Chi square Flashcards
3 types of chi square test
• Test for goodness of fit
• Test of normality
• Tests using contingency tables
2 types of contingency table
➢ Test for independence
➢ Test for homogeneity of proportions
could be parametric and Non-parametric but mostly Non-parametric if solving the aforementioned above.
Chi-square
Use the _______________ to decide whether a population with an unknown distribution “fits” a known distribution
goodness-of-fit test
Use when you have one nominal variable with two or more values rejected daw
goodness-of-fit test
Observed frequency and expected frequency are very important
goodness-of-fit test
how you phrase your null and alternative hypothesis when you use Test for Goodness Fit:
➢ H0 : The population fits the given distribution
➢ Ha : The population does not fit the given distribution
– actual frequencies of each variables under study obtained from a sample
Observed Frequencies
– frequencies obtained by calculation as if there were no preference
Expected Frequencies
• It is rarely being used that is why in terms of MegaStat, we don’t have Test of Normality. We resort to manual input of formula in MS Excel
TEST OF NORMALITY
Used to test a variable to see if it is normally distributed
Test of Normality
Test of Normality hypothesis
Ho: The variable is normally distributed.
H1: The variable is not normally distributed.
Involves finding the expected frequencies for each class of a frequency distribution by using the standard normal distribution
Test of Normality
Actual frequencies (i.e. observed frequencies) are compared to the expected frequencies, using the chi-square goodness-of-fit test
Test of Normality
• If the observed frequencies are close in value to the expected frequencies, the chi-square test value will be small, and the null hypothesis cannot be rejected.
Test of Normality
• If there is a large difference between the observed frequencies and the expected frequencies, the chi-square test value will be larger, and the null hypothesis can be rejected
Test of Normality
Alternatives to Chi-Square Test for Normality:
- Kolmogorov-Smirnov (K-S) test
- Lilliefors corrected K-S test
- Shapiro-Wilk test, Anderson-Darling test
- Cramer-von Mises test
- D’Agostino-Pearson omnibus test
- Jarque-Bera test
Test of Normality hypotheses
Ho: The variable is normally distributed.
H1: The variable is not normally distributed.
TESTS USING CONTINGENCY TABLES
• Test for Independence
• Test for Homogeneity of Proportions
• Used to determine whether two variables are independent of or related to each other when a single sample is selected
TEST FOR INDEPENDENCE
Used to determine whether the proportions for a variable are equal when several samples are selected from different populations.
TEST FOR HOMOGENEITY OF PROPORTIONS
Samples are selected from several different populations and the researcher is interested in determining whether the proportions of elements that have a common characteristic are the same for each population
TEST FOR HOMOGENEITY OF PROPORTIONS
For example, a researcher may select a sample of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors and then find the proportion of students who are smokers in each level. The researcher will then compare the proportions for each group to see if they are equal.
TEST FOR HOMOGENEITY OF PROPORTIONS
TEST FOR HOMOGENEITY OF PROPORTIONS Hypothesis
Ho:P1 = P2 = P3 = P4
H1: At least one proportion is different from the others.
samples are selected from several different populations, and the researcher is interested in determining whether the proportions of elements that have a common characteristic are the same for each population.
Test for Homogeneity of Proportions
