lecture14 - Psych 100A Winter 2010 Lecture 14: Statistical...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Psych 100A Winter 2010 Lecture 14: Statistical Inference Categorical data Multinomial experiment Chi-square test ontingency table Contingency table
Background image of page 1

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

View Full DocumentRight Arrow Icon
Categorical data Previous inference methods applicable to quantitative data. Inference on qualitative data . umber of observations at each level of a 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 .
Background image of page 2
1. Multinomial experiment. A natural extension of a binomial experiment ultinomial experiments re defined by the Multinomial experiments are defined by the following conditions: xperiment consists of d ials 1. Experiment consists of n iid trials 2. Polychotomous outcome on each trial: each ial results in one of utcomes trial results in one of k outcomes 3. Pr(outcome i) = i , i = 1,…,k; constant from trial to trial;  = 1 . I 4. Variables of interest are n i = the number of trials with outcome i observed during the n trials .
Background image of page 3

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

View Full DocumentRight Arrow Icon
Formula: Pr(outcomes) in a multinomial xperiment experiment Probability for the number of observations esulting in each of the k outcomes is given by resulting in each of the k outcomes is given by k n n n n 2 1 ! r   k k n n n n n n 3 2 1 2 1 2 1 ! ! ! , , , Pr where n = number of trials probability of i th utcome i = probability of i outcome n i = number of i th outcomes x! = x(x-1)(x-2)…(2)(1)
Background image of page 4
Multinomial experiment (cont.) ne use is to test specified probabilities ( for 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 :   k i E n 2 2 where n i ’s = observed cell counts and E i ’s = 1 expected cell counts .
Background image of page 5

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

View Full DocumentRight Arrow Icon
2. Chi-square distribution Pearson showed that if the n i ’s are sufficiently large, the test statistic 2
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/15/2010 for the course PSYCHOLOGY 100B taught by Professor Firstenberg,i. during the Winter '10 term at UCLA.

Page1 / 22

lecture14 - Psych 100A Winter 2010 Lecture 14: Statistical...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online