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Chi-square goodness of fit test - Hypothesis Testing

Chi-square goodness of fit test


The chi-square distribution is the sum of standard normal distribution(s) squared. The degrees of freedom for a chi-square distribution is how many standard normal distribution(s) squared you are summing.

Normal distribution:

XN(μ,σ2)=X\sim N (\mu, \sigma^2)= Normal Distribution with mean ‘μ\mu’ and standard deviation ‘σ\sigma

So Chi-Square Distribution with k degrees of freedom:

Hypothesis Testing

Chi-Square distribution hypothesis testing comes in handy for seeing whether the observed value of some experiment fit the expected values.

OiO_i: the ithi^{th} observed data point
EiE_i: the ithi^{th} estimated data point


The critical value is found by looking at the Chi Distribution table
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Chi-square goodness of fit test

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