Null-hypothesis for a Chi-Square Goodness of Fit Test

With hypothesis testing we are setting up a null-hypothesis –

With hypothesis testing we are setting up a null-hypothesis – the probability that there is no effect or relationship –

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 Chi-square Goodness of Fit test is a method that tests the degree to which the distribution of a nominal variable (e.g., gender, political affiliation, ethnic group, levels of age, etc.) from a sample fits the hypothesized distribution.

Example

ProblemA public opinion poll surveyed a simple random sample of 1000 voters in the blue state of Connecticut. Respondents were asked to share their party affiliation (Republican or Democrat)

Results are shown in the table below.Respondents were asked to share their party affiliation (Republican or Democrat)

Results are shown in the table below.

The expectation is that the distribution would be even or 50/50. To what degree does the sample distribution fit the expected distribution?

ProblemA public opinion poll surveyed a simple random sample of 1000 voters in the blue state of Connecticut. Respondents were asked to share their party affiliation (Republican or Democrat)

Results are shown in the table below.Respondents were asked to share their party affiliation (Republican or Democrat)

Results are shown in the table below.

The expectation is that the distribution would be even or 50/50. To what degree does the sample distribution fit the expected distribution?

ProblemA public opinion poll surveyed a simple random sample of 1000 voters in the blue state of Connecticut. Respondents were asked to share their party affiliation (Republican or Democrat)

Results are shown in the table below.

Results are shown in the table below.

The expectation is that the distribution would be even or 50/50. To what degree does the sample distribution fit the expected distribution?

ProblemA public opinion poll surveyed a simple random sample of 1000 voters in the blue state of Connecticut. Respondents were asked to share their party affiliation (Republican or Democrat)

Results are shown in the table below.

Results are shown in the table below.

The expectation is that the distribution would be even or 50/50. To what degree does the sample distribution fit the expected distribution?

Party AffiliationRepublican Democrat

320 680

ProblemA public opinion poll surveyed a simple random sample of 1000 voters in the blue state of Connecticut. Respondents were asked to share their party affiliation (Republican or Democrat)

Results are shown in the table below.

Results are shown in the table below.

The expectation is that the distribution would be even or 40/60. To what degree does the sample distribution fit the expected distribution?

Party AffiliationRepublican Democrat

320 680

ProblemA public opinion poll surveyed a simple random sample of 1000 voters in the blue state of Connecticut. Respondents were asked to share their party affiliation (Republican or Democrat)

Results are shown in the table below.

The expectation is that the distribution would be even or 40/60. To what degree does the sample distribution fit the expected distribution?

Party AffiliationRepublican Democrat

320 680

Here is a template for writing a null-hypothesis for a Chi-square Goodness of Fit Test:

Here is a template for writing a null-hypothesis for a Chi-square Goodness of Fit Test:

The [Insert Category Heading] of [Insert Nominal Variable] occur with a [Insert Probability].

Let’s go back to our problem:

ProblemA public opinion poll surveyed a simple random sample of 1000 voters in the blue state of Connecticut. Respondents were asked to share their party affiliation (Republican or Democrat)

Results are shown in the table below.

The expectation is that the distribution would be even or 40/60. To what degree does the sample distribution fit the expected distribution?

Party AffiliationRepublican Democrat

320 680

ProblemA public opinion poll surveyed a simple random sample of 1000 voters in the blue state of Connecticut. Respondents were asked to share their party affiliation (Republican or Democrat)

Results are shown in the table below.

The expectation is that the distribution would be even or 40/60. To what degree does the sample distribution fit the expected distribution?

Party AffiliationRepublican Democrat

320 680

The null-hypothesis: The [Insert Category Heading] of [Insert Categories] occur at a [Insert Hypothesized Probability] probability in Connecticut.

ProblemA public opinion poll surveyed a simple random sample of 1000 voters in the blue state of Connecticut. Respondents were asked to share their party affiliation (Republican or Democrat)

Results are shown in the table below.

The expectation is that the distribution would be even or 40/60. To what degree does the sample distribution fit the expected distribution?

Party AffiliationRepublican Democrat

320 680

The null-hypothesis: The [Insert Category Heading] of [Insert Categories] occur at a [Insert Hypothesized Probability] probability in Connecticut.

ProblemA public opinion poll surveyed a simple random sample of 1000 voters in the blue state of Connecticut. Respondents were asked to share their party affiliation (Republican or Democrat)

Results are shown in the table below.

The expectation is that the distribution would be even or 40/60. To what degree does the sample distribution fit the expected distribution?

Party AffiliationRepublican Democrat

320 680

The null-hypothesis: The party affiliation of [Insert Categories] occur at a [Insert Hypothesized Probability] probability in Connecticut.

ProblemA public opinion poll surveyed a simple random sample of 1000 voters in the blue state of Connecticut. Respondents were asked to share their party affiliation (Republican or Democrat)

Results are shown in the table below.

The expectation is that the distribution would be even or 40/60. To what degree does the sample distribution fit the expected distribution?

Party AffiliationRepublican Democrat

320 680

The null-hypothesis: The party affiliation of Republican / Democrat occur at a [Insert Hypothesized Probability] probability in Connecticut.

ProblemA public opinion poll surveyed a simple random sample of 1000 voters in the blue state of Connecticut. Respondents were asked to share their party affiliation (Republican or Democrat)

Results are shown in the table below.

The expectation is that the distribution would be even or 40/60. To what degree does the sample distribution fit the expected distribution?

Party AffiliationRepublican Democrat

320 680

The null-hypothesis: The party affiliation of Republican / Democrat occur at a .4/.6 probability in Connecticut.

Here is a template:

Here is a template:

The null-hypothesis: The [Insert Category Heading] of [Insert Categories] occur at a [Insert Hypothesized Probability] probability.