How do you find chi squared?
and how do you find the expected values for chi squared?
I understand the formula but i conducted the experiment and it doesnt give me the theoretical value of it?
To find the chi-squared (χ²) value, you need to perform a chi-squared test. Here's how you can calculate it:
1. Set up your hypothesis: Start by defining your null hypothesis (H₀) and alternate hypothesis (H₁). This will depend on the question you are trying to answer.
2. Determine the observed frequencies: Count the number of occurrences or frequencies for each category in your data. These observed frequencies should be your actual data from the experiment.
3. Calculate the expected frequencies: The expected frequencies represent the values you would expect to see if there were no relationship between the variables. To find the expected frequency for each category, you need to calculate the expected proportion and then multiply it by the total number of observations. The formula to calculate the expected frequency is:
Expected frequency = (Total frequency for that category) * (Total frequency for that observation) / (Total number of observations)
4. Compute the chi-square value: To find the chi-square value, calculate the sum of the squared differences between the observed and expected frequencies for each category. Then divide this sum by the expected frequency for each category. Continue this process for all categories and sum up the results. The formula for computing the chi-square value is:
Chi-square (χ²) = Σ [ ( (Observed frequency - Expected frequency)² ) / Expected frequency ]
5. Determine the degrees of freedom (df): The degrees of freedom represent the number of independent pieces of information used to make the calculation. For chi-squared tests, the degrees of freedom are calculated as (number of categories - 1).
6. Look up the critical value: Use the degrees of freedom to consult a chi-squared distribution table or a statistical software to find the critical value for a given level of significance.
7. Compare the chi-square value to the critical value: If the calculated chi-square value is greater than the critical value, you reject the null hypothesis and conclude that there is a relationship between the variables. If it is smaller, you fail to reject the null hypothesis and state that there is no significant relationship.
It's worth noting that if you calculated the chi-square value and it differs from the theoretical value, there could be a few reasons for this discrepancy. These include rounding errors, sample size limitations, or mistakes in calculations. Review your steps and calculations to ensure accuracy.
Remember, performing a chi-squared test requires a good understanding of the underlying statistical concepts, so you may want to consult with a statistician or use a statistical software to ensure accurate results.