Mastering the Chi-Square Test

What is the shape of the chi-square distribution?

• The chi-square distribution is positively skewed.

• The chi-square distribution is uniformly distributed.

• The chi-square distribution is circular in shape.

• The chi-square distribution is negatively skewed.

How do you calculate expected frequencies in a chi-square test?

• Expected frequency = Grand total / (Row total * Column total)

• Expected frequency = (Row total - Column total) / Grand total

• Expected frequency = Row total + Column total

• Expected frequency = (Row total * Column total) / Grand total.

What is the formula for calculating the chi-square statistic?

• χ² = Σ(O × E) / O

• χ² = Σ(O - E) / E²

• χ² = Σ((O - E)² / E)

• χ² = Σ(O + E)² / E

What does a high chi-square statistic indicate about the observed data?

• It indicates a significant difference between observed and expected data.

• It suggests that the observed data is irrelevant.

• It indicates a perfect match between observed and expected data.

• It shows that the expected data is incorrect.

What is the significance level commonly used in chi-square tests?

• 0.05

• 0.10

• 0.20

• 0.01

What are the degrees of freedom in a chi-square test?

• Degrees of freedom are always equal to the sample size

• Degrees of freedom in a chi-square test depend on the type of test: df = k - 1 for goodness-of-fit, and df = (rows - 1) * (columns - 1) for independence.

• df = k + 1 for goodness-of-fit

• df = (rows + 1) * (columns + 1) for independence

What is the null hypothesis in a chi-square test for independence?

• The null hypothesis states that the two categorical variables are dependent.

• The null hypothesis states that the two categorical variables are independent.

• The null hypothesis states that the two variables are correlated.

• The null hypothesis states that one variable causes changes in the other.

How do you handle expected frequencies that are less than 5?

• Use a larger sample size

• Apply a normal approximation method

• Combine categories or use Fisher's Exact Test.

• Ignore the low frequencies

Which of the following assumptions must be met for a valid Chi-Square test?

• The data should be normally distributed

• The sample size must be less than 30

• The observations must be independent

• The data should be continuous