Chapter 13. Job Hunting: Everything up to One-Way Within-Groups ANOVA

Introduction

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

Job Hunting: Everything up to One-Way Within-Groups ANOVA

By: Warren Fass, University of Pittsburgh Bradford, Marsha J. McCartney, University of Kansas, and Susan A. Nolan, Seton Hall University

National Center for O*NET Development. (2017). O*NET OnLine. Retrieved from https://www.onetonline.org/.

Introduction

Everything up to One-Way Within-Groups ANOVA

Friends and education, group of university students studying, reviewing homework and preparing test
Diego Cervo/Shutterstock

Students enter college with different expectations and knowledge about their future careers. Some know exactly what career they want, and seek the degree to prepare for that career. Others only know that they will need a degree to obtain a job, but are uncertain which major would provide adequate preparation (e.g., coursework, applied experiences). Still others know what their major would be, but lack the knowledge related to the types of jobs for which that major prepares them. Fortunately, there are various career-related online database sites (e.g., Career Builder, Occupational Outlook Handbook, O*NET Online) that might assist students with career decisions. For this activity, we will explore career-related information from the O*NET Online database. You can use that database to search for occupations related to your skills, view salary information, compare related occupations, and more.

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 5

    Everything up to One-Way Within-Groups ANOVA

    O*NET allows students to explore the expected job growth for a variety of industries. For example, a total of 143 different job titles are categorized as health care and social assistance (e.g., physician assistants, registered nurses, and mental health counselors). Additionally, 134 different job titles are categorized as educational services (e.g., special education teachers, education administrators, and criminal justice post-secondary teachers). For each job title, O*NET provides the number of projected job openings for a 10-year period (2014-2024). Imagine that we randomly selected 40 different job titles from the health care and social assistance occupation category, and 40 different job titles from the educational services occupation category. We then record the projected number of jobs for each job title during the 10-year time period.

    Which statistical test could be used to determine if there was a significant difference in the number of projected jobs between the two groups?

    Question

    PXH+EtVueLJiMjSCqkXC1vEP3ay0tCoMZZszP8r1OcYlPg9stTbwqD1MXiyZ3MhRyQU/3Hgy7jqazPqNfPgdl1Vxfrhd/Qi+iTFqQVFHauOdp/cX6Q1AEin/L/R+4HeMgg8h4cuOiVrrtZBOcmT3R5hK0j+fAuUC7pMW9xNkUAfnbhNG65muX8OY3EgyE8VQteFjHBiZDtog6wHgPjfAeDm58gttKizguDkvZ6AXXmeR/QnnFir40LR2HarkCFi6VkvRB1yP3dl2fI6OKIT6gCnPDxYvSFW497LosQ==
    Correct! The researchers could have used an independent-samples t test, because there is one nominal independent variable, job category, with two levels or groups: health-care and education-related. There is a scale dependent variable, projected number of openings for each job title. And participants (job titles) are only in one of the two groups, so it is a between-groups design.
     
    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.
    Actually, that’s not the correct statistical analysis. Let’s walk through the questions on the flowchart in Appendix E to determine what analysis could be used in this case.

    Example 1 of 5

    Everything up to One-Way Within-Groups ANOVA

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

    O*NET allows students to explore the expected job growth for a variety of industries. For example, a total of 143 different job titles are categorized as health care and social assistance (e.g., physician assistance, registered nurses, and mental health counselors). Additionally, 134 different job titles are categorized as educational services (e.g., special education teachers, education administrators, and criminal justice post-secondary teachers). For each job title, O*NET provides the number of projected job openings for that job for a 10-year period (2014-2024). Imagine that we randomly selected 40 different job titles from the health care and social assistance occupation category, and 40 different job titles from the education services occupation category. We then record the projected number of jobs for each job title during the 10-year time period.

    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 5

    Everything up to One-Way Within-Groups ANOVA

    How many nominal independent variables are there?

    Question

    Q/Akfrz/Qz13c1iia8RuB7BeUIbXiznSo1NNai0VR8qmpJfvVlqVP27jevCpjgCDm8TkDdykb5M1S/VixN6aB3xHZ1nWsgEVBEMob+G6Aok=
    Correct! There is one nominal independent variable, job category. (The dependent variable, projected number of job openings, is scale.)
    Actually, there is one nominal independent variable, job category. (The dependent variable, projected number of job openings, is scale.)

    Example 1 of 5

    Everything up to One-Way Within-Groups ANOVA

    How many levels does the independent variable have?

    Question

    Mo2sQ1oCUhznV+GnK8Wf81khqMWDU6hRlouB3iPgqhGwNqp8hV5Xo2x5F8H4dQW44S93hes84sOVhvoga+5CnZv5lto=
    Correct! There are two levels or groups.
    Actually, there are two levels or groups.

    Example 1 of 5

    Everything up to One-Way Within-Groups ANOVA

    How many samples are there?

    Question

    erSrES0ZAKOTuDVIOkPYxo68vABJGDaUDXG6TmSIRkLosxO6LJX5akrQUQ0rEiotwDB3vhjEbWAnDNb8Ym+vlk3W3Cgp99rCvSXF1j7D9Odq2PTFPriRGfn1CyHSGVpFnDibDyZQo6o8DkbWaY85rZeLSiabcqypOzYupdwx3rUVpNJt
    Correct! There are two samples, one consisting of health-care jobs and one consisting of education-related jobs.
    Actually, there are two samples, one consisting of health-care jobs and one consisting of education-related jobs.

    Example 1 of 5

    Everything up to One-Way Within-Groups ANOVA

    What type of design is this?

    Question

    k5gfwlifhUJcajKPDYPy7aXBa2aHyzwx/UO795ojOcNz+53Tt0mf3xcM0Nm5g8cOaYpjbioWobo5Lcuf5tNpzQ==
    Correct! This is a between-groups design. Each participant (job title) appears in only one of the two groups.
    Actually, this is a between-groups design. Each participant (job title) appears in only one of the two groups.

    Example 1 of 5

    Everything up to One-Way Within-Groups ANOVA

    Based on the answers to these questions, what statistical analysis could be used to determine if there was a significant difference in the number of projected jobs between the two groups?

    Question

    PXH+EtVueLJiMjSCqkXC1vEP3ay0tCoMZZszP8r1OcYlPg9stTbwqD1MXiyZ3MhRyQU/3Hgy7jqazPqNfPgdl1Vxfrhd/Qi+iTFqQVFHauOdp/cX6Q1AEin/L/R+4HeMgg8h4cuOiVrrtZBOcmT3R5hK0j+fAuUC7pMW9xNkUAfnbhNG65muX8OY3EgyE8VQteFjHBiZDtog6wHgPjfAeDm58gttKizguDkvZ6AXXmeR/QnnFir40LR2HarkCFi6VkvRB1yP3dl2fI6OKIT6gCnPDxYvSFW497LosQ==
    Correct! The researchers could have used an independent-samples t test, because there is one nominal independent variable, job category, with two levels or groups: health-care jobs and education-related jobs. There is a scale dependent variable, projected number of job openings. And participants (job titles) are only in one of the two groups, so it is a between-groups design.
    Actually, that’s not the correct statistical analysis. The researchers could have used an independent-samples t test, because there is one nominal independent variable, job category, with two levels or groups: health-care jobs and education-related jobs. There is a scale dependent variable, projected number of job openings. And participants (job titles) are only in one of the two groups, so it is a between-groups design.

    Example 2 of 5

    Everything up to One-Way Within-Groups ANOVA

    The O*NET site also sorts occupations by ‘job zones’ based on the required levels of education, experience, and training. For example, occupations in the Job Zone 1 category require little or no preparation (e.g., may require either a high school degree or GED, minimal work experience related to the occupation). Occupations categorized in Job Zones 2, 3, and 4 increase in the level of preparation required for the occupation. Occupations in the Job Zone 5 category require extensive preparation (e.g., graduate school degree, more than 3 years of post-graduate degree experience). So, the larger the job zone number, the more experience and preparation necessary for that occupation. For example, there are 40 occupations (e.g., laundry/dry-cleaner, dishwasher) listed in Job Zone 1, and 159 occupations (e.g., statistician, counseling psychologist, biologist) listed in Job Zone 5. Do first-semester university students have preferences for different occupations based on job zone?
    Imagine that we recruited 90 first-semester university students as participants. We randomly assign 30 of the participants to each of three groups. One group reads a vignette containing a description of qualifications for a generic occupation using O*NET’s criteria for Job Zone 3 (medium preparation); one group reads a vignette containing a description of qualifications for a generic occupation using criteria for Job Zone 4 (considerable preparation); and finally, one group reads a vignette containing a description of qualifications of a generic occupation using criteria for Job Zone 5 (extensive preparation). After reading their respective vignettes, all participants are asked to rate, on a 7-point scale, their preference (1 = very little, 7 = a lot) for the occupation described in the vignette.

    Which statistical test could be used to determine if there was a significant difference in preference ratings among the three groups?

    Question

    Zwhsyw7IXjKMaWfz0S4Ea7qsbbLaC+MfrFYU35Qkns9k2c9Qlga7tdnXjLD1UQGtISbzODPD8SuDTBTgoDIcO12SqQgb2EJx9xhZvVaHxmWzq8L3+NrqObVQJf9szzdWSd5EM4n4FoUtRGcE8sEx+3N5+RPPyGgrDmCjwiDj57ZtHNeYnB+MbsoLfFmY5I0Ac8MXyMIFacmYntxrIvQcccyw4ZVWlhWPfRbTu7w75xoXuzXwAEPLAtD6RycCEBCiEfmQPz9Lt+EUzRCA3v0XyarXoA0pje7W
    Correct! The researchers could have used a one-way between-groups ANOVA, because there is one nominal independent variable, job-zone description, with three levels or groups: medium preparation, considerable preparation, and extensive preparation. There is a scale dependent variable, preference rating. And participants are only in one of the three groups, so it is a between-groups design.
     
    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.
    Actually, that’s not the correct statistical analysis. Let’s walk through the questions on the flowchart in Appendix E to determine what analysis could be used in this case.

    Example 2 of 5

    Everything up to One-Way Within-Groups ANOVA

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

    Imagine that we recruited 90 first-semester university students as participants. We randomly assign 30 of the participants to each of three groups. One group reads a vignette containing a description of qualifications for a generic occupation using O*NET’s criteria for Job Zone 3 (medium preparation); one group reads a vignette containing a description of qualifications for a generic occupation using criteria for Job Zone 4 (considerable preparation); and finally, one group reads a vignette containing a description of qualifications of a generic occupation using criteria for Job Zone 5 (extensive preparation). After reading their respective vignettes, all participants are asked to rate, on a 7-point scale, their preference (1 = very little, 7 = a lot) for the occupation described in the vignette.

    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 5

    Everything up to One-Way Within-Groups ANOVA

    How many nominal independent variables are there?

    Question

    Q/Akfrz/Qz13c1iia8RuB7BeUIbXiznSo1NNai0VR8qmpJfvVlqVP27jevCpjgCDm8TkDdykb5M1S/VixN6aB3xHZ1nWsgEVBEMob+G6Aok=
    Correct! There is one nominal independent variable, job-zone description. (The dependent variable, preference rating, is scale.)
    Actually, there is one nominal independent variable, job-zone description. (The dependent variable, preference rating, is scale.)

    Example 2 of 5

    Everything up to One-Way Within-Groups ANOVA

    How many levels does this independent variable have?

    Question

    00ErOc1wHr4jpEx4xSfAG7XF2pZKJ5VQm4yTntfvdymPVxBPbhn75hoYgM0mqijY2LGR7fahQLEmRiJIbc0cIhNrwg07VPheb3HzfbjfQ5dGlaHe
    Correct! There are three levels or groups: medium preparation, considerable preparation, and extensive preparation.
    Actually, there are there are three levels or groups: medium preparation, considerable preparation, and extensive preparation.

    Example 2 of 5

    Everything up to One-Way Within-Groups ANOVA

    What type of design is this?

    Question

    k5gfwlifhUJcajKPDYPy7aXBa2aHyzwx/UO795ojOcNz+53Tt0mf3xcM0Nm5g8cOaYpjbioWobo5Lcuf5tNpzQ==
    Correct! This is a between-groups design. Each participant appears in only one of the three groups.
    Actually, this is a between-groups design. Each participant appears in only one of the three groups.

    Example 2 of 5

    Everything up to One-Way Within-Groups ANOVA

    Based on the answers to these questions, what statistical analysis could be used to determine if there was a significant difference in preference ratings among the three groups?

    Question

    Zwhsyw7IXjKMaWfz0S4Ea7qsbbLaC+MfrFYU35Qkns9k2c9Qlga7tdnXjLD1UQGtISbzODPD8SuDTBTgoDIcO12SqQgb2EJx9xhZvVaHxmWzq8L3+NrqObVQJf9szzdWSd5EM4n4FoUtRGcE8sEx+3N5+RPPyGgrDmCjwiDj57ZtHNeYnB+MbsoLfFmY5I0Ac8MXyMIFacmYntxrIvQcccyw4ZVWlhWPfRbTu7w75xoXuzXwAEPLAtD6RycCEBCiEfmQPz9Lt+EUzRCA3v0XyarXoA0pje7W
    Correct! The researchers could have used a one-way between-groups ANOVA, because there is one nominal independent variable, job-zone description, with three levels or groups: medium preparation, considerable preparation, and extensive preparation. There is a scale dependent variable, preference rating. And participants are only in one of the three groups, so it is a between-groups design.
    Actually, that’s not the correct statistical analysis. The researchers could have used a one-way between-groups ANOVA, because there is one nominal independent variable, job-zone description, with three levels or groups: medium preparation, considerable preparation, and extensive preparation. There is a scale dependent variable, preference rating. And participants are only in one of the three groups, so it is a between-groups design.

    Example 3 of 5

    Everything up to One-Way Within-Groups ANOVA

    Are you concerned about preserving and improving the environment, conservation, recycling, or sustainability? If the answer is yes, then you may be interested in exploring the O*NET database for occupations that are considered ‘green occupations.’ The database contains 12 categories of green occupations (e.g., environment protection, energy efficiency, green construction). Imagine that we recruited 40 undergraduates to participate in the following study: We selected three green job categories: 1) environment protection, 2) energy efficiency, and 3) green construction, and ask the participants to rate their interest in each category on a 10-point scale (1 = not very, 10 = very).

    Which statistical test could be used to determine if there was a significant difference in interest ratings among the three groups?

    Question

    jC51nhTz2bD4HRNCOb8bLrctwrFgUh2a3zMEVokIGc0Q5LSReYcfNwWPBmzoTZiWnLKECooVHb3y2YBFY5I6Y2q9v390al7flAGCHnTZjihj+oJYW4rjGeGhhiqOcKiuDtGCABBTBwSe2rN8QPjA3ZXIJ6Oy29vehH3cqdJ7vV8hUVCHs7IoI30iAmbVvfbkRUaR4Pk/f73QbUmuV92u4S4mx8+LGkcsbzgUkksoJg9uMGEH5jo9zWx9IsbyE4fnksCurtHF/y+EvFkE2jr5d5kZndUQIItc
    Correct! The researchers could have used a one-way within-groups ANOVA, because there is one nominal independent variable, green job category, with three levels or groups: environment protection, energy efficiency, and green construction. There is a scale dependent variable, interest rating. And participants rated the three occupations, so it is a within-groups design.
     
    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.
    Actually, that’s not the correct statistical analysis. Let’s walk through the questions on the flowchart in Appendix E to determine what analysis could be used in this case.

    Example 3 of 5

    Everything up to One-Way Within-Groups ANOVA

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

    Are you concerned about preserving and improving the environment, conservation, recycling, or sustainability? If the answer is yes, then you may be interested in exploring the O*NET database for occupations that are considered ‘green occupations.’ The database contains 12 categories of green occupations (e.g., environment protection, energy efficiency, green construction). Imagine that we recruited 40 undergraduates to participate in the following study: We selected three green job categories: 1) environment protection, 2) energy efficiency, and 3) green construction, and ask the participants to rate their interest in each category on a 10-point scale (1 = not very, 10 = very).

    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 5

    Everything up to One-Way Within-Groups ANOVA

    How many nominal independent variables are there?

    Question

    Q/Akfrz/Qz13c1iia8RuB7BeUIbXiznSo1NNai0VR8qmpJfvVlqVP27jevCpjgCDm8TkDdykb5M1S/VixN6aB3xHZ1nWsgEVBEMob+G6Aok=
    Correct! There is one nominal independent variable, green job category. (The dependent variable, interest rating, is scale.)
    Actually, there is one nominal independent variable, green job category. (The dependent variable, interest rating, is scale.)

    Example 3 of 5

    Everything up to One-Way Within-Groups ANOVA

    How many levels does this independent variable have?

    Question

    00ErOc1wHr4jpEx4xSfAG7XF2pZKJ5VQm4yTntfvdymPVxBPbhn75hoYgM0mqijY2LGR7fahQLEmRiJIbc0cIhNrwg07VPheb3HzfbjfQ5dGlaHe
    Correct! There are three levels or groups: environment protection, energy efficiency, and green construction.
    Actually, there are there are three levels or groups: environment protection, energy efficiency, and green construction.

    Example 3 of 5

    Everything up to One-Way Within-Groups ANOVA

    What type of design is this?

    Question

    mE/BzzBhIzYNHpmwBzVj8ykwikrj4Fnq2o5IoPYXFHrvU024YN3He5knq55rB3PIO7MtPaayb1wkko+EmmvgnQ==
    Correct! This is a within-groups design. Each participant rated all three green job categories.
    Actually, this is a within-groups design. Each participant rated all three green job categories.

    Example 3 of 5

    Everything up to One-Way Within-Groups ANOVA

    Based on the answers to these questions, what statistical analysis could be used to determine if there was a significant difference in interest ratings among the three groups?

    Question

    jC51nhTz2bD4HRNCOb8bLrctwrFgUh2a3zMEVokIGc0Q5LSReYcfNwWPBmzoTZiWnLKECooVHb3y2YBFY5I6Y2q9v390al7flAGCHnTZjihj+oJYW4rjGeGhhiqOcKiuDtGCABBTBwSe2rN8QPjA3ZXIJ6Oy29vehH3cqdJ7vV8hUVCHs7IoI30iAmbVvfbkRUaR4Pk/f73QbUmuV92u4S4mx8+LGkcsbzgUkksoJg9uMGEH5jo9zWx9IsbyE4fnksCurtHF/y+EvFkE2jr5d5kZndUQIItc
    Correct! The researchers could have used a one-way within-groups ANOVA, because there is one nominal independent variable, green job categories, with three levels or groups: environment protection, energy efficiency, and green construction. There is a scale dependent variable, interest rating. And each participant rated all three job categories, so it is a within-groups design.
    Actually, that’s not the correct statistical analysis. The researchers could have used a one-way within-groups ANOVA, because there is one nominal independent variable, green job categories, with three levels or groups: environment protection, energy efficiency, and green construction. There is a scale dependent variable, interest rating. And each participant rated all three job categories, so it is a within-groups design.

    Example 4 of 5

    Everything up to One-Way Within-Groups ANOVA

    The O*NET database provides information for the 10-year (2014-2024) projected percentage increase in the number of jobs for over 900 occupations (e.g., occupational therapy assistant, computer systems analyst, credit counselors) in the U.S. You have decided to pursue a degree as an occupational therapy assistant due in part to a substantial projected percentage increase in jobs between 2014-2024. The projected mean percent increase for occupational therapy assistant jobs during the 10-year period for the entire United States is 42.70. You want to obtain a job in a state east of the Mississippi River (e.g., New York, New Jersey, Michigan). You randomly select a sample of 12 of these states east of the Mississippi River and calculate a projected mean percent increase of 44.19, with a standard deviation of 10.62.

    What statistical analysis could you use to determine whether the states east of the Mississippi River have a significantly different projected percentage increase in jobs, on average, than all of the states in the U.S.?

    Question

    z4NS8JQmO7f4vXwsJJUgeUK/ZjJa5NkAurBoVmydLe7MytcYtddLqYFuyGoGM6GExW552sIpRtCIz06qkbZ/B03BmdzEs3rNog0wtV85AHiIA5ySsb+ZoZK6bBPv4tdHsOK3KYPN64UjGLXlAQbiFdkWivdcAQdTdinas8+BePS58IZVAT/MoMalyhj978rO0kssL2Fio15S0m6qn/sBeMbqsYxedSMpPg+2GvREWGLYVCjfEvN61S8hy9nIT847OwyLHxPwz2bDGkjGw7MbEPFBP0AU9cEl
    Correct! The researchers could have used a single-sample t test because there is one nominal independent variable, region. There are two levels or groups: states east of the Mississippi River and all states in the U.S. The former is represented by a sample and the latter by a population. There is a scale dependent variable, projected percentage increase in jobs, and we know the population mean, but not the population standard deviation.
     
    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.
    Actually, that’s not the correct statistical analysis. Let’s walk through the questions on the flowchart in Appendix E to determine what analysis could be used in this case.

    Example 4 of 5

    Everything up to One-Way Within-Groups ANOVA

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

    The O*NET database provides information for the 10-year (2014-2024) projected percentage increase in the number of jobs for over 900 occupations (e.g., occupational therapy assistant, computer systems analyst, credit counselors) in the U.S. You have decided to pursue a degree as an occupational therapy assistant due in part to knowing that there is a substantial projected percent increase in jobs between 2014-2024. The projected mean percent increase for occupational therapy assistant during the 10-year period for the entire United States is 42.70. You want to obtain a job in a state east of the Mississippi River (e.g., New York, New Jersey, Michigan). You randomly select a sample of 12 of these states east of the Mississippi River and calculate a projected mean percent increase of 44.19, with a standard deviation of 10.62.

    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 5

    Everything up to One-Way Within-Groups ANOVA

    How many nominal independent variables are there?

    Question

    Q/Akfrz/Qz13c1iia8RuB7BeUIbXiznSo1NNai0VR8qmpJfvVlqVP27jevCpjgCDm8TkDdykb5M1S/VixN6aB3xHZ1nWsgEVBEMob+G6Aok=
    Correct! There is one nominal independent variable, region. (The dependent variable, projected percentage increase in jobs, is scale.)
    Actually, there is only one nominal independent variable, region. (The dependent variable, projected percentage increase in jobs, is scale.)

    Example 4 of 5

    Everything up to One-Way Within-Groups ANOVA

    How many levels does the independent variable have?

    Question

    IT3RX3MJwtF7GgYl+iNa/dJZJhxwRRUUKIn9r01Et7+vr9kOisbym/np9vAhu/THNK82wPHEusHAUrcJM+9xcqv1HwxtZ37X1lWZlhOADlSH48Gv
    Correct! There are two levels or groups: states east of the Mississippi River and all states in the U. S.
    Actually, there are two levels or groups: states east of the Mississippi River and all states in the U.S.

    Example 4 of 5

    Everything up to One-Way Within-Groups ANOVA

    How many samples are there?

    Question

    F+6tP8Au4CvEs3lOf9LMVirQuTgSrCPBtsRZ6RM5Tj2W+NkAFedJqhj/DWdmlpIVzg1W27TEBgaFHxMHQBEkYpDXiHLca2YHqRv9WFfZBoNxS4IEOEpGWdg86Z5JyYAzL372HLwnwXTo4aYtWrYGZ1po2GYLoIIIrxLGY4oRDiSbWzO8
    Correct! There are two levels or groups: states east of the Mississippi River and all states in the U.S. The former is represented by a sample and the latter by a population.
    Actually, there are two levels or groups: states east of the Mississippi River and all states in the U.S. The former is represented by a sample and the latter by a population.

    Example 4 of 5

    Everything up to One-Way Within-Groups ANOVA

    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, projected percentage increase in jobs, we know only the population mean of 42.70% – not the population standard deviation.
    Actually, for the scale dependent variable, projected percentage increase in jobs, we know only the population mean of 42.70% – not the population standard deviation.

    Example 4 of 5

    Everything up to One-Way Within-Groups ANOVA

    Based on the answers to these questions, what statistical analysis could you use to determine whether the sample of states east of the Mississippi River has a significantly different projected percentage increase in jobs, on average, than all of the states in the U.S.?

    Question

    z4NS8JQmO7f4vXwsJJUgeUK/ZjJa5NkAurBoVmydLe7MytcYtddLqYFuyGoGM6GExW552sIpRtCIz06qkbZ/B03BmdzEs3rNog0wtV85AHiIA5ySsb+ZoZK6bBPv4tdHsOK3KYPN64UjGLXlAQbiFdkWivdcAQdTdinas8+BePS58IZVAT/MoMalyhj978rO0kssL2Fio15S0m6qn/sBeMbqsYxedSMpPg+2GvREWGLYVCjfEvN61S8hy9nIT847OwyLHxPwz2bDGkjGw7MbEPFBP0AU9cEl
    Correct! The researchers could have used a single-sample t test because there is one nominal independent variable, region. There are two levels or groups: states east of the Mississippi River and all states in the U.S. The former is represented by a sample and the latter by a population. There is a scale dependent variable, projected percentage increase in jobs, and we know the population mean, but not the population standard deviation.
    Actually, that’s not the correct statistical analysis. The researchers could have used a single-sample t test because there is one nominal independent variable, region. There are two levels or groups: states east of the Mississippi River and all states in the U.S. The former is represented by a sample and the latter by a population. There is a scale dependent variable, projected percentage increase in jobs, and we know the population mean, but not the population standard deviation.

    Example 5 of 5

    Everything up to One-Way Within-Groups ANOVA

    Let’s look at one final example using data from O*NET. O*NET has created a category for 392 occupations called, Bright Outlook occupations. Those occupations (e.g., carpenter, critical care nurse, radiologist) are “expected to grow rapidly in the next several years, will have large numbers of job openings, or are new and emerging occupations.” Do you think the same occupation would have identical salaries regardless of the location (i.e., state) of employment? Unfortunately, the salary data for each occupation obtainable from O*NET are medians; however, we will use salary means in our example. Imagine that we are interested in comparing salaries for two states, Texas and Ohio. We then randomly select 40 of the 392 Bright Outlook occupations that are listed for both states. We calculate salary means for those 40 occupations for both Texas and Ohio.

    Which statistical test could be used to determine if there was a significant difference in salaries between the two states?

    Question

    qRkmZusB/SLvSRIIh0JfL6t3O9lgpvUWTPmcgsumjbX5llMvRA95pIGLllegUJ/f2Pj3/KplkyeEarBRczSkgA6Xai/H3PHPs2k9sxmcIv2gl9ix0iiIGRVLx/MVMMyCR47uftW3gdtmUNntNK3lDaR+kltqmRc4VTLiXJrSGsam/pRaLIsMP+82lW15IX/H/fGtx3zOAX3tShB6bmqj4p32PXvdwzYF+HXmMCZkGFNZEMmB1KDXimLxpwecJACGtQPbbNhwH+N5QxQpRli/h2CPHM9yKBQV
    Correct! The researchers could have used a paired-samples t test. There is one nominal independent variable, state, with two levels or groups, Texas and Ohio. There is a scale dependent variable, salary mean for each occupation. All participants (occupations) are in both groups (states), so it is a within-groups design.
     
    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.
    Actually, that’s not the correct statistical analysis. Let’s walk through the questions on the flowchart in Appendix E to determine what analysis could be used in this case.

    Example 5 of 5

    Everything up to One-Way Within-Groups ANOVA

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

    Let’s look at one final example using data from O*NET. O*NET has created a category for 392 occupations called, Bright Outlook occupations. Those occupations (e.g., carpenter, critical care nurse, radiologist) are “expected to grow rapidly in the next several years, will have large numbers of job openings, or are new and emerging occupations.” Do you think the same occupation would have identical salaries regardless of the location (i.e., state) of employment? Unfortunately, the salary data for each occupation obtainable from O*NET are medians; however, we will use salary means in our example. Imagine that we are interested in comparing salaries for two states, Texas and Ohio. We then randomly select 40 of the 392 Bright Outlook occupations that are listed for both states. We calculate salary means for those 40 occupations for both Texas and Ohio.

    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 5 of 5

    Everything up to One-Way Within-Groups ANOVA

    How many nominal independent variables are there?

    Question

    Q/Akfrz/Qz13c1iia8RuB7BeUIbXiznSo1NNai0VR8qmpJfvVlqVP27jevCpjgCDm8TkDdykb5M1S/VixN6aB3xHZ1nWsgEVBEMob+G6Aok=
    Correct! There is one nominal independent variable, state. (The dependent variable, salary means, is scale.)
    Actually, there is one nominal independent variable, state. (The dependent variable, salary mean for each occupation, is scale.)

    Example 5 of 5

    Everything up to One-Way Within-Groups ANOVA

    How many levels does the independent variable have?

    Question

    Mo2sQ1oCUhznV+GnK8Wf81khqMWDU6hRlouB3iPgqhGwNqp8hV5Xo2x5F8H4dQW44S93hes84sOVhvoga+5CnZv5lto=
    Correct! The independent variable has two levels or groups: Texas and Ohio.
    Actually, the independent variable has two levels or groups: Texas and Ohio.

    Example 5 of 5

    Everything up to One-Way Within-Groups ANOVA

    How many samples are there?

    Question

    erSrES0ZAKOTuDVIOkPYxo68vABJGDaUDXG6TmSIRkLosxO6LJX5akrQUQ0rEiotwDB3vhjEbWAnDNb8Ym+vlk3W3Cgp99rCvSXF1j7D9Odq2PTFPriRGfn1CyHSGVpFnDibDyZQo6o8DkbWaY85rZeLSiabcqypOzYupdwx3rUVpNJt
    Correct! There are two samples, one consisting of salary for each occupation in Texas and one consisting of salary for each occupation in Ohio.
    Actually, there are two samples, one consisting of salary for each occupation in Texas and one consisting of salary for each occupation in Ohio.

    Example 5 of 5

    Everything up to One-Way Within-Groups ANOVA

    What type of design is this?

    Question

    mE/BzzBhIzYNHpmwBzVj8ykwikrj4Fnq2o5IoPYXFHrvU024YN3He5knq55rB3PIO7MtPaayb1wkko+EmmvgnQ==
    Correct! This is a within-groups design. Each participant (occupation) has salary means from both states.
    Actually, this is a within-groups design. Each participant (occupations) has salary means from both states.

    Example 5 of 5

    Everything up to One-Way Within-Groups ANOVA

    Based on the answers to these questions, which statistical test could be used to determine if there was a significant difference between the salary means from the two groups?

    Question

    qRkmZusB/SLvSRIIh0JfL6t3O9lgpvUWTPmcgsumjbX5llMvRA95pIGLllegUJ/f2Pj3/KplkyeEarBRczSkgA6Xai/H3PHPs2k9sxmcIv2gl9ix0iiIGRVLx/MVMMyCR47uftW3gdtmUNntNK3lDaR+kltqmRc4VTLiXJrSGsam/pRaLIsMP+82lW15IX/H/fGtx3zOAX3tShB6bmqj4p32PXvdwzYF+HXmMCZkGFNZEMmB1KDXimLxpwecJACGtQPbbNhwH+N5QxQpRli/h2CPHM9yKBQV
    Correct! The researchers could have used a paired-samples t test. There is one nominal independent variable, state, with two levels or groups, Texas and Ohio. There is a scale dependent variable, salary mean for each occupation. All participants (occupations) are in both groups (states), so it is a within-groups design.
    Actually, that’s not the correct statistical analysis. The researchers could have used a paired-samples t test. There is one nominal independent variable, state, with two levels or groups, Texas and Ohio. There is a scale dependent variable, salary mean for each occupation. All participants (occupations) are in both groups (states), so it is a within-groups design.

    13.1 Activity Completed!

    Congratulations! You have completed this activity.