The Chi-Square Goodness of Fit Test Calculator helps you determine whether your observed data follows an expected distribution pattern. This statistical test compares observed frequencies with expected frequencies to assess if deviations are due to chance or indicate a significant difference. It's commonly used in research to analyze categorical data, such as testing if dice rolls are fair, if genetic traits follow Mendelian ratios, or if customer preferences match expected market distributions. for a quick example.
Chi-Square Goodness of Fit Test is used to determine whether sample data is consistent with a hypothesized probability distribution. It compares observed frequencies with expected frequencies to test if the differences are statistically significant.
Test Statistic:
Where:
Die roll frequencies from 60 rolls:
| Face | Observed (O) | Expected (E) | (O-E)²/E |
|---|---|---|---|
| 1 | 10 | 10 | 0.000 |
| 2 | 8 | 10 | 0.400 |
| 3 | 12 | 10 | 0.400 |
| 4 | 10 | 10 | 0.000 |
| 5 | 15 | 10 | 2.500 |
| 6 | 5 | 10 | 2.500 |
Chi-square statistic:
Degrees of freedom =
At with :
Using chi-square distribution:
Since and -value = , we fail to reject . There is insufficient evidence to conclude that the die is unfair.
Cramer's V for goodness of fit test:
Where:
For our example:
Interpretation guidelines:
With V = 0.139, this indicates a small to medium effect size, suggesting that while there are some deviations from the expected frequencies, they are relatively modest in practical terms.
# Chi-Square Goodness of Fit Test
# Observed frequencies
observed <- c(10, 8, 12, 10, 15, 5)
# Perform chi-square test
result <- chisq.test(
observed,
p = rep(1/6, 6) # Equal probabilities for each face
)
print(result)# Chi-Square Goodness of Fit Test
from scipy.stats import chisquare
# Observed frequencies
observed = [10, 8, 12, 10, 15, 5]
# Expected frequencies (equal probabilities)
n = sum(observed) # total observations
p = 1/6 # probability for each face
expected = [n * p] * 6
# Perform chi-square test
stat, pvalue = chisquare(observed, expected)
print(f'Chi-square statistic: {stat:.4f}')
print(f'p-value: {pvalue:.4f}')
# Calculate degrees of freedom
df = len(observed) - 1
# Calculate critical value
from scipy.stats import chi2
critical_value = chi2.ppf(0.95, df)
print(f'Critical value (α=0.05): {critical_value:.4f}')Consider these alternatives:
The Chi-Square Goodness of Fit Test Calculator helps you determine whether your observed data follows an expected distribution pattern. This statistical test compares observed frequencies with expected frequencies to assess if deviations are due to chance or indicate a significant difference. It's commonly used in research to analyze categorical data, such as testing if dice rolls are fair, if genetic traits follow Mendelian ratios, or if customer preferences match expected market distributions. for a quick example.
Chi-Square Goodness of Fit Test is used to determine whether sample data is consistent with a hypothesized probability distribution. It compares observed frequencies with expected frequencies to test if the differences are statistically significant.
Test Statistic:
Where:
Die roll frequencies from 60 rolls:
| Face | Observed (O) | Expected (E) | (O-E)²/E |
|---|---|---|---|
| 1 | 10 | 10 | 0.000 |
| 2 | 8 | 10 | 0.400 |
| 3 | 12 | 10 | 0.400 |
| 4 | 10 | 10 | 0.000 |
| 5 | 15 | 10 | 2.500 |
| 6 | 5 | 10 | 2.500 |
Chi-square statistic:
Degrees of freedom =
At with :
Using chi-square distribution:
Since and -value = , we fail to reject . There is insufficient evidence to conclude that the die is unfair.
Cramer's V for goodness of fit test:
Where:
For our example:
Interpretation guidelines:
With V = 0.139, this indicates a small to medium effect size, suggesting that while there are some deviations from the expected frequencies, they are relatively modest in practical terms.
# Chi-Square Goodness of Fit Test
# Observed frequencies
observed <- c(10, 8, 12, 10, 15, 5)
# Perform chi-square test
result <- chisq.test(
observed,
p = rep(1/6, 6) # Equal probabilities for each face
)
print(result)# Chi-Square Goodness of Fit Test
from scipy.stats import chisquare
# Observed frequencies
observed = [10, 8, 12, 10, 15, 5]
# Expected frequencies (equal probabilities)
n = sum(observed) # total observations
p = 1/6 # probability for each face
expected = [n * p] * 6
# Perform chi-square test
stat, pvalue = chisquare(observed, expected)
print(f'Chi-square statistic: {stat:.4f}')
print(f'p-value: {pvalue:.4f}')
# Calculate degrees of freedom
df = len(observed) - 1
# Calculate critical value
from scipy.stats import chi2
critical_value = chi2.ppf(0.95, df)
print(f'Critical value (α=0.05): {critical_value:.4f}')Consider these alternatives: