The Chi-Square Distribution  Chi-square tests for ….. goodness of fit, and independence 1.

Slides:

Advertisements

Similar presentations

Parametric/Nonparametric Tests. Chi-Square Test It is a technique through the use of which it is possible for all researchers to:  test the goodness.

Advertisements

Multinomial Experiments Goodness of Fit Tests We have just seen an example of comparing two proportions. For that analysis, we used the normal distribution.

CHAPTER 23: Two Categorical Variables: The Chi-Square Test

Please turn in your signed syllabus. We will be going to get textbooks shortly after class starts. Homework: Reading Guide – Chapter 2: The Chemical Context.

Chapter 26: Comparing Counts

CHAPTER 11 Inference for Distributions of Categorical Data

CHI-SQUARE TEST OF INDEPENDENCE

Chapter 11 Chi-Square Procedures 11.1 Chi-Square Goodness of Fit.

CHI-SQUARE GOODNESS OF FIT TEST What Are Nonparametric Statistics? What is the Purpose of the Chi-Square GOF? What Are the Assumptions? How Does it Work?

Chapter 26: Comparing Counts. To analyze categorical data, we construct two-way tables and examine the counts of percents of the explanatory and response.

11-3 Contingency Tables In this section we consider contingency tables (or two-way frequency tables), which include frequency counts for categorical data.

Chi-square Goodness of Fit Test

Presentation 12 Chi-Square test.

Chapter 13 Chi-Square Tests. The chi-square test for Goodness of Fit allows us to determine whether a specified population distribution seems valid. The.

The Chi-square Statistic. Goodness of fit 0 This test is used to decide whether there is any difference between the observed (experimental) value and.

Chapter 13: Inference for Tables – Chi-Square Procedures

Testing Distributions Section Starter Elite distance runners are thinner than the rest of us. Skinfold thickness, which indirectly measures.

AP Statistics Section 14.2 B. We can use the chi-square test of association/independence to test the null hypothesis when you have a two-way table from.

AP STATISTICS LESSON 13 – 1 (DAY 1) CHI-SQUARE PROCEDURES TEST FOR GOODNESS OF FIT.

Chapter 26: Comparing Counts AP Statistics. Comparing Counts In this chapter, we will be performing hypothesis tests on categorical data In previous chapters,

Section 10.1 Goodness of Fit. Section 10.1 Objectives Use the chi-square distribution to test whether a frequency distribution fits a claimed distribution.

1 1 Slide IS 310 – Business Statistics IS 310 Business Statistics CSU Long Beach.

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.

AP Statistics Chapter 26 Notes

Chapter 11: Inference for Distributions of Categorical Data.

Multinomial Experiments Goodness of Fit Tests We have just seen an example of comparing two proportions. For that analysis, we used the normal distribution.

Warm-up Researchers want to cross two yellow- green tobacco plants with genetic makeup (Gg). See the Punnett square below. When the researchers perform.

Chapter 26 Chi-Square Testing

Chapter 11 Inference for Tables: Chi-Square Procedures 11.1 Target Goal:I can compute expected counts, conditional distributions, and contributions to.

The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers CHAPTER 11 Inference for Distributions of Categorical.

Chi-Square Procedures Chi-Square Test for Goodness of Fit, Independence of Variables, and Homogeneity of Proportions.

United Stats Of AMERICA. Unit 7 chapters Jordo, Rob III, Kins and Toph.

FPP 28 Chi-square test. More types of inference for nominal variables Nominal data is categorical with more than two categories Compare observed frequencies.

Data Analysis for Two-Way Tables. The Basics Two-way table of counts Organizes data about 2 categorical variables Row variables run across the table Column.

Chapter 11 Chi- Square Test for Homogeneity Target Goal: I can use a chi-square test to compare 3 or more proportions. I can use a chi-square test for.

Warm up On slide.

Chapter 13 Inference for Tables: Chi-Square Procedures AP Statistics 13 – Chi-Square Tests.

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

Copyright © 2010 Pearson Education, Inc. Slide

Comparing Counts.  A test of whether the distribution of counts in one categorical variable matches the distribution predicted by a model is called a.

Inference for Distributions of Categorical Variables (C26 BVD)

1 Chapter 10. Section 10.1 and 10.2 Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION.

Practice Is there a significant (  =.01) relationship between opinions about the death penalty and opinions about the legalization of marijuana? 933.

AGENDA:. AP STAT Ch. 14.: X 2 Tests Goodness of Fit Homogeniety Independence EQ: What are expected values and how are they used to calculate Chi-Square?

Seven Steps for Doing  2 1) State the hypothesis 2) Create data table 3) Find  2 critical 4) Calculate the expected frequencies 5) Calculate  2 6)

Copyright © 2013, 2009, and 2007, Pearson Education, Inc. Chapter 11 Analyzing the Association Between Categorical Variables Section 11.2 Testing Categorical.

Chapter 14 Chi-Square Tests.  Hypothesis testing procedures for nominal variables (whose values are categories)  Focus on the number of people in different.

Chapter 13- Inference For Tables: Chi-square Procedures Section Test for goodness of fit Section Inference for Two-Way tables Presented By:

Lecture PowerPoint Slides Basic Practice of Statistics 7 th Edition.

By.  Are the proportions of colors of each M&M stated by the M&M company true proportions?

Science Practice 2: The student can use mathematics appropriately. Science Practice 5: The student can perform data analysis and evaluation of evidence.

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.

+ Section 11.1 Chi-Square Goodness-of-Fit Tests. + Introduction In the previous chapter, we discussed inference procedures for comparing the proportion.

Section 13.2 Chi-Squared Test of Independence/Association.

11.1 Chi-Square Tests for Goodness of Fit Objectives SWBAT: STATE appropriate hypotheses and COMPUTE expected counts for a chi- square test for goodness.

CHAPTER 11: INFERENCE FOR DISTRIBUTIONS OF CATEGORICAL DATA 11.1 CHI-SQUARE TESTS FOR GOODNESS OF FIT OUTCOME: I WILL STATE APPROPRIATE HYPOTHESES AND.

Chapter 11: Categorical Data n Chi-square goodness of fit test allows us to examine a single distribution of a categorical variable in a population. n.

Class Seven Turn In: Chapter 18: 32, 34, 36 Chapter 19: 26, 34, 44 Quiz 3 For Class Eight: Chapter 20: 18, 20, 24 Chapter 22: 34, 36 Read Chapters 23 &

AP Stats Check In Where we’ve been… Chapter 7…Chapter 8… Where we are going… Significance Tests!! –Ch 9 Tests about a population proportion –Ch 9Tests.

Chi Square Test of Homogeneity. Are the different types of M&M’s distributed the same across the different colors? PlainPeanutPeanut Butter Crispy Brown7447.

Check your understanding: p. 684

CHAPTER 11 Inference for Distributions of Categorical Data

11.1 Chi-Square Tests for Goodness of Fit

Test of independence: Contingency Table

Active Learning Lecture Slides

Day 66 Agenda: Quiz Ch 12 & minutes.

Analyzing the Association Between Categorical Variables

Chi-square = 2.85 Chi-square crit = 5.99 Achievement is unrelated to whether or not a child attended preschool.

Inference for Distributions of Categorical Data

Presentation transcript:

The Chi-Square Distribution  Chi-square tests for ….. goodness of fit, and independence 1

Hypothesis Tests (also called “Tests of Significance”) Standardized test statistic Use “HCCC” for writing FR answers that involve Tests of Significance: H: Write the Hypotheses. Be sure to define any parameter used in them. C: What distribution Can I use? Address each one of the Conditions precisely. C: Do the Calculations – either by hand or on your calculator. C: Write a two-sentence Conclusion. 2

As always, the structure of the Hypothesis Test does NOT change. Conclusions should always be in the context of the problem. 3

Chi-Square Tests – 2 types Goodness of Fit - testing a claim about the distribution of a categorical variable in a single population Independence – testing to determine whether there is an association between two variables 4

Conditions in order to be able to use the Chi-Square Distribution 1.The data come from random samples or random assignment to treatments. 2. All expected counts are at least 5 – be sure to show the expected counts. 3. Independent observations 5

Chi-square Goodness of Fit Test This test begins with a claim about the distribution of a single categorical variable (stated as a list of probabilities or proportions), and you are testing to see if the claim is correct. Hypotheses: Ho: Specified distribution is correct (probabilities or proportions are correct as stated) Ha: Specified distribution is not correct (some probabilities or proportions are incorrect as stated in the null hypothesis) 6

Chi-Square Goodness of Fit Test Example: “According to one genetics theory, half of the population should have brown eyes, and the other half evenly split between blue eyes and green eyes. “A random sample of 60 people results in 34 browns, 15 greens, and 11 blues. Does this sample provide good evidence for the theory?”  See page 4 of the packet, #19.  Correct answer: B 7

The Calculation for GOF: Degrees of freedom = # of categories - 1 8

Chi-Square Test of Independence You are given a two-way table showing counts for two characteristics for a single sample. Hypotheses: Ho: 2 variables are independent (or no association between the variables) Ha: 2 variables are not independent (or there is an association, or they are related to each other) (one of these coming up in the packet in a minute…) 9

Good Luck! 10