1 2 Test for Independence 2 Test for Independence.

Slides:



Advertisements
Similar presentations
TWO STEP EQUATIONS 1. SOLVE FOR X 2. DO THE ADDITION STEP FIRST
Advertisements

Slide 1 Insert your own content. Slide 2 Insert your own content.
Prepared by Lloyd R. Jaisingh
STATISTICS HYPOTHESES TEST (II) One-sample tests on the mean and variance Professor Ke-Sheng Cheng Department of Bioenvironmental Systems Engineering National.
Combining Like Terms. Only combine terms that are exactly the same!! Whats the same mean? –If numbers have a variable, then you can combine only ones.
1 2 Test for Independence 2 Test for Independence.
Jeopardy Q 1 Q 6 Q 11 Q 16 Q 21 Q 2 Q 7 Q 12 Q 17 Q 22 Q 3 Q 8 Q 13
Jeopardy Q 1 Q 6 Q 11 Q 16 Q 21 Q 2 Q 7 Q 12 Q 17 Q 22 Q 3 Q 8 Q 13
0 - 0.
DIVIDING INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.
MULTIPLYING MONOMIALS TIMES POLYNOMIALS (DISTRIBUTIVE PROPERTY)
ADDING INTEGERS 1. POS. + POS. = POS. 2. NEG. + NEG. = NEG. 3. POS. + NEG. OR NEG. + POS. SUBTRACT TAKE SIGN OF BIGGER ABSOLUTE VALUE.
MULTIPLICATION EQUATIONS 1. SOLVE FOR X 3. WHAT EVER YOU DO TO ONE SIDE YOU HAVE TO DO TO THE OTHER 2. DIVIDE BY THE NUMBER IN FRONT OF THE VARIABLE.
SUBTRACTING INTEGERS 1. CHANGE THE SUBTRACTION SIGN TO ADDITION
MULT. INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.
Addition Facts
Overview of Lecture Parametric vs Non-Parametric Statistical Tests.
STATISTICAL INFERENCE ABOUT MEANS AND PROPORTIONS WITH TWO POPULATIONS
EPI809/Spring Chapter 10 Hypothesis testing: Categorical Data Analysis.
Statistics for Business and Economics
Chapter 13: Chi-Square Test
© 2011 Pearson Education, Inc
Statistics for Business and Economics Chapter 9 Categorical Data Analysis.
STATISTICS ELEMENTARY MARIO F. TRIOLA
O X Click on Number next to person for a question.
© S Haughton more than 3?
1 Directed Depth First Search Adjacency Lists A: F G B: A H C: A D D: C F E: C D G F: E: G: : H: B: I: H: F A B C G D E H I.
Take from Ten First Subtraction Strategy -9 Click on a number below to go directly to that type of subtraction problems
Past Tense Probe. Past Tense Probe Past Tense Probe – Practice 1.
Module 16: One-sample t-tests and Confidence Intervals
Addition 1’s to 20.
25 seconds left…...
Test B, 100 Subtraction Facts
11 = This is the fact family. You say: 8+3=11 and 3+8=11
Week 1.
Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Chapter 10 One- and Two-Sample Tests of Hypotheses.
McGraw-Hill/Irwin Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved. Chi-Square Tests Chapter 12.
1 Ke – Kitchen Elements Newport Ave. – Lot 13 Bethesda, MD.
Chapter 18: The Chi-Square Statistic
O X Click on Number next to person for a question.
Categorical Data Analysis
Lecture 16 chi-square test (continued) Suppose 160 pairs of consecutive nucleotides are selected at random. Are data compatible with the independent occurrence.
CHI-SQUARE(X2) DISTRIBUTION
 2 Test of Independence. Hypothesis Tests Categorical Data.
© 2002 Prentice-Hall, Inc.Chap 10-1 Statistics for Managers using Microsoft Excel 3 rd Edition Chapter 10 Tests for Two or More Samples with Categorical.
Chapter 13: The Chi-Square Test
12.The Chi-square Test and the Analysis of the Contingency Tables 12.1Contingency Table 12.2A Words of Caution about Chi-Square Test.
Ch. 28 Chi-square test Used when the data are frequencies (counts) or proportions for 2 or more groups. Example 1.
11-3 Contingency Tables In this section we consider contingency tables (or two-way frequency tables), which include frequency counts for categorical data.
For testing significance of patterns in qualitative data Test statistic is based on counts that represent the number of items that fall in each category.
1 In this case, each element of a population is assigned to one and only one of several classes or categories. Chapter 11 – Test of Independence - Hypothesis.
Contingency Tables 1.Explain  2 Test of Independence 2.Measure of Association.
© 2000 Prentice-Hall, Inc. Statistics The Chi-Square Test & The Analysis of Contingency Tables Chapter 13.
Chapter Outline Goodness of Fit test Test of Independence.
Chapter 11: Chi-Square  Chi-Square as a Statistical Test  Statistical Independence  Hypothesis Testing with Chi-Square The Assumptions Stating the Research.
Chapter 14 Chi-Square Tests.  Hypothesis testing procedures for nominal variables (whose values are categories)  Focus on the number of people in different.
Chapter 14 – 1 Chi-Square Chi-Square as a Statistical Test Statistical Independence Hypothesis Testing with Chi-Square The Assumptions Stating the Research.
1 1 Slide © 2008 Thomson South-Western. All Rights Reserved Chapter 12 Tests of Goodness of Fit and Independence n Goodness of Fit Test: A Multinomial.
Chi Square Test for Goodness of Fit Determining if our sample fits the way it should be.
Statistics 300: Elementary Statistics Section 11-3.
Test of independence: Contingency Table
Chapter 11 – Test of Independence - Hypothesis Test for Proportions of a Multinomial Population In this case, each element of a population is assigned.
Chi-Square hypothesis testing
Chi Square Two-way Tables
Relations in Categorical Data
Contingency Tables: Independence and Homogeneity
Chapter 13 – Applications of the Chi-Square Statistic
CHI SQUARE TEST OF INDEPENDENCE
Inference for Two Way Tables
Chapter Outline Goodness of Fit test Test of Independence.
Presentation transcript:

1 2 Test for Independence 2 Test for Independence

2 Data Types

3 Hypothesis Tests Qualitative Data

4 2 Test of Independence 2 Test of Independence 1.Shows If a Relationship Exists Between 2 Qualitative Variables, but does Not Show Causality 2.Assumptions Multinomial Experiment All Expected Counts 5 3.Uses Two-Way Contingency Table

5 2 Test of Independence Contingency Table 2 Test of Independence Contingency Table 1.Shows # Observations From 1 Sample Jointly in 2 Qualitative Variables 1.Shows # Observations From 1 Sample Jointly in 2 Qualitative Variables

6 2 Test of Independence Contingency Table 2 Test of Independence Contingency Table 1.Shows # Observations From 1 Sample Jointly in 2 Qualitative Variables Levels of variable 2 Levels of variable 1

7 2 Test of Independence Hypotheses & Statistic 2 Test of Independence Hypotheses & Statistic 1.Hypotheses H 0 : Variables Are Independent H 0 : Variables Are Independent H a : Variables Are Related (Dependent) H a : Variables Are Related (Dependent)

8 2 Test of Independence Hypotheses & Statistic 2 Test of Independence Hypotheses & Statistic 1.Hypotheses H 0 : Variables Are Independent H a : Variables Are Related (Dependent) 2.Test Statistic Observed count Expected count

9 2 Test of Independence Hypotheses & Statistic 2 Test of Independence Hypotheses & Statistic 1.Hypotheses H 0 : Variables Are Independent H a : Variables Are Related (Dependent) 2.Test Statistic Degrees of Freedom: (r - 1)(c - 1) Rows Columns Observed count Expected count

10 Expected Count Example

11 Expected Count Example Marginal probability =

12 Expected Count Example Marginal probability =

13 Expected Count Example Marginal probability = Joint probability =

14 Expected Count Example Marginal probability = Joint probability = Expected count = 160· = 54.6

15 Expected Count Calculation

16 Expected Count Calculation

17 Expected Count Calculation 112x x x x78 160