Hi there, I'm an expert in statistical analysis with a focus on hypothesis testing. One of the most common tests used in this field is the Chi-Square test, which is a statistical tool used to determine if there is a significant difference between the expected frequencies and the observed frequencies in one or more categories. It's a non-parametric test, meaning it doesn't require data to be normally distributed. Here's a step-by-step guide on how to calculate the Chi-Square statistic:


1. Formulate the Hypotheses: Before you start calculating, you need to set up your null hypothesis (H0) and alternative hypothesis (H1). The null hypothesis typically states that there is no significant difference between the observed and expected frequencies.


2. Create a Contingency Table: Organize your data into a contingency table. This table will have the observed frequencies (O) for each category.


3. Determine Expected Frequencies (E): Calculate the expected frequencies based on the null hypothesis. If you're testing for independence, the expected frequency for each cell in the table can be calculated by multiplying the row total and column total for that cell and then dividing by the overall total.


4. Calculate the Chi-Square Statistic (x²): Now, follow these steps for each cell in your table:
- Subtract the expected frequency (E) from the observed frequency (O) to get the difference (O - E).
- Square this difference to get (O - E)².
- Divide this squared difference by the expected frequency for that cell to get (O - E)² / E.


5. Sum the Results: Add up the (O - E)² / E values from each cell to get the Chi-Square statistic (x²).


6. Determine Degrees of Freedom (df): The degrees of freedom for a Chi-Square test is calculated as (number of rows - 1) * (number of columns - 1).

7.
Find the Critical Value or p-value: Using your Chi-Square statistic and the degrees of Freedom, you can look up the critical value in a Chi-Square distribution table or calculate the p-value using statistical software.

8.
Make a Decision: If your Chi-Square statistic is greater than the critical value or if the p-value is less than your significance level (commonly set at 0.05), you reject the null hypothesis. This suggests that there is a significant difference between the observed and expected frequencies.

Now, let's move on to the translation.

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Calculate the chi square statistic x2 by completing the following steps:For each observed number in the table subtract the corresponding expected number (O -- E).Square the difference [ (O --E)2 ].Divide the squares obtained for each cell in the table by the expected number for that cell [ (O - E)2 / E ].More items...read more >>