Lecture 8 Flashcards
What is a binomial variable?
A nominal (categorical) dependent variable with only two mutually exclusive categories. E.g. correct vs incorrect production
When can the binomial (sign) test be used?
The binomial test applies when there is ONE sample and TWO categories, in a RELATED SAMPLES TWO GROUP design
What is the z test of independent proportions?
Proportions = x/n (where x is the number of participants that IMPROVED after treatment)
Measures how many standard errors of difference separate the two independent proportions
Only works when x is not extreme (i.e. close to 0 or close to n)
What is the null hypothesis of the z test of independent proportions?
H0: all possible differences between p1 and p2 are normally distributed around 0. If the difference is greater than 1.96 standard errors above 0, then we reject H0.
How can you test for differences between two dependent proportions?
- E.g. when a single group of subjects are sampled one two different occasions, when the DV is a binomial variable.
McNemar test: test the same patient TWICE (i.e. before and after treatment) on the same set of items (that can be either correct or incorrect). Record the number correct/incorrect on first test and second test. We need the proportion of items that have gone from correct –> incorrect and vice versa. The McNemar test evaluates whether change is significant or simply due to chance.
What is a key difference between chi-squared tests and the z test of independent proportions/McNemar test?
Chi squared tests apply to FREQUENCY data, rather than proportions.
What does the Chi square goodness of fit test examine?
To assess whether there is a difference between observed category membership and expected/predicted category membership (e.g. 50% on a binomial variable).
E.g. Do students prefer Pepsi to Coke? (expected category membership = 50% for each)
What does the Chi-square test of independence examine?
Assesses whether category membership on one (nominal) variable is contingent on category membership on a second variable.
E.g. Does a child’s correct production of past tense verbs depend on whether the verbs are regular or irregular?
If the frequency of correct verbs is different in irregular compared to regular verbs by more than we would expect from chance factors, then we can conclude that the “correctness” depends on the type of verb.
What does the z test of independent proportions compare? What is it analogous to?
Compares two independent groups (e.g. Male/female) where the DV is a binomial variable (e.g. Agree/disagree)
Analogous to the independent samples t test
When do we reject the H0 in a z test of independent proportions?
When there is more than 1.96 standard errors of difference between the two independent proportions
