null hypothesis for wilcoxon test

Null-hypothesis for a Wilcoxon Test

Conceptual Explanation

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.

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 Wilcoxon Test, like 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.

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 Wilcoxon Test, like 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. The difference between the two lies in the fact that the Wilcoxon Test is used with distributions that are heavily skewed or data that is ordinal.

Here is a template for writing a Wilcoxon Test null hypothesis.

Here is a template for writing a Wilcoxon Test null hypothesis.

*Note It is identical to the paired-sample t-test.

Here is a template for writing a Wilcoxon Test null hypothesis.

There is no significant difference in [insert the Dependent Variable] between [insert the information about the first time data on the dependent variable was collected for a sample]

and [insert the information about the second time data on the dependent variable was collected for the same sample]

Example #1

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.

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.Template:

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.

There is no significant difference in [insert the Dependent Variable] between [insert the information about the first time data on the dependent variable was collected for a sample]

and [insert the information about the second time data on the dependent variable was collected for the same sample]

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.

Null-hypothesis:

There is no significant difference in [insert the Dependent Variable] between [insert the information about the first time data on the dependent variable was collected for a sample]

and [insert the information about the second time data on the dependent variable was collected for the same sample]

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.

There is no significant difference in [insert the Dependent Variable] between [insert the information about the first time data on the dependent variable was collected for a sample]

and [insert the information about the second time data on the dependent variable was collected for the same sample]

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.

Example #2

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.

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:

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.

There is no significant difference in [insert the Dependent Variable] between [insert the information about the first time data on the dependent variable was collected for a sample]

and [insert the information about the second time data on the dependent variable was collected for the same sample]

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.

Null-hypothesis:

There is no significant difference in [insert the Dependent Variable] between [insert the information about the first time data on the dependent variable was collected for a sample]

and [insert the information about the second time data on the dependent variable was collected for the same sample]

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.

There is no significant difference in [insert the Dependent Variable] between [insert the information about the first time data on the dependent variable was collected for a sample]

and [insert the information about the second time data on the dependent variable was collected for the same sample]

There is no significant difference for “A Sense of Wellbeing” scores across two survey administrations

separated by a months.

Time for practice:

Problem #1

Researchers wish to determine if there is a significant difference in blood pressure before and after administration of an experimental medication.

Researchers wish to determine if there is a significant difference in blood pressure before and after administration of an experimental medication.

Before going on, state the

null-hypothesis in

your own words.

Researchers wish to determine if there is a significant difference in blood pressure before and after administration of an experimental medication.Template:

Researchers wish to determine if there is a significant difference in blood pressure before and after administration of an experimental medication.Template:There is no significant difference in [insert the Dependent Variable] between [insert the information about the first time data on the dependent variable was collected for a sample] and [insert the information about the second time data on the dependent variable was collected for the same sample]

Researchers wish to determine if there is a significant difference in blood pressure before and after administration of an experimental medication.Template:There is no significant difference in [insert the Dependent Variable] between [insert the information about the first time data on the dependent variable was collected for a sample] and [insert the information about the second time data on the dependent variable was collected for the same sample] Null Hypothesis:

Researchers wish to determine if there is a significant difference in blood pressure before and after administration of an experimental medication.Template:There is no significant difference in [insert the Dependent Variable] between [insert the information about the first time data on the dependent variable was collected for a sample] and [insert the information about the second time data on the dependent variable was collected for the same sample] Null Hypothesis:There is no significant difference in blood pressure

between pre and post tests of patience who took a new drug.

Problem #2

Auto-engineers equip twelve cars with a special brand of radial tires. These vehicles were then driven over a test course. Then the same 12 cars were equipped with regular belted tires and driven over the same course. After each run, the cars’ miles per gallon was measured.

Auto-engineers equip twelve cars with a special brand of radial tires. These vehicles were then driven over a test course. Then the same 12 cars were equipped with regular belted tires and driven over the same course. After each run, the cars’ miles per gallon was measured.

Before going on, state the

null-hypothesis in

your own words.

Auto-engineers equip twelve cars with a special brand of radial tires. These vehicles were then driven over a test course. Then the same 12 cars were equipped with regular belted tires and driven over the same course. After each run, the cars’ miles per gallon was measured. Template:

Auto-engineers equip twelve cars with a special brand of radial tires. These vehicles were then driven over a test course. Then the same 12 cars were equipped with regular belted tires and driven over the same course. After each run, the cars’ miles per gallon was measured. There is no significant difference in [insert the Dependent Variable] between [insert the information about the first time data on the dependent variable was collected for a sample] and [insert the information about the second time data on the dependent variable was collected for the same sample]

Auto-engineers equip twelve cars with a special brand of radial tires. These vehicles were then driven over a test course. Then the same 12 cars were equipped with regular belted tires and driven over the same course. After each run, the cars’ miles per gallon was measured. There is no significant difference in [insert the Dependent Variable] between [insert the information about the first time data on the dependent variable was collected for a sample] and [insert the information about the second time data on the dependent variable was collected for the same sample] Null Hypothesis:

Auto-engineers equip twelve cars with a special brand of radial tires. These vehicles were then driven over a test course. Then the same 12 cars were equipped with regular belted tires and driven over the same course. After each run, the cars’ miles per gallon was measured. There is no significant difference in [insert the Dependent Variable] between [insert the information about the first time data on the dependent variable was collected for a sample] and [insert the information about the second time data on the dependent variable was collected for the same sample]

There is no significant difference in gas mileage between cars equipped with radial tires and the same cars equipped with regular belted tires.