Question

A researcher obtains a negative value for chi-square statistic. What can you conclude because the value is negative?

Answer 1

The researcher has made a mistake chi-square statistic can never be negative

Explanation:

Pearson's chi-squared test

`\sum_(i=1)^kp_i=1`

`\sum_(i=1)^km_i=n\sum_(i=1)^kp_i=\sum_(i=1)^kx_i`

`\chi^2=\sum_(i=1)^k((x_i-m_i)^2)/(m_i)=\sum_(i=1)^k(x_i^2)/(m_i)-n`

Where

`x_i`= Observed numbers

n = Number of observations

k = Mutually exclusive classes

`p_i`= Probability of events

`m_i=np_i`

So, the value of χ² can never be negative otherwise χ value will be an imaginary number.