Chi-square goodness of fit test - Hypothesis Testing

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Chi-square goodness of fit test

Lessons

Notes:
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:

X∼N(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:
X2=N1(0,1)2+N2(0,1)2+⋯+Nk(0,1)2X^2=N_1(0,1)^2+N_2(0,1)^2+\cdots+N_k(0,1)^2

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

Test-Statistic:
X2=(O1−E1)E1+(O2−E2)E2+⋯+(On−En)EnX^2=\frac{(O_1-E_1)}{E_1}+\frac{(O_2-E_2)}{E_2}+\cdots+\frac{(O_n-E_n)}{E_n}

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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