Chi-squared test for independence

Question 1

what is this about?

Answer 1

is thee=re a relationship between two categorical variables? is one dependent on another?

Question 2

null hypothesis and chi-squared

Answer 2

that there is no association between row and column variables
is the difference due to chance and significantly insignificant

Question 3

alternative hypothesis

Answer 3

that the H0 does not occur
does not specify a direction
not onesided or two sided

Question 4

calculations

Answer 4

calculate expected values and compare to observed values

note: chi squared should only be used when expected numbers are greater or equal to five

Question 5

what is the chi squared statisic?

Answer 5

(observed - expected)^2/expected

this is summed over all r x c

If the expected and observed counts are very different, a large chi-squared results and this is evidence against H0

Question 6

determine the p value from chi squared

Answer 6

chi squared are described by degrees of freedom

positive values are skewed to the right

Question 7

chi-square test for r x c table

Answer 7

H0: no association

Ha: row and column are associated

If H0 is true, the statistic X^2 is approximatly chi distributed with df (r-1)(c-1)

conclusion: reject based on p value