Chi-Square Goodness of Fit Test

What is the main purpose of the Chi-Square Goodness of Fit test?

Which assumption must be met for the Chi-Square Goodness of Fit test?

What is the null hypothesis in a Chi-Square Goodness of Fit test?

Which is a requirement for the expected frequency in each category in a Chi-Square Goodness of Fit test?

Which of the following statements describes the alternative hypothesis (H1) in a Chi-Square Goodness of Fit test?

When calculating the chi-squared statistic, which component represents the expected frequency?

What is the formula to calculate the degrees of freedom (df) in the chi-squared test?

Which Google Sheets formula is used to obtain the P-value in a chi-squared test?

What is the expected frequency when all expected frequencies are equal and there are 50 observations across 10 categories?

Which term in the chi-squared formula represents the observed frequency?

What is the significance level in the Google Sheets formula to obtain the critical value of the chi-squared test?

Chi-Square Goodness of Fit Test

The Chi-Square Goodness of Fit test is a statistical method used to determine if a set of observed frequencies fits a specific theoretical distribution.
The test is used to determine if there is a significant difference between the observed frequency distribution and the theoretical distribution.
If there is no significant difference, it is said that the observed frequencies fit the expected frequencies.

Hypotheses

The null hypothesis (HO) states that the observed frequencies fit the expected frequencies.
The alternative hypothesis (H1) states that the observed frequencies do not fit the expected frequencies.
Hypotheses must be stated in a relevant manner for each specific problem.

Assumptions

The data must be obtained from a random sample.
The expected frequency for each category must be 5 or more.

Chi-Squared Test Formula

The chi-squared test statistic is calculated as: χ² = ∑[(Oi - Ei)² / Ei], where Oi is the observed frequency and Ei is the expected frequency.

Degrees of Freedom

The degrees of freedom (df) is calculated as: df = n - 1, where n is the number of observations.

Critical Value

The critical value is obtained using the Google Sheets formula: =CHISQ.INV.RT(α, df), where α is the significance level and df is the degrees of freedom.

P-Value

The P-value is obtained using the Google Sheets formula: =CHISQ.DIST.RT(x², df), where x² is the calculated chi-squared statistic and df is the degrees of freedom.

Calculating Expected Frequencies

Equal Expected Frequencies

When all expected frequencies are equal, the expected frequency (E) is calculated as: E = n/k, where n is the total number of observations and k is the number of categories.

Unequal Expected Frequencies

When the expected frequencies are not equal, the expected frequency (E) is calculated as: E = n * p, where n is the total number of observations and p is the probability for that category.

Learn about the Chi-Square Goodness of Fit test, a statistical method used to determine if observed frequencies fit a specific theoretical distribution. Understand the hypotheses and applications of this non-parametric test.