lecture14note

# lecture14note - Psych 100A Winter 2010 Categorical data...

This preview shows pages 1–2. Sign up to view the full content.

1 Psych 100A Winter 2010 Lecture 14: Statistical Inference Categorical data Multinomial experiment Chi-square test Contingency table Categorical data Previous inference methods applicable to quantitative data. Inference on qualitative data. Number of observations at each level of a qualitative variable = count or enumeration data. Population: individuals can be placed into various categories according to some characteristic. Sample: count of number of individuals who fall into each category. Data is characteristic of multinomial experiment. 1. Multinomial experiment. A natural extension of a binomial experiment Multinomial experiments are defined by the following conditions: 1. Experiment consists of n iid trials 2 Polychotomous outcome on each trial: each 2. Polychotomous outcome on each trial: each trial results in one of k outcomes 3. Pr(outcome i) = i , i = 1,…,k; constant from trial to trial;  I = 1. 4. Variables of interest are n i = the number of trials with outcome i observed during the n trials. Formula: Pr(outcomes) in a multinomial experiment Probability for the number of observations resulting in each of the k outcomes is given by  k n n n k k n n n n n n n 3 2 1 2 1 2 1 2 1 ! ! ! ! , , , Pr where n = number of trials i = probability of i th outcome n i = number of i th outcomes x! = x(x-1)(x-2)…(2)(1) Multinomial experiment (cont.) One use is to test specified probabilities ( iO ) for each outcome in a categorical study. In an study with k outcomes, the expected number of outcomes of type I in n trials equals: E i = n iO In 1900, Pearson devised a test statistic to test specified categorical probabilities called the 2 (chi-square) goodness-of-fit statistic: where n i ’s = observed cell counts and E i ’s = expected cell counts.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

lecture14note - Psych 100A Winter 2010 Categorical data...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online