Chi Square 11.1 Chi Square

All the tests we’ve learned so far assume that our data is normally distributed z-test t-test We test hypotheses about parameters of these normal distributions We call these tests “Parametric Tests” 11.1 Chi Square

Review What if our data is not normally distributed? Skewed distributions Nominal or ordinal data Then we use “Nonparametric Tests” Tests that do not deal with parameters 11.1 Chi Square

Parametric vs. Nonparametric Tests Parametric Tests – tests used to analyze data from which parameters such as the mean, median, and mode can be calculated e.g. reaction time, height jumped, grade on a test, etc. Nonparametric Tests – tests used to analyze data that cannot be described by the mean, median, or mode e.g. letter grades, state of residence, gender Chi Square

Parametric vs. Nonparametric Tests Parametric Tests Test hypotheses about some parameter (e.g. about the mean) Nonparametric Tests Test hypotheses about entire distribution 11.1 Chi Square

Nonparametric Tests Chi square Nonparametric test to analyze nominal data. Recall – with nominal data, the data consist of mutually exclusive categories that have no order Chi Square

Chi Square goodness of fit One variable, 2 or more levels Compare observed data with the expected data Predicted data Based on chance Based on data 11.1 Chi Square

f o = observed value f e = expected value d.f. = (rows –1)(columns – 1) 11.1 Chi Square

Is there a difference between grade level and soda preference? Soda High School Elementary Total Coke Pepsi Sprite Mist Total F e (coke at high school) = (90)(80)/200 = 36 /36/54 /20/30 /16/24 /8 / Chi Square

1.H 0 : The two qualitative variables, grade and soda preference are independent of each other. H A : The two qualitative variables, grade and soda preference are not independent of each other. 2.Use Chi-Square distribution model. 3.Determine endpoints of the rejection region. 4.Compute Chi-Square test statistic. 5.State the conclusion Chi Square

χ 2 = At the α =.01 for (4 - 1)(2 - 1) = 3 d.f. χ critical = > 11.34, conclude that grade school and high school soda preference are not independent Chi Square

Confidence interval for σ 2 A B middle C% of model Right Tail Area for a C% Confidence Interval C% Right of A Right of B 60% % % Chi Square

Find an 80 % confidence interval for σ with n = 9 and s = Chi Square

Find an 80 % confidence interval for σ with n = 9 and s = Chi Square

Find an 60 % confidence interval for σ with n = 14 and s = Chi Square

Find an 80 % confidence interval for σ with n = 9 and s = Chi Square