11.1 Facts About the Chi-Square Distribution
χ2 = (Z1)2 + (Z2)2 + . . . (Zdf)2 chi-square distribution random variable
μχ2 = df chi-square distribution population mean
chi-square distribution population standard deviation
11.2 Goodness-of-Fit Test
goodness-of-fit test statistic where
O: observed values
E: expected values
k: number of different data cells or categories
df = k − 1 degrees of freedom
11.3 Test of Independence
- The number of degrees of freedom is equal to (number of columns–1)(number of rows–1).
- The test statistic is where O = observed values, E = expected values, i = the number of rows in the table, and j = the number of columns in the table.
- If the null hypothesis is true, the expected number .
11.4 Test for Homogeneity
Homogeneity test statistic where O = observed values
E = expected values
i = number of rows in data contingency table
j = number of columns in data contingency table
df = (i −1)(j −1) degrees of freedom
11.6 Test of a Single Variance
Test of a single variance statistic where
n: sample size
s: sample standard deviation
σ: population standard deviation
df = n – 1 degrees of freedom
- Use the test to determine variation.
- The degrees of freedom is the number of samples – 1.
- The test statistic is , where n = the total number of data, s2 = sample variance, and σ2 = population variance.
- The test may be left-, right-, or two-tailed.