ0EbNFFxH5eS1bf2GZ8sMwV6K6EIQ4ef/XW9nyNdS1iE2U6c0LtvlZs=
    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.

    Example 1 of 4

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

    How many nominal independent variables are there?

    Question

    Q/Akfrz/Qz13c1iia8RuB7BeUIbXiznSo1NNai0VR8qmpJfvVlqVP27jevCpjgCDm8TkDdykb5M1S/VixN6aB3xHZ1nWsgEVBEMob+G6Aok=
    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.)

    Example 1 of 4

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

    How many levels does this independent variable have?

    Question

    Mo2sQ1oCUhznV+GnK8Wf81khqMWDU6hRlouB3iPgqhGwNqp8hV5Xo2x5F8H4dQW44S93hes84sOVhvoga+5CnZv5lto=
    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.

    Example 1 of 4

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

    How many samples are there?

    Question

    F+6tP8Au4CvEs3lOf9LMVirQuTgSrCPBtsRZ6RM5Tj2W+NkAFedJqhj/DWdmlpIVzg1W27TEBgaFHxMHQBEkYpDXiHLca2YHqRv9WFfZBoNxS4IEOEpGWdg86Z5JyYAzL372HLwnwXTo4aYtWrYGZ1po2GYLoIIIrxLGY4oRDiSbWzO8
    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.

    Example 1 of 4

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

    For the level represented by a population, what parameters are known with respect to the scale dependent variable?

    Question

    7BSg33vOF8SxPKBbphxM/s7HI7R2yy2ICvH+C+t8FIZULy440VfU+4A0sbgz8vaZhTBd5uNgj4ZzbigUPhJgOMam//BAS/6XiyvwO1AxeA38zVaIfnaWSerTKidpPsUyOpT0x1iBhEk7HC937OfidA==
    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.

    Example 1 of 4

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

    Based on the answers to these questions, what test could be used?

    Question

    +j2VpUbzMzJfoYmV3iKjIlUCw/8+FFzyckI6OiIkX/pD6q7sf3Id1d5Llj7aAIwu3YoGZRdBbP5OAdNWyhCCU4v3vxdWLMHKtCQVWTP9YJIQO2KMl7Hc087VVxkYE4ENjYqN7tHIuaeIVmWlPw7Px7O4Y/c=
    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.

    Example 2 of 4

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

    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

    Example 2 of 4

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

    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?

    Question

    hUHqrCDAxABSX7FZRmPNFe5TcLeizos9/6vy+BSfxptHjKqqdQM8/23TvDpmmqYVF5+xU8ZF1iB8huEAs0x8ZK6dOTIaSKVZ+u/uIsOsPiOPSglUzloIkrLe3JtpkHNoOAcLx9jRs5bEQOFRqMIuSM3S378=
    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.

    Example 2 of 4

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

    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?

    Question

    sk97pNhgnDdS8cMuwHIcNGkOQu8zhZMruu2u88fM0qGdW97cS4aHwZRZbj0MaoIISfOaTTPjzGWg1FzVajDZage/lPkk+YotrDyrM4QRuYSjUH7OQ2HACIQv/DswADhdI5A+huzRe13qreW2Z1Br7AMENdjNksgE7me7mwahmFhtkzVYuVwBFlOiJ9OZW5vUlsPBQYcLL3jLqBfNxdCDJ0EbNFFxH5eS1bf2GZ8sMwV6K6EIQ4ef/XW9nyNdS1iE2U6c0LtvlZs=
    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.

    Example 2 of 4

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

    How many nominal independent variables are there?

    Question

    Q/Akfrz/Qz13c1iia8RuB7BeUIbXiznSo1NNai0VR8qmpJfvVlqVP27jevCpjgCDm8TkDdykb5M1S/VixN6aB3xHZ1nWsgEVBEMob+G6Aok=
    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.)

    Example 2 of 4

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

    How many levels does this independent variable have?

    Question

    Mo2sQ1oCUhznV+GnK8Wf81khqMWDU6hRlouB3iPgqhGwNqp8hV5Xo2x5F8H4dQW44S93hes84sOVhvoga+5CnZv5lto=
    Correct! There are two levels/groups, 2005-2007 and 2013-2015.
    Actually, there are two levels/groups, 2005-2007 and 2013-2015.

    Example 2 of 4

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

    How many samples are there?

    Question

    erSrES0ZAKOTuDVIOkPYxo68vABJGDaUDXG6TmSIRkLosxO6LJX5akrQUQ0rEiotwDB3vhjEbWAnDNb8Ym+vlk3W3Cgp99rCvSXF1j7D9Odq2PTFPriRGfn1CyHSGVpFnDibDyZQo6o8DkbWaY85rZeLSiabcqypOzYupdwx3rUVpNJt
    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.

    Example 2 of 4

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

    What type of design is this?

    Question

    +qC2k3IH9qJD/7+1wzkoyGLi3yn1xB+Mczz3tDKf5aO+s+6r5M34Ecy/W3ZlAVaONs672OLSR/8V4x5JMBbQQg==
    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.

    Example 2 of 4

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

    Based on the answers to these questions, what test could be used?

    Question

    hUHqrCDAxABSX7FZRmPNFe5TcLeizos9/6vy+BSfxptHjKqqdQM8/23TvDpmmqYVF5+xU8ZF1iB8huEAs0x8ZK6dOTIaSKVZ+u/uIsOsPiOPSglUzloIkrLe3JtpkHNoOAcLx9jRs5bEQOFRqMIuSM3S378=
    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.

    Example 3 of 4

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

    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

    Example 3 of 4

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

    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?

    Question

    N24VowEMOqssIovHPrehDG8MVOcbFsNFSIX5bYlP1W9bcvjQMZuISDE+A+UbrgvVBDHMt+OfWNUyUVEtoeUqF5E9BE7hczaiIYah2QMzm/b4IuIyf0QTYkwjGVct31QwSXtfBIWjF9/7ffxQ9rnzvDkBtpI=
    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.

    Example 3 of 4

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

    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?

    Question

    sk97pNhgnDdS8cMuwHIcNGkOQu8zhZMruu2u88fM0qGdW97cS4aHwZRZbj0MaoIISfOaTTPjzGWg1FzVajDZage/lPkk+YotrDyrM4QRuYSjUH7OQ2HACIQv/DswADhdI5A+huzRe13qreW2Z1Br7AMENdjNksgE7me7mwahmFhtkzVYuVwBFlOiJ9OZW5vUlsPBQYcLL3jLqBfNxdCDJ0EbNFFxH5eS1bf2GZ8sMwV6K6EIQ4ef/XW9nyNdS1iE2U6c0LtvlZs=
    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.

    Example 3 of 4

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

    How many nominal independent variables are there?

    Question

    Q/Akfrz/Qz13c1iia8RuB7BeUIbXiznSo1NNai0VR8qmpJfvVlqVP27jevCpjgCDm8TkDdykb5M1S/VixN6aB3xHZ1nWsgEVBEMob+G6Aok=
    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.)

    Example 3 of 4

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

    How many levels does this independent variable have?

    Question

    Mo2sQ1oCUhznV+GnK8Wf81khqMWDU6hRlouB3iPgqhGwNqp8hV5Xo2x5F8H4dQW44S93hes84sOVhvoga+5CnZv5lto=
    Correct! There are two levels/groups, Canadian university students and all Canadians.
    Actually, there are two levels/groups, Canadian university students and all Canadians.

    Example 3 of 4

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

    How many samples are there?

    Question

    erSrES0ZAKOTuDVIOkPYxo68vABJGDaUDXG6TmSIRkLosxO6LJX5akrQUQ0rEiotwDB3vhjEbWAnDNb8Ym+vlk3W3Cgp99rCvSXF1j7D9Odq2PTFPriRGfn1CyHSGVpFnDibDyZQo6o8DkbWaY85rZeLSiabcqypOzYupdwx3rUVpNJt
    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.

    Example 3 of 4

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

    For the level represented by a population, what parameters are known with respect to the scale dependent variable?

    Question

    f+xoaMsVRA8/kHGTamnYqLXVqtMn9oexz80p5bW94H0EpT/L4ID+m9uRFtS04DNC72DlEK5HkvdKHBoyXbtIyR46QO4wIUXsH5opPVNhFAJrPTQ4zJO3QnAsNZK2ROz/Pn6mOMUz1qhgjrGWB05VEw==
    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.

    Example 3 of 4

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

    Based on the answers to these questions, what test could be used?

    Question

    N24VowEMOqssIovHPrehDG8MVOcbFsNFSIX5bYlP1W9bcvjQMZuISDE+A+UbrgvVBDHMt+OfWNUyUVEtoeUqF5E9BE7hczaiIYah2QMzm/b4IuIyf0QTYkwjGVct31QwSXtfBIWjF9/7ffxQ9rnzvDkBtpI=
    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.

    Example 4 of 4

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

    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

    Example 4 of 4

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

    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?

    Question

    hUHqrCDAxABSX7FZRmPNFe5TcLeizos9/6vy+BSfxptHjKqqdQM8/23TvDpmmqYVF5+xU8ZF1iB8huEAs0x8ZK6dOTIaSKVZ+u/uIsOsPiOPSglUzloIkrLe3JtpkHNoOAcLx9jRs5bEQOFRqMIuSM3S378=
    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.

    Example 4 of 4

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

    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?

    Question

    sk97pNhgnDdS8cMuwHIcNGkOQu8zhZMruu2u88fM0qGdW97cS4aHwZRZbj0MaoIISfOaTTPjzGWg1FzVajDZage/lPkk+YotrDyrM4QRuYSjUH7OQ2HACIQv/DswADhdI5A+huzRe13qreW2Z1Br7AMENdjNksgE7me7mwahmFhtkzVYuVwBFlOiJ9OZW5vUlsPBQYcLL3jLqBfNxdCDJ0EbNFFxH5eS1bf2GZ8sMwV6K6EIQ4ef/XW9nyNdS1iE2U6c0LtvlZs=
    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.

    Example 4 of 4

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

    How many nominal independent variables are there?

    Question

    Q/Akfrz/Qz13c1iia8RuB7BeUIbXiznSo1NNai0VR8qmpJfvVlqVP27jevCpjgCDm8TkDdykb5M1S/VixN6aB3xHZ1nWsgEVBEMob+G6Aok=
    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.)

    Example 4 of 4

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

    How many levels does this independent variable have?

    Question

    Mo2sQ1oCUhznV+GnK8Wf81khqMWDU6hRlouB3iPgqhGwNqp8hV5Xo2x5F8H4dQW44S93hes84sOVhvoga+5CnZv5lto=
    Correct! There are two levels/groups, 2005-2007 and 2013-2015.
    Actually, there are two levels/groups, 2005-2007 and 2013-2015.

    Example 4 of 4

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

    How many samples are there?

    Question

    erSrES0ZAKOTuDVIOkPYxo68vABJGDaUDXG6TmSIRkLosxO6LJX5akrQUQ0rEiotwDB3vhjEbWAnDNb8Ym+vlk3W3Cgp99rCvSXF1j7D9Odq2PTFPriRGfn1CyHSGVpFnDibDyZQo6o8DkbWaY85rZeLSiabcqypOzYupdwx3rUVpNJt
    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.

    Example 4 of 4

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

    What type of design is this?

    Question

    +qC2k3IH9qJD/7+1wzkoyGLi3yn1xB+Mczz3tDKf5aO+s+6r5M34Ecy/W3ZlAVaONs672OLSR/8V4x5JMBbQQg==
    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.

    Example 4 of 4

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

    Based on the answers to these questions, what test could be used?

    Question

    hUHqrCDAxABSX7FZRmPNFe5TcLeizos9/6vy+BSfxptHjKqqdQM8/23TvDpmmqYVF5+xU8ZF1iB8huEAs0x8ZK6dOTIaSKVZ+u/uIsOsPiOPSglUzloIkrLe3JtpkHNoOAcLx9jRs5bEQOFRqMIuSM3S378=
    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.

    10.1 Activity Completed!

    Congratulations! You have completed this activity.