Body Temperatures Listed below are body temperatures from six different subjects measured at two different times in a day (from Data Set 5 “Body Temperatures” in Appendix B).

a. Are the two sets of data independent or dependent? Explain.

[Image]

Verified step by step guidance

Identify the nature of the data: The problem involves body temperatures measured from the same subjects at two different times in a day.

Understand the concept of dependent and independent data: Dependent data (or paired data) means that the data points are related or paired in some way, such as measurements taken from the same subject at different times. Independent data means that the data points are not related or paired.

Analyze the data collection method: Since the body temperatures are measured from the same subjects at two different times, the data points are paired. This means that each subject's temperature at one time is related to their temperature at another time.

Conclude the relationship: Based on the analysis, the two sets of data are dependent because they involve repeated measurements from the same subjects.

Explain the implication: Understanding that the data is dependent is crucial for choosing the correct statistical test for analysis, such as a paired t-test, which is used for comparing two related samples.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Independent vs. Dependent Samples

Independent samples are those where the observations in one sample do not affect or relate to the observations in another. Dependent samples, also known as paired samples, involve observations that are related or matched in some way, such as measurements taken from the same subjects at different times. In this context, since the body temperatures are measured from the same subjects at two different times, the data sets are dependent.

Paired Sample Analysis

Paired sample analysis is used when comparing two related samples, such as measurements taken from the same subjects under different conditions. This analysis accounts for the natural pairing of the data, allowing for more accurate comparisons by considering the differences within each pair. In the given question, since the body temperatures are measured from the same individuals at two different times, a paired sample analysis would be appropriate.

Repeated Measures Design

A repeated measures design involves collecting multiple measurements from the same subjects over time or under different conditions. This design helps control for individual variability, as each subject serves as their own control. In the context of the question, the body temperatures are measured at two different times for the same subjects, indicating a repeated measures design, which is crucial for understanding the dependency between the data sets.

Watch next

Master Introduction to Statistics Channel with a bite sized video explanation from Patrick

Start learning