Basic Data Structures

Elementary Statistics

MTH-161D | Spring 2025 | University of Portland

January 27, 2025

Objectives

Know how data is organized into data tables
Develop the ability to understand and identify relationships between variables
Activity: Identify Variable Relationships

Previously…

Types of Variables (Diez et al., 2012)

Case Study 1

A survey was conducted on students in an introductory statistics course. Below are a few of the questions on the survey, and the corresponding variables the data from the responses were stored in:

gender: What is your gender?
intro_extra: Are you an introvert or an extrovert?
sleep: How many hours do you sleep at night, on average?
bedtime: What time do you usually go to bed?
countries: How many countries have you visited?
dread: On a scale of 1-5, how much do you dread being here?

Case Study 1: Data Matrix

Data collected on students in a statistics class on a variety of variables:

Example Data Matrix

Case Study 1: Identify Types of Variables

gender: nominal categorical
sleep: continuous numerical
bedtime: ordinal categorical
countries: discrete numerical
dread: ordinal categorical - could also be used as numerical

Relationship Among Variables

Does there appear to be a relationship between the hours of study per week and the GPA of a student?

\(\star\) As hours of study increases, the GPA also increases but for study hours around 0 to 30 hours, there is a lot of variation. There is one student with GPA > 4.0, this is likely a data error.

Explanatory vs Response Variables

To identify the explanatory variable in a pair of variables, identify which of the two is suspected of affecting the other:

\[\text{explanatory variable} \xrightarrow{\text{might affect}} \text{response variable}\]

Labeling variables as explanatory and response does not guarantee the relationship between the two is actually causal, even if there is an association identified between the two variables. We use these labels only to keep track of which variable we suspect affects the other.

Associated vs Independent Variables

When two variables show some connection with one another, they are called associated variables.
Associated variables can also be called dependent variables and vice-versa.
If two variables are not associated, i.e. there is no evident connection between the two, then they are said to be independent.
In general, association does not imply causation, and causation can only be inferred from a randomized experiment.

Activity: Identify Variable Relationships

Make sure you have a copy of the M 1/27 Worksheet. This will be handed out physically and it is also digitally available on Moodle.
Work on your worksheet by yourself for 10 minutes. Please read the instructions carefully. Ask questions if anything need clarifications.
Get together with another student.
Discuss your results.
Submit your worksheet on Moodle as a .pdf file.

References

Diez, D. M., Barr, C. D., & Çetinkaya-Rundel, M. (2012). OpenIntro statistics (4th ed.). OpenIntro. https://www.openintro.org/book/os/