# nominal, ordinal, and interval/ratio variables

1. Define nominal, ordinal, and interval/ratio variables and provide an example of each
variable type. (6)
2. Construct a hypothesis to connect each of the following concepts and identify the
independent and dependent variable for each hypothesis. (Your hypotheses do not have to
be based on an understanding of the literature. Just use your best guess and be sure to
a. Age and Happiness
b. Race and Political Party Affiliation
c. Gender and Income
3. For a research project in a political science course, a student collected data and
information about 50 countries. She used infant mortality rates to measure quality of life
in each country and the percentage of all adults who are permitted to vote as a measure of
the country’s level of democratization. Her hypothesis was that quality of life is higher in
more democratic nations. (8)
a. Identify the two concepts and how the student will operationalize (measure) each.
b. What is the level of measurement of the two variables?
c. Which is the dependent variable and which is the independent variable?
d. What is the unit of analysis?
SPSS Exercises. For these exercises, please copy and paste ALL of your output that is
produced in SPSS (remember, just right click on a table or graph in your output window to copy
it and then paste it in a Word document).
place in the document that corresponds to the question being answered (for example, paste the
appropriate SPSS output for #5 with your other answers for #5). Please do not save and attach
your SPSS output file (Canvas doesn’t like that). Rather, everything should be in a Word or PDF
document and you should only upload one document for this assignment.
For the following questions, use the dataset “GSS2018_AbbreviatedDataset.sav” (found in
“Files” on Canvas).
4. (25 points) Select three variables from the General Social Survey (GSS) data set: 1
Nominal; 1 Ordinal; and 1 Interval/Ratio. (Remember: you cannot rely on the level of
measurement label in SPSS’ “Variable View”).

For each variable, answer the following:
a. State the variable name and variable description (label).
b. Measure of Central Tendency and Measures of Variability
i. For the Nominal variable, use SPSS to create a frequency distribution in
SPSS and calculate the most appropriate measure of central tendency.
Provide a 1 sentence description of what the measure tells you.
ii. For the Ordinal variable, use SPSS to create a frequency distribution in
SPSS and calculate the most appropriate measure of central tendency.
Provide a 1 sentence description of what the measure tells you.
iii. For the Interval/Ratio variable, use SPSS to calculate the mean, median,
range, and standard deviation. In a few sentences, describe what these
measures tell you.
NOTE: You must include SPSS output (including your frequency
distribution table and descriptive statistics) AND a written description of
what the measures of central tendency and measures of variability mean
using the variable labels.
c. Graphs
i. Construct a pie chart for the Nominal variable.
ii. Construct a bar graph for the Ordinal variable.
For each graph, use the chart editor to add a title, edit the titles of your
axes, add data value labels, and add at least one “effect” (i.e., color,
NOTE: You do not need to graph the interval/ratio variable. For this
section, just copy and paste your SPSS output (i.e., the graphs) into the file
you submit to Canvas.
5. (20 points) Calculate the average years of education (EDUC) for the sample and then
calculate Z Scores for the variable EDUC (we can assume the data for this variable is
normally distributed since the sample size is so large) and answer the prompts below.
a. What is the average years of education for the sample?
b.What is the Z Score for a respondent with 12 years of education?
c. What percent of the sample falls between 12 years of education and the
mean years of education for the sample?
d.What percent of the sample has fewer than 12 years of education?
e. What percent of the sample has more than 12 years of education?
Note: You will need to use the Z-score table to answer c-e. You are not required
to paste SPSS output for this question. However, if you would like me to be able to
see your process, you can paste a screenshot of the new variable that was created
in the “Data View” of SPSS — where you will find the Z Score for a respondent
with 12 years of education.

6. (20 points) For each of the variables listed below, state the average for women and men
(SEX) and run an independent samples t-test. For each variable, state whether you reject
or fail to reject the null hypothesis (and explain what that means in each case).
a. Days of poor mental health in past 30 days (MNTLHLTH)
b. Respondents age when 1st child was born (AGEKDBRN)
c. Respondent’s income in constant dollars (REALRINC)
d. Number of hours respondent spends watching TV every day (TVHOURS)
NOTE: In addition to writing answers to the questions above, you should copy
and paste all of your SPSS output into the file you submit to Canvas. Your
interpretation of the results for this question does require a written response that
incorporates the specific variables and their descriptions. For example, “I reject
the null hypothesis. Therefore, the difference between the average age of male
and female respondents is statistically significant.”
7. (15 points) What is the average number of children (CHILDS) for each marital status
grouping (MARITAL)? Run ANOVA to determine if these differences are statistically
significant or due to sampling error.
a. State whether the differences are statistically significant or due to sampling error
and explain what information led you to that conclusion (i.e., how do you know?).
NOTE: SPSS output should include output from the ANOVA test. Your
interpretation of the results for this question also requires a written response that
incorporates the specific variables and their descriptions.

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