Chi-square statistic

What Chi-square statistic is

The Chi-square statistic is a test used to determine whether two categorical variables have a significant relationship with each other. It is a non-parametric test, meaning it does not make any assumptions about the underlying distribution of the data. The Chi-square statistic is used to compare observed data with expected data, and to measure the strength of the association between two variables.

Steps for Chi-square statistic:

  1. Collect data: Gather the data for the two categorical variables that you would like to test for association.
  2. Calculate expected frequencies: Calculate the expected frequency for each cell in the contingency table using the formulae: expected frequency = (row total*column total)/sample size.
  3. Calculate Chi-square statistic: Calculate the Chi-square statistic using the formulae: Chi-square statistic = Σ((observed – expected)2/expected).
  4. Determine degrees of freedom: Determine the degrees of freedom (df) using the formulae: df = (number of rows – 1)*(number of columns – 1).
  5. Find the critical value: Look up the critical value in a Chi-square distribution table using the degrees of freedom and the significance level.
  6. Determine significance: Compare the calculated Chi-square statistic with the critical value. If the calculated value is greater than the critical value, then the null hypothesis is rejected and the variables are significantly associated. If the calculated value is less than the critical value, then the null hypothesis is accepted and the variables are not significantly associated.

Examples

  1. Chi-square statistic is used to compare two or more categorical variables to determine if there is a significant association between them.

  2. Chi-square statistic is used to compare observed frequencies with expected frequencies in a contingency table to determine if there is a significant difference between them.

  3. Chi-square statistic is used to assess the goodness of fit of an observed distribution to a theoretical one.

  4. Chi-square statistic is used to test for homogeneity of proportions between groups.

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