Goodness of Fit
The chi-square goodness of fit test is a statistical method used to determine if a set of observed categorical data matches an expected distribution. You use this test when you want to check whether the frequencies of different categories in your data are consistent with a hypothesized distribution. For example, you might want to know if a six-sided die is fair by comparing the observed counts of each number rolled to the counts you would expect if each side were equally likely. The null hypothesis for the test states that the observed frequencies follow the expected distribution, while the alternative hypothesis suggests they do not.
1234567891011121314import numpy as np from scipy.stats import chisquare # Example: Testing if a die is fair # Observed counts from 60 rolls observed = np.array([8, 9, 10, 11, 12, 10]) # Expected counts if the die is fair (each side should appear 10 times) expected = np.array([10, 10, 10, 10, 10, 10]) # Perform chi-square goodness of fit test chi2_stat, p_value = chisquare(f_obs=observed, f_exp=expected) print("Chi-square statistic:", chi2_stat) print("p-value:", p_value)
When you interpret the results of a chi-square goodness of fit test, the main value to consider is the p-value. If the p-value is less than your chosen significance level (such as 0.05), you reject the null hypothesis and conclude that the observed data does not fit the expected distribution. In the die example, a high p-value would suggest the die behaves as expected, while a low p-value would indicate the die may be biased or unfair. Always ensure your expected frequencies are appropriate and that you have sufficient sample size for the test to be valid.
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Can you explain what the chi-square statistic means in this context?
How do I choose the appropriate significance level for my test?
What should I do if my expected frequencies are very small?
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The chi-square goodness of fit test is a statistical method used to determine if a set of observed categorical data matches an expected distribution. You use this test when you want to check whether the frequencies of different categories in your data are consistent with a hypothesized distribution. For example, you might want to know if a six-sided die is fair by comparing the observed counts of each number rolled to the counts you would expect if each side were equally likely. The null hypothesis for the test states that the observed frequencies follow the expected distribution, while the alternative hypothesis suggests they do not.
1234567891011121314import numpy as np from scipy.stats import chisquare # Example: Testing if a die is fair # Observed counts from 60 rolls observed = np.array([8, 9, 10, 11, 12, 10]) # Expected counts if the die is fair (each side should appear 10 times) expected = np.array([10, 10, 10, 10, 10, 10]) # Perform chi-square goodness of fit test chi2_stat, p_value = chisquare(f_obs=observed, f_exp=expected) print("Chi-square statistic:", chi2_stat) print("p-value:", p_value)
When you interpret the results of a chi-square goodness of fit test, the main value to consider is the p-value. If the p-value is less than your chosen significance level (such as 0.05), you reject the null hypothesis and conclude that the observed data does not fit the expected distribution. In the die example, a high p-value would suggest the die behaves as expected, while a low p-value would indicate the die may be biased or unfair. Always ensure your expected frequencies are appropriate and that you have sufficient sample size for the test to be valid.
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