7.1.7 Chi-Squared Test

• What is the term for the number of values in the final calculation of a statistic that are free to vary?

  Degrees of freedom
• The chi-squared test is used to determine if the observed results are significantly different from what would be expected by chance
• What is the hypothesis in the chi-squared test that assumes there is no significant difference between observed and expected results?

  Null hypothesis
• What does the null hypothesis state in the chi-squared test?

  No significant difference
• Steps to collect data for a chi-squared test

  1️⃣ Define the null and alternative hypotheses

  2️⃣ Record observed values in a contingency table

  3️⃣ Calculate expected values based on marginal totals
• The expected value for the top-left cell in the example is 25.45
• Steps to calculate expected values for a chi-squared test

  1️⃣ Multiply each row total by each column total

  2️⃣ Divide the result by the grand total
• In the chi-squared test, the null hypothesis states that there is no significant difference
• The null hypothesis in the chi-squared test assumes there is no significant difference between observed and expected results.


  True
• Match the hypothesis with its definition in the chi-squared test:

  Null Hypothesis ↔️ No significant difference between observed and expected values

  Alternative Hypothesis ↔️ Significant difference between observed and expected values
• The chi-squared test is used to determine if the observed results are significantly different from what would be expected by chance.

  True
• What is the formula to calculate the expected value for a cell in a chi-squared test?

  $\frac{\text{Row Total} \times \text{Column Total}}{\text{Grand Total}}$
• What type of table is used to record observed values for a chi-squared test?

  Contingency table
• What does the null hypothesis state in a chi-squared test?

  No significant difference
• Under what condition is the alternative hypothesis supported in a chi-squared test?

  Substantial deviation from expected values
• How do you calculate expected values in a chi-squared test?

  \frac{\text{Row Total} \times \text{Column Total}}{\text{Grand Total}}</latex>
• Steps to apply the chi-squared formula

  1️⃣ Calculate (O - E)² / E for each cell

  2️⃣ Sum the results to find the total chi-squared value
• In the chi-squared formula, χ² represents the chi-squared value
• Degrees of freedom in a chi-squared test are calculated as (number of rows - 1) × (number of columns - 1
• If the calculated chi-squared statistic exceeds the critical value, we reject the null hypothesis.


  True
• Steps in interpreting the results of a chi-squared test

  1️⃣ Calculate the chi-squared value

  2️⃣ Find the critical value using degrees of freedom and α

  3️⃣ Compare the calculated and critical values

  4️⃣ Reject or fail to reject the null hypothesis
• Rejecting the null hypothesis implies there is a significant difference between the observed and expected values.


  True
• What statistical test is used to determine if there is a significant difference between observed and expected results?

  Chi-squared test
• How is the chi-squared statistic calculated in the chi-squared test?

  $\sum \frac{(O - E)^{2}}{E}$
• What does the alternative hypothesis in the chi-squared test state?

  Significant difference exists
• What formula is used to calculate the chi-squared statistic?

  $\sum \frac{(O - E)^{2}}{E}$
• What does the alternative hypothesis state in the chi-squared test?

  Significant difference exists
• What formula is used to calculate the expected value for a cell in a contingency table?

  $\frac{(Row \, Total \times Column \, Total)}{Grand \, Total}$
• Defining null and alternative hypotheses is the first step in collecting data for a chi-squared test.


  True
• The chi-squared test is used to determine if there is a significant difference between observed and expected results.

  True
• The alternative hypothesis in a chi-squared test posits that there is no significant difference between observed and expected values.

  False
• What is the formula for the chi-squared statistic?

  $\chi^{2} =$$\Sigma \frac{(O - E)^{2}}{E}$
• The second step in calculating the chi-squared value is to sum the results from the previous step
• What is the chi-squared formula expressed as?

  $\chi^{2} =$$\Sigma \frac{(O - E)^{2}}{E}$
• The chi-squared formula involves summing the term (O - E)² / E across all categories.


  True
• What is the commonly used significance level (α) in a chi-squared test?

  0.05
• What does it mean if the calculated chi-squared value is greater than the critical value?

  Reject the null hypothesis
• The degrees of freedom in a chi-squared test refer to the number of values free to vary in the final calculation
• Steps to collect data for a chi-squared test

  1️⃣ Define the null and alternative hypotheses

  2️⃣ Record observed values in a contingency table

  3️⃣ Calculate expected values based on marginal totals
• Match the components of the chi-squared test with their descriptions:

  Null Hypothesis ↔️ No significant difference between observed and expected values

  Alternative Hypothesis ↔️ There is a significant difference

  Degrees of Freedom ↔️ Number of values free to vary