CHI SQUARE TEST

CHI SQUARE TEST

▪A chi square test also referred as to x2 test is any statistical hypothesis test in which the sampling distribution of the test
Statistic is a chi squared distribution when the null hypothesis is true.

▪It is introduced by Karl Pearson.

▪Value of x2 can never be negative.

▪Pearson’s chi square test also known as the chi square goodness of fit test & chi squared test for independence.

▪Yates correction for continuity – to reduce the error in approximation frank yates suggested a correction for continuity that
adjusts the formula for Pearson chi squared test by subtracting 0.5 from the difference between each observed value & its expected
value in a 2*2 contingency table.

▪Mean of chi square= v

▪Variance of chi square = v2

▪It is interested in dealing with more than two populations

▪It enable us to test whether more than two population proportions are equal.

▪The chi square test distribution is known by its only parameter numbers of degrees of freedom

▪Df = ( row-1) ( column -1)

▪It should be noted that the chi square test only tells us whether two principles of classification are significantly related or not
but not measure of the degree or form of relationship.

▪The arrangement of data according to attributes in cells are called a contingency table.

▪Chi square is also known as:-

1) Goodness of fit accumulation
2) Contingency table
3) Quantitative variables
4) Co efficient of association.

▪Conditions for applying chi square test:-
1) Population & sample mean is not given in the question
2) It talks about degree of freedom

▪Chi square= n.s2/σ2

▪Chi square lies between 0 to ∞

▪It is a non- parametric test.

▪One tailed test- In this test direction is mentioned (< >), it is also known as right tailed test ( f test and chi square test is one
tailed test)

▪Two tailed test- In this direction is not mentioned (= ≠)it is also known as left tailed test.