Chi-Square Test Section 12.1
Categorical Variables • Based on observations • Univariate – single categorical variable • Example: Sample 100 people & ask if they agree or disagree with a question. • Bivariate – uses two categorical variables • Example: Sample 100 people & ask if they are male/female and what political party they support.
One-Way Frequency Table - univariate Data Vertical One-Way Table Horizontal One-Way Table
Goodness of Fit Test • Used to measure the extent to which the observed counts differ from the expected counts. • K = # categories of a catagorical variable • Df = k – 1 • Test Statistic:
Assumptions • Observed Values are based on random Samples • Sample size is large – each cell count is at least 5.
Hypotheses • Ho: State each proportion’s hypothesized value. • HA: At least 1 of the proportions differ from the hypothesized value.
It uses the Chi-Square Chart • Positively Skewed • Uses d.f. • On calculator!
Is there a preference in type of car? P1=proportion who prefer a SUV P2=proportion who prefer a truck p3=proportion who prefer a sedan P4=proportion who prefer a sports car Assumptions: Random Samples & all cell counts are at least 5. Use a Chi-Square goodness of fit Test P-val = xcdf(2.24,∞, 3)=0.52
A researcher believes that the number of homicides crimes in CA by season is uniformly distributed. To test this claim, you randomly select 1200 homicides from a recent year and record the season when each happened.
Results from a previous survey asking people who go to movies at least once a month are shown in the table below. To determine whether this distribution is still the same, you randomly select 1000 people who go to movies at least once a month and record the age of each. Are the distributions the same?
Homework • Worksheet