Joseph KK Ho e-resources: A brief note on hypothesis and hypothesis testing: for Housing Studies students

A brief note on hypothesis and hypothesis testing: for Housing Studies students (information from perplexity.ai)

My question 1a: "Highlight the main ideas of hypothesis and hypothesis testing in the context of Research Methods of Housing Studies."

The reply: "Hypothesis and hypothesis testing in the context of Research Methods of Housing Studies revolve around the formulation of testable statements about housing phenomena and using statistical procedures to evaluate these statements. The main ideas are:

Main Ideas of Hypotheses in Housing Studies

Hypotheses are clear, testable statements that propose a relationship or difference concerning housing-related variables, such as housing prices, housing conditions, or demographic factors.
They often take the form of null hypotheses (H0), stating no effect or no difference, and alternative hypotheses (Ha), which the researcher aims to support.
Formulating these hypotheses is fundamental for setting the direction of research and guiding the analysis of housing data.

Main Ideas of Hypothesis Testing in Housing Studies

Hypothesis testing involves using sample data to determine whether there is enough evidence to reject the null hypothesis, implying that the observed effects are unlikely due to chance alone.
The process includes selecting an appropriate test (e.g., correlation analysis, t-tests), calculating a test statistic, and interpreting the p-value to make informed decisions about the hypotheses.
It allows researchers to establish scientifically supported claims about housing phenomena, such as how housing conditions relate to health, affordability, or social outcomes.

In the context of Housing Studies, hypothesis testing is crucial for validating relationships between variables like housing quality, accessibility, price determinants, or demographic impacts, providing empirical support for policy and practice decisions."

My question 1b: "Briefly explain what is critical value in hypothesis testing."

The reply: "A critical value in hypothesis testing is a cutoff point that separates the acceptance region and the rejection region on the distribution of the test statistic. It is used to decide whether to reject the null hypothesis. If the test statistic falls beyond this critical value in the rejection region, the null hypothesis is rejected; otherwise, it is not rejected.

The critical value depends on the chosen significance level (alpha, α) and whether the test is one-tailed or two-tailed. For example, in a two-tailed test with a 0.05 significance level, there are two critical values marking both tails of the distribution. In a one-tailed test, there is only one critical value corresponding to the direction of the test.

In summary, the critical value acts as a threshold against which the calculated test statistic is compared to make a decision in hypothesis testing."

My question 2: "Please briefly explain the topic of one-tailed and two-tailed test in hypothesis testing."

The reply: "A one-tailed test examines whether a parameter is significantly greater than or less than a specific value, focusing on a single direction of effect, while a two-tailed test assesses whether the parameter is simply different from that value, in either direction.

Brief Explanation:

One-Tailed Test:
- Checks for an effect in only one direction (greater than or less than).
- The critical region (area for rejecting the null hypothesis) is concentrated in one tail of the distribution.
- Used when the research hypothesis predicts a specific direction of the effect (e.g., increase or decrease).
Two-Tailed Test:
- Checks for effects in both directions (whether the parameter is either significantly higher or lower).
- The critical region is split into two tails of the distribution.
- Applied when the effect could go either way, or no specific direction is predicted (e.g., testing for difference, not necessarily an increase or decrease).

Examples:

One-Tailed Example:
Testing whether a new housing policy results in higher average property values.
- Null
  $H_{0}$
  : The policy has no effect or reduces values.
- Alternative
  $H_{a}$
  : The policy increases property values.
Two-Tailed Example:
Testing whether the average construction costs in a region differ from a standard cost.
- Null
  $H_{0}$
  : The costs are equal to the standard.
- Alternative
  $H_{a}$
  : The costs are either higher or lower than the standard.

In summary, the choice depends on whether the hypothesis predicts a specific direction of the effect (one-tailed) or simply tests for any difference or change (two-tailed)."

My question 3: "Could you provide examples of 2 hypothesis tests that examine two kinds of data relationship?"

The reply: "Here are two examples of hypothesis tests examining different types of data relationships in housing studies:

Comparing Means (Difference Relationship)

Example: Testing whether houses with air conditioning sell at a higher price than those without.
Hypotheses:
- Null (H0): There is no difference in average sale price between houses with and without air conditioning.
- Alternative (Ha): Houses with air conditioning have a higher average sale price.
Test: Two-sample t-test comparing mean house prices for the two groups.
Interpretation: If the p-value is below the significance level (e.g., 0.05), reject H0, suggesting air conditioning affects price significantly.

Comparing Sample Mean to Population Value (Mean Relationship)

Example: Testing if the average cost per square foot for homes sold by an agency is above the regional average price per square foot.
Hypotheses:
- Null (H0): The average cost per square foot by the agency is less than or equal to the regional average.
- Alternative (Ha): The agency's average cost per square foot is higher than the regional average.
Test: One-sample t-test comparing the sample mean to the known regional average.
Interpretation: A significant result indicates the agency's sales price per square foot is statistically higher than the regional average.

These examples illustrate testing relationships for: