The document discusses the null hypothesis for a paired sample t-test. It explains that a paired sample t-test compares a dependent variable between two measurements of the same sample. It provides a template for writing the null hypothesis as "There is no significant difference in [dependent variable] between [first measurement] and [second measurement]." Two examples applying this template to compare red blood cell counts before and after moving locations, and wellbeing survey scores before and after listening to music, are given.

1. Null-hypothesis for a Paired-
Sample t-test
Conceptual Explanation

2. With hypothesis testing we are setting up a null-hypothesis
– the probability that there is no effect or
relationship – and then we collect evidence that leads
us to either accept or reject that null hypothesis.

3. With hypothesis testing we are setting up a null-hypothesis
– the probability that there is no effect or
relationship – and then we collect evidence that leads
us to either accept or reject that null hypothesis.
As you may recall, a paired-sample t-test attempts to
compare a dependent variable (e.g., test scores)
between a sample on one occasion with that same
sample on another occasion.

4. Here is a template for writing a single sample t-test null
hypothesis.

5. Here is a template for writing a single sample t-test null
hypothesis:
There is no significant difference in [insert the Dependent Variable]
between [insert description of the sample and the time information
on the dependent variable was collected] and [insert information
on the dependent variable that was collected the second time]

6. Example #1

7. Health researchers want to know if there is a
statistically significant difference in red cell counts in
individuals who move from the city to rural areas. Red-cell
counts are collected prior to leaving the city and
three months after arriving in the rural location.

8. Health researchers want to know if there is a
statistically significant difference in red cell counts in
individuals who move from the city to rural areas. Red-cell
counts are collected prior to leaving the city and
three months after arriving in the rural location.
Here is the template:
There is no significant difference in [insert the Dependent Variable]
between [insert description of the sample and the time information
on the dependent variable was collected] and [insert information
on the dependent variable that was collected the second time]

9. Health researchers want to know if there is a
statistically significant difference in red cell counts in
individuals who move from the city to rural areas. Red-cell
counts are collected prior to leaving the city and
three months after arriving in the rural location.
Here is the template:
There is no significant difference in [insert the Dependent Variable]
between [insert description of the sample and the time information
on the dependent variable was collected] and [insert information
on the dependent variable that was collected the second time]
Null-hypothesis:
There is no significant difference in red cell count between
individuals who live in the city and those same individuals after
moving to a rural community three months later.

10. Example #2

11. Let’s say we want to know if “A Sense of Wellbeing”
survey scores for teenagers listening to elevator music
increases after two months of listening.

12. Let’s say we want to know if “A Sense of Wellbeing”
survey scores for teenagers listening to elevator music
increases after one month of listening.
Template:
There is no significant difference in [insert the Dependent Variable]
between [insert description of the sample and the time information
on the dependent variable was collected] and [insert information
on the dependent variable that was collected the second time]

13. Let’s say we want to know if “A Sense of Wellbeing”
survey scores for teenagers listening to elevator music
increases after one month of listening.
Template:
There is no significant difference in [insert the Dependent Variable]
between [insert description of the sample and the time information
on the dependent variable was collected] and [insert information
on the dependent variable that was collected the second time]
Null Hypothesis:
There is no significant difference for “A Sense of Wellbeing” scores
across two survey administrations separated by one month.