A brief note on the Chi-squared test: for Housing Studies students

A brief note on the Chi-squared test: for Housing Studies students (information from perplexity.ai)

My question 1: "Highlight the main ideas of the Chi-squared test in the context of quantitative research for Housing Studies."

The reply: "The Chi-squared test in quantitative research for Housing Studies is a statistical method used to examine relationships between categorical variables, such as types of housing tenure and outcomes like premature delivery. It works by comparing observed frequencies in a contingency table with expected frequencies under the null hypothesis of no association. The test helps determine if any observed differences are due to chance or indicate a real relationship between variables.

Key ideas include:

• The test is applied to categorical data arranged in contingency tables.

• It tests the null hypothesis that there is no association between variables.

• Expected frequencies are calculated based on marginal totals assuming independence.

• The test statistic is calculated by summing the squared differences between observed and expected frequencies divided by expected frequencies.

• Degrees of freedom depend on the table size: (number of rows - 1) × (number of columns - 1).

• A significant Chi-squared result suggests an association between variables, while a non-significant result supports independence.

• Assumptions include independence of observations, sufficient sample size, and categorical data.

• It is useful for testing relationships such as between housing type and health outcomes, resident characteristics, or other categorical variables relevant in Housing Studies.

The Chi-squared test provides a rigorous way to validate hypotheses about associations between categorical factors in housing research, supporting evidence-based insights into social, health, or demographic patterns."

My question 2: "Please provide an illustrative example of the Chi-squared test employed to study the research theme of "the relatedness of the gender of the middle-class Gen Zs of Hong Kong and the willingness to purchase a residential apartment in 204-2025".."

The reply: "Here is an illustrative example of the Chi-squared test applied to the research theme of the relatedness between gender of middle-class Gen Zs in Hong Kong and their willingness to purchase a residential apartment in 2024-2025:

1. Define Variables:

   • Gender: Male, Female (categorical)

   • Willingness to Purchase Residential Apartment: Yes, No (categorical)

2. Data Collection:
   Survey a sample of middle-class Gen Z individuals in Hong Kong, recording their gender and their willingness to purchase a residential apartment in the specified years.

3. Create a Contingency Table:

Gender	Willing to Purchase (Yes)	Not Willing (No)	Total
Male	a	b	a+b
Female	c	d	c+d
Total	a+c	b+d	N

4. Hypotheses:

   • Null (H0): Gender and willingness to purchase are independent (no association).

   • Alternative (H1): Gender and willingness to purchase are related (association exists).

5. Chi-squared Test Calculation:
   Calculate expected frequencies for each cell assuming independence, then compute the Chi-squared statistic:

   $${\chi }^2=\sum \frac{(O-E{)}^2}{E}$$

   where $O$ = observed frequency, $E$ = expected frequency.

6. Decision:
   Compare the computed Chi-squared value against the critical value from Chi-squared distribution with degrees of freedom $(rows-1)\times (columns-1)=1$.

   • If ${\chi }^2$ is greater than critical value, reject H0, implying a significant association.

   • Otherwise, fail to reject H0, implying no significant association.

This test helps determine if middle-class Gen Z males and females in Hong Kong differ significantly in their willingness to buy residential apartments in 2024-2025. For example, a significant result might suggest gender-based differences in market behavior, informing targeted housing policy or marketing strategies related to this demographic in Hong Kong."

** also study a set of videos on the Chi-squared test.

A collection of blog notes on using chatgpt for research purpose.