Chapter 13

The Chi Square Test ( ) : is a nonparametric test of significance - used with nominal data -it makes no assumptions about the shape of the distribution **ie. It does not assume the distribution is normal -therefore, it is considered a distribution-free test of significance -always tests the hypothesis of difference Note: Parametric tests (EX: ANOVA) are usually preferred because they have greater sensitivity. -however, when the assumption of normality is violated then a nonparametric test can be just as powerful -other nonparametric tests include: For nominal data: The Binomial Test For Ordinal data: The Sign Test (for correlated samples) Wilcoxon matched-pairs signed-rank test (correlated) Mann-Whitney U-test (for independent samples)

-used when you have only 1 IV with a number of levels -also called the Goodness of Fit Test (or 1×k chi-square) --k = number of levels of the IV Formula: fo = observed frequencies fe = expected frequencies EXAMPLE: A researcher wants to know if there is a significant difference in people’s preference for fast food restaurants. IV: Fast Food Restaurants (In n Out, Baker’s, and McDonald’s) DV (Data): Number of people preferring each restaurant fo = actual # of preferences fe = expected # of preferences based purely on chance Calculate fe : This would be called a 1x3 chi square test

Evaluation of goodness of fit Tests the Chi-Square Hypothesis: Ho: fo = fe Ha: fo ≠ fe After calculating : -calculate the degrees of freedom **df = k – 1 -find critical values on Table I -if the calculated is equal to or greater than the table value, Reject Ho

-used when you have 2 IV’s -also called the Test of Independence (or r×k chi-square) --k = number of levels of the IV Calculation: -Step 1: Make a contingency table *label each column with a level of the first IV & each row with a level of the 2 nd IV *put the corresponding fo in the cell *add the cells in the same rows together ( fr ) *add the cells in the same columns together ( fc ) -Step 2: Plug values into Chi-Square Formula *Formula is the same as goodness of fit with one difference - fe is calculated using this formula -Step 3: Evaluate *df= (r -1) (k – 1) *Critical Values on Table I -if the calculated value is equal to or greater than the table value, Reject Ho

Looking at the chi-square formula, a rule of thumb is: -if fo-fe is small then chi square will be small -if fo-fe is large then chi square will be large Each observation must be independent of all other observations -ie. You can not make several observations of the same person and then treat those observations like they came from different people -EX: a person can not be marked as a republican and a democrat Chi Square will never produce a negative value -you can’t have a negative number of observations