Download presentation

Presentation is loading. Please wait.

1
**Categorical Data Analysis**

Chapter 13 Categorical Data Analysis Slides for Optional Sections No Optional Sections

2
**Categorical Data and the Multinomial Distribution**

Properties of the Multinomial Experiment Experiment has n identical trials There are k possible outcomes to each trial, called classes, categories or cells Probabilities of the k outcomes remain constant from trial to trial Trials are independent Variables of interest are the cell counts, n1, n2…nk, the number of observations that fall into each of the k classes

3
**Testing Category Probabilities: One-Way Table**

In a multinomial experiment with categorical data from a single qualitative variable, we summarize data in a one-way table.

4
**Testing Category Probabilities: One-Way Table**

Hypothesis Testing for a One-Way Table Based on the 2 statistic, which allows comparison between the observed distribution of counts and an expected distribution of counts across the k classes Expected distribution = E(nk)=npk, where n is the total number of trials, and pk is the hypothesized probability of being in class k according to H0 The test statistic, 2, is calculated as and the rejection region is determined by the 2 distribution using k-1 df and the desired

5
**Testing Category Probabilities: One-Way Table**

Hypothesis Testing for a One-Way Table The null hypothesis is often formulated as a no difference, where H0: p1=p2=p3=…=pk=1/k, but can be formulated with non-equivalent probabilities Alternate hypothesis states that Ha: at least one of the multinomial probabilities does not equal its hypothesized value

6
**Testing Category Probabilities: One-Way Table**

Hypothesis Testing for a One-Way Table The null hypothesis is often formulated as a no difference, where H0: p1=p2=p3=…=pk=1/k, but can be formulated with non-equivalent probabilities Alternate hypothesis states that Ha: at least one of the multinomial probabilities does not equal its hypothesized value

7
**Testing Category Probabilities: One-Way Table**

One-Way Tables: an example H0: pLegal=.07, pdecrim=.18, pexistlaw=.65, pnone=.10 Ha: At least 2 proportions differ from proposed plan Rejection region with =.01, df = k-1 = 3 is Since the test statistic falls in the rejection region, we reject H0

8
**Testing Category Probabilities: One-Way Table**

Conditions Required for a valid 2 Test Multinomial experiment has been conducted Sample size is large, with E(ni) at least 5 for every cell

9
**Testing Category Probabilities: Two-Way (Contingency) Table**

Used when classifying with two qualitative variables H0: The two classifications are independent Ha: The two classifications are dependent Test Statistic: Rejection region:2>2, where 2 has (r-1)(c-1) df

10
**Testing Category Probabilities: Two-Way (Contingency) Table**

Conditions Required for a valid 2 Test N observed counts are a random sample from the population of interest Sample size is large, with E(ni) at least 5 for every cell

11
**Testing Category Probabilities: Two-Way (Contingency) Table**

Sample Statistical package output

12
**A Word of Caution about Chi-Square Tests**

When an expected cell count is less than 5, 2 probability distribution should not be used If H0 is not rejected, do not accept H0 that the classifications are independent, due to the implications of a Type II error. Do not infer causality when H0 is rejected. Contingency table analysis determines statistical dependence only.

Similar presentations

OK

AP Statistics Section 14.. The main objective of Chapter 14 is to test claims about qualitative data consisting of frequency counts for different categories.

AP Statistics Section 14.. The main objective of Chapter 14 is to test claims about qualitative data consisting of frequency counts for different categories.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on solid dielectrics and waves Ppt on business etiquette in india Ppt on low level language and high level Ppt on as 14 amalgamation Problem solution reading ppt on ipad Ppt on viruses and anti viruses available Ppt on child development Ppt on kingdom monera examples Ppt on asymptotic notation of algorithms to solve Fun ppt on biomes of the world