SlideShare a Scribd company logo
1 of 24
© aSup-2007
CHI SQUARE   
1
The CHI SQUARE Statistic
Tests for Goodness of Fit
and Independence
© aSup-2007
CHI SQUARE   
2
Preview
 Color is known to affect human moods and
emotion. Sitting in a pale-blue room is more
calming than sitting in a bright-red room
 Based on the known influence of color, Hill
and Barton (2005) hypothesized that the
color of uniform may influence the outcome
of physical sports contest
 The study does not produce a numerical
score for each participant. Each participant
is simply classified into two categories
(winning or losing)
© aSup-2007
CHI SQUARE   
3
Preview
 The data consist of frequencies or proportions
describing how many individuals are in each
category
 This study want to use a hypothesis test to
evaluate data. The null hypothesis would state
that color has no effect on the outcome of the
contest
 Statistical technique have been developed
specifically to analyze and interpret data
consisting of frequencies or proportions 
CHI SQUARE
© aSup-2007
CHI SQUARE   
4
PARAMETRIC AND NONPARAMETRIC
STATISTICAL TESTS
 The tests that concern parameter and
require assumptions about parameter are
called parametric tests
 Another general characteristic of parametric
tests is that they require a numerical score
for each individual in the sample. In terms
of measurement scales, parametric tests
require data from an interval or a ratio scale
© aSup-2007
CHI SQUARE   
5
PARAMETRIC AND NONPARAMETRIC
STATISTICAL TESTS
 Often, researcher are confronted with
experimental situation that do not conform to
the requirements of parametric tests. In this
situations, it may not be appropriate to use a
parametric test because may lead to an
erroneous interpretation of the data
 Fortunately, there are several hypothesis
testing techniques that provide alternatives to
parametric test that called nonparametric tests
© aSup-2007
CHI SQUARE   
6
NONPARAMETRIC TEST
 Nonparametric tests sometimes are called
distribution free tests
 One of the most obvious differences
between parametric and nonparametric
tests is the type of data they use
 All the parametric tests required numerical
scores. For nonparametric, the subjects are
usually just classified into categories
© aSup-2007
CHI SQUARE   
7
NONPARAMETRIC TEST
 Notice that these classification involve
measurement on nominal or ordinal scales,
and they do not produce numerical values
that can be used to calculate mean and
variance
 Nonparametric tests generally are not as
sensitive as parametric test; nonparametric
tests are more likely to fail in detecting a
real difference between two treatments
© aSup-2007
CHI SQUARE   
8
THE CHI SQUARE TEST FOR GOODNESS OF FIT
… uses sample data to test hypotheses about
the shape or proportions of a population
distribution. The test determines how well the
obtained sample proportions fit the
population proportions specified by the null
hypothesis
© aSup-2007
CHI SQUARE   
9
THE NULL HYPOTHESIS FOR THE GOODNESS OF FIT
 For the chi-square test of goodness of fit, the
null hypothesis specifies the proportion (or
percentage) of the population in each category
 Generally H0 will fall into one of the following
categories:
○ No preference
H0 states that the population is divided equally
among the categories
○ No difference from a Known population
H0 states that the proportion for one population are
not different from the proportion that are known to
exist for another population
© aSup-2007
CHI SQUARE   
10
THE DATA FOR THE GOODNESS OF FIT TEST
 Select a sample of n individuals and count how
many are in each category
 The resulting values are called observed
frequency (fo)
 A sample of n = 40 participants was given a
personality questionnaire and classified into
one of three personality categories: A, B, or C
Category A Category B Category C
15 19 6
© aSup-2007
CHI SQUARE   
11
EXPECTED FREQUENCIES
 The general goal of the chi-square test for goodness
of fit is to compare the data (the observed
frequencies) with the null hypothesis
 The problem is to determine how well the data fit the
distribution specified in H0 – hence name goodness of
fit
 Suppose, for example, the null hypothesis states that
the population is distributed into three categories
with the following proportion
Category A Category B Category C
25% 50% 25%
© aSup-2007
CHI SQUARE   
12
EXPECTED FREQUENCIES
To find the exact frequency expected for each
category, multiply the same size (n) by the
proportion (or percentage) from the null
hypothesis
25% of 40 = 10 individual in category A
50% of 40 = 20 individual in category B
25% of 40 = 10 individual in category C
© aSup-2007
CHI SQUARE   
13
THE CHI-SQUARE STATISTIC
 The general purpose of any hypothesis test
is to determine whether the sample data
support or refute a hypothesis about
population
 In the chi-square test for goodness of fit, the
sample expressed as a set of observe
frequencies (fovalues) and the null
hypothesis is used to generate a set of
expected frequencies (fe values)
© aSup-2007
CHI SQUARE   
14
THE CHI-SQUARE STATISTIC
 The chi-square statistic simply measures ho
well the data (fo) fit the hypothesis (fe)
 The symbol for the chi-square statistic is χ2
 The formula for the chi-square statistic is
χ2
= ∑
(fo – fe)2
fe
© aSup-2007
CHI SQUARE   
15
A researcher has developed three different
design for a computer keyboard. A sample of n
= 60 participants is obtained, and each
individual tests all three keyboard and identifies
his or her favorite.
The frequency distribution of preference is:
Design A = 23, Design B = 12, Design C = 25.
Use a chi-square test for goodness of fit with α
= .05 to determine whether there are significant
preferences among three design
LEARNING CHECK
© aSup-2007
CHI SQUARE   
16
Dari https://twitter.com/#!/palangmerah
diketahui bahwa persentase golongan darah
di Indonesia adalah:
A : 25,48%,
B : 26,68%,
O : 40,77 %,
AB : 6,6 %
Golongan darah di kelas kita?
Apakah berbeda dengan data PMI?
LEARNING CHECK
© aSup-2007
CHI SQUARE   
17
THE CHI-SQUARE TEST FOR INDEPENDENCE
 The chi-square may also be used to test
whether there is a relationship between two
variables
 For example, a group of students could be
classified in term of personality (introvert,
extrovert) and in terms of color preferences
(red, white, green, or blue).
RED WHITE GREEN BLUE ∑
INTRO 10 3 15 22 50
EXTRO 90 17 25 18 150
100 20 40 40 200
© aSup-2007
CHI SQUARE   
18
OBSERVED AND EXPECTED FREQUENCIES
fo
RED WHITE GREEN BLUE ∑
INTRO 10 3 15 22 50
EXTRO 90 17 25 18 150
∑ 100 20 40 40 200
fe
RED WHITE GREEN BLUE ∑
INTRO 50
EXTRO 150
∑ 100 20 40 40 200
© aSup-2007
CHI SQUARE   
19
OBSERVED AND EXPECTED FREQUENCIES
fo
RED WHITE GREEN BLUE ∑
INTRO 10 3 15 22 50
EXTRO 90 17 25 18 150
∑ 100 20 40 40 200
fe
RED WHITE GREEN BLUE ∑
INTRO 25 5 10 10 50
EXTRO 75 15 30 30 150
∑ 100 20 40 40 200
© aSup-2007
CHI SQUARE   
20
OBSERVED AND EXPECTED FREQUENCIES
fo R W G B ∑
INTRO 10 3 15 22 50
EXTRO 90 17 25 18 150
∑ 100 20 40 40 200
(fo– fe)2
R W G B
INTRO
EXTRO
fe R W G B ∑
INTRO 25 5 10 10 50
EXTRO 75 15 30 30 150
∑ 100 20 40 40 200
© aSup-2007
CHI SQUARE   
21
OBSERVED AND EXPECTED FREQUENCIES
fo R W G B ∑
INTRO 10 3 15 22 50
EXTRO 90 17 25 18 150
∑ 100 20 40 40 200
(fo– fe)2
R W G B
INTRO (-15)2
(-2)2
(5)2
(12)2
EXTRO (15)2
(-2)2
(-5)2
(-12)2
fe R W G B ∑
INTRO 25 5 10 10 50
EXTRO 75 15 30 30 150
∑ 100 20 40 40 200
© aSup-2007
CHI SQUARE   
22
OBSERVED AND EXPECTED FREQUENCIES
(fo– fe)2
/fe R W G B
INTRO
EXTRO
fe R W G B
INTRO 25 5 10 10
EXTRO 75 15 30 30
(fo– fe)2
R W G B
INTRO 225 4 25 144
EXTRO 225 4 25 144
© aSup-2007
CHI SQUARE   
23
OBSERVED AND EXPECTED FREQUENCIES
(fo– fe)2
/fe R W G B
INTRO 9 0,8 2,5 14,4
EXTRO 3 0,267 0,833 4,8
fe R W G B
INTRO 25 5 10 10
EXTRO 75 15 30 30
(fo– fe)2
R W G B
INTRO 225 4 25 144
EXTRO 225 4 25 144
© aSup-2007
CHI SQUARE   
24
THE CHI-SQUARE STATISTIC
χ2
= ∑
(fo – fe)2
fe
χ2
= 35,6
df = (C-1) (R-1) = (3) (1) = 3
χ2
critical at α = .05 is 7,81

More Related Content

What's hot

Chi square test
Chi square testChi square test
Chi square testNayna Azad
 
Hypothesis testing an introduction
Hypothesis testing an introductionHypothesis testing an introduction
Hypothesis testing an introductionGeetika Gulyani
 
Chi square test final
Chi square test finalChi square test final
Chi square test finalHar Jindal
 
Statistical inference concept, procedure of hypothesis testing
Statistical inference   concept, procedure of hypothesis testingStatistical inference   concept, procedure of hypothesis testing
Statistical inference concept, procedure of hypothesis testingAmitaChaudhary19
 
TEST OF SIGNIFICANCE.pptx
TEST OF SIGNIFICANCE.pptxTEST OF SIGNIFICANCE.pptx
TEST OF SIGNIFICANCE.pptxJoicePjiji
 
Data Analysis using SPSS: Part 1
Data Analysis using SPSS: Part 1Data Analysis using SPSS: Part 1
Data Analysis using SPSS: Part 1Taddesse Kassahun
 
Categorical data analysis.pptx
Categorical data analysis.pptxCategorical data analysis.pptx
Categorical data analysis.pptxBegashaw3
 
Chi-square, Yates, Fisher & McNemar
Chi-square, Yates, Fisher & McNemarChi-square, Yates, Fisher & McNemar
Chi-square, Yates, Fisher & McNemarAzmi Mohd Tamil
 
Descriptive statistics
Descriptive statisticsDescriptive statistics
Descriptive statisticsAnand Thokal
 
Inferential statistics
Inferential statisticsInferential statistics
Inferential statisticsMaria Theresa
 
Central limit theorem
Central limit theoremCentral limit theorem
Central limit theoremVijeesh Soman
 
Descriptive statistics
Descriptive statisticsDescriptive statistics
Descriptive statisticsAileen Balbido
 
Basics of Educational Statistics (Descriptive statistics)
Basics of Educational Statistics (Descriptive statistics)Basics of Educational Statistics (Descriptive statistics)
Basics of Educational Statistics (Descriptive statistics)HennaAnsari
 

What's hot (20)

statistic
statisticstatistic
statistic
 
Hypothesis Testing
Hypothesis TestingHypothesis Testing
Hypothesis Testing
 
Chi square test
Chi square testChi square test
Chi square test
 
Hypothesis Testing
Hypothesis TestingHypothesis Testing
Hypothesis Testing
 
Hypothesis testing an introduction
Hypothesis testing an introductionHypothesis testing an introduction
Hypothesis testing an introduction
 
Chi square test final
Chi square test finalChi square test final
Chi square test final
 
Statistical inference concept, procedure of hypothesis testing
Statistical inference   concept, procedure of hypothesis testingStatistical inference   concept, procedure of hypothesis testing
Statistical inference concept, procedure of hypothesis testing
 
TEST OF SIGNIFICANCE.pptx
TEST OF SIGNIFICANCE.pptxTEST OF SIGNIFICANCE.pptx
TEST OF SIGNIFICANCE.pptx
 
Data Analysis using SPSS: Part 1
Data Analysis using SPSS: Part 1Data Analysis using SPSS: Part 1
Data Analysis using SPSS: Part 1
 
Chi square mahmoud
Chi square mahmoudChi square mahmoud
Chi square mahmoud
 
Descriptive statistics
Descriptive statisticsDescriptive statistics
Descriptive statistics
 
Categorical data analysis.pptx
Categorical data analysis.pptxCategorical data analysis.pptx
Categorical data analysis.pptx
 
Chi-square, Yates, Fisher & McNemar
Chi-square, Yates, Fisher & McNemarChi-square, Yates, Fisher & McNemar
Chi-square, Yates, Fisher & McNemar
 
Descriptive statistics
Descriptive statisticsDescriptive statistics
Descriptive statistics
 
Biostatistics khushbu
Biostatistics khushbuBiostatistics khushbu
Biostatistics khushbu
 
Inferential statistics
Inferential statisticsInferential statistics
Inferential statistics
 
Central limit theorem
Central limit theoremCentral limit theorem
Central limit theorem
 
Descriptive statistics
Descriptive statisticsDescriptive statistics
Descriptive statistics
 
Basics of Educational Statistics (Descriptive statistics)
Basics of Educational Statistics (Descriptive statistics)Basics of Educational Statistics (Descriptive statistics)
Basics of Educational Statistics (Descriptive statistics)
 
t test
t testt test
t test
 

Similar to Chi square

chisquare-150401011836-conversion-gate01.ppt
chisquare-150401011836-conversion-gate01.pptchisquare-150401011836-conversion-gate01.ppt
chisquare-150401011836-conversion-gate01.pptSoujanyaLk1
 
Mb0040 statistics for management
Mb0040   statistics for managementMb0040   statistics for management
Mb0040 statistics for managementsmumbahelp
 
Chi square test evidence based dentistry
Chi square test evidence based dentistryChi square test evidence based dentistry
Chi square test evidence based dentistryPiyushJain163909
 
2.0.statistical methods and determination of sample size
2.0.statistical methods and determination of sample size2.0.statistical methods and determination of sample size
2.0.statistical methods and determination of sample sizesalummkata1
 
Marketing Research Hypothesis Testing.pptx
Marketing Research Hypothesis Testing.pptxMarketing Research Hypothesis Testing.pptx
Marketing Research Hypothesis Testing.pptxxababid981
 
Categorical Data and Statistical Analysis
Categorical Data and Statistical AnalysisCategorical Data and Statistical Analysis
Categorical Data and Statistical AnalysisMichael770443
 
Chi square test final presentation
Chi square test final presentationChi square test final presentation
Chi square test final presentationRitesh Tiwari
 
Sct2013 boston,randomizationmetricsposter,d6.2
Sct2013 boston,randomizationmetricsposter,d6.2Sct2013 boston,randomizationmetricsposter,d6.2
Sct2013 boston,randomizationmetricsposter,d6.2Dennis Sweitzer
 
Mba103 statistics for management
Mba103  statistics for managementMba103  statistics for management
Mba103 statistics for managementsmumbahelp
 
Data Analysis for Graduate Studies Summary
Data Analysis for Graduate Studies SummaryData Analysis for Graduate Studies Summary
Data Analysis for Graduate Studies SummaryKelvinNMhina
 
Chi-square tests are great to show if distributions differ or i.docx
 Chi-square tests are great to show if distributions differ or i.docx Chi-square tests are great to show if distributions differ or i.docx
Chi-square tests are great to show if distributions differ or i.docxMARRY7
 
SPSS statistics - get help using SPSS
SPSS statistics - get help using SPSSSPSS statistics - get help using SPSS
SPSS statistics - get help using SPSScsula its training
 
Aron chpt 11 ed (2)
Aron chpt 11 ed (2)Aron chpt 11 ed (2)
Aron chpt 11 ed (2)Sandra Nicks
 
Nonparametric Test Chi-Square Test for Independence Th.docx
Nonparametric Test Chi-Square Test for Independence Th.docxNonparametric Test Chi-Square Test for Independence Th.docx
Nonparametric Test Chi-Square Test for Independence Th.docxpauline234567
 

Similar to Chi square (20)

chi square-.ppt
chi square-.pptchi square-.ppt
chi square-.ppt
 
chisquare-150401011836-conversion-gate01.ppt
chisquare-150401011836-conversion-gate01.pptchisquare-150401011836-conversion-gate01.ppt
chisquare-150401011836-conversion-gate01.ppt
 
Mb0040 statistics for management
Mb0040   statistics for managementMb0040   statistics for management
Mb0040 statistics for management
 
Chi square test evidence based dentistry
Chi square test evidence based dentistryChi square test evidence based dentistry
Chi square test evidence based dentistry
 
2.0.statistical methods and determination of sample size
2.0.statistical methods and determination of sample size2.0.statistical methods and determination of sample size
2.0.statistical methods and determination of sample size
 
Marketing Research Hypothesis Testing.pptx
Marketing Research Hypothesis Testing.pptxMarketing Research Hypothesis Testing.pptx
Marketing Research Hypothesis Testing.pptx
 
Chi square test
Chi square testChi square test
Chi square test
 
Categorical Data and Statistical Analysis
Categorical Data and Statistical AnalysisCategorical Data and Statistical Analysis
Categorical Data and Statistical Analysis
 
Chi square test final presentation
Chi square test final presentationChi square test final presentation
Chi square test final presentation
 
Sct2013 boston,randomizationmetricsposter,d6.2
Sct2013 boston,randomizationmetricsposter,d6.2Sct2013 boston,randomizationmetricsposter,d6.2
Sct2013 boston,randomizationmetricsposter,d6.2
 
Mba103 statistics for management
Mba103  statistics for managementMba103  statistics for management
Mba103 statistics for management
 
Chi Square & Anova
Chi Square & AnovaChi Square & Anova
Chi Square & Anova
 
Data Analysis for Graduate Studies Summary
Data Analysis for Graduate Studies SummaryData Analysis for Graduate Studies Summary
Data Analysis for Graduate Studies Summary
 
Chi square
Chi squareChi square
Chi square
 
Chi-square tests are great to show if distributions differ or i.docx
 Chi-square tests are great to show if distributions differ or i.docx Chi-square tests are great to show if distributions differ or i.docx
Chi-square tests are great to show if distributions differ or i.docx
 
Practice test1 solution
Practice test1 solutionPractice test1 solution
Practice test1 solution
 
SPSS statistics - get help using SPSS
SPSS statistics - get help using SPSSSPSS statistics - get help using SPSS
SPSS statistics - get help using SPSS
 
Aron chpt 11 ed (2)
Aron chpt 11 ed (2)Aron chpt 11 ed (2)
Aron chpt 11 ed (2)
 
Nonparametric Test Chi-Square Test for Independence Th.docx
Nonparametric Test Chi-Square Test for Independence Th.docxNonparametric Test Chi-Square Test for Independence Th.docx
Nonparametric Test Chi-Square Test for Independence Th.docx
 
Chi square
Chi square Chi square
Chi square
 

More from Andi Koentary

Statistical techniques for ordinal data
Statistical techniques for ordinal dataStatistical techniques for ordinal data
Statistical techniques for ordinal dataAndi Koentary
 
Introduction to statistics
Introduction to statisticsIntroduction to statistics
Introduction to statisticsAndi Koentary
 
Inference about means and mean differences
Inference about means and mean differencesInference about means and mean differences
Inference about means and mean differencesAndi Koentary
 
Distribution of sampling means
Distribution of sampling meansDistribution of sampling means
Distribution of sampling meansAndi Koentary
 
Analysis of variance
Analysis of varianceAnalysis of variance
Analysis of varianceAndi Koentary
 

More from Andi Koentary (7)

Statistical techniques for ordinal data
Statistical techniques for ordinal dataStatistical techniques for ordinal data
Statistical techniques for ordinal data
 
Regression
RegressionRegression
Regression
 
Introduction to statistics
Introduction to statisticsIntroduction to statistics
Introduction to statistics
 
Inference about means and mean differences
Inference about means and mean differencesInference about means and mean differences
Inference about means and mean differences
 
Distribution of sampling means
Distribution of sampling meansDistribution of sampling means
Distribution of sampling means
 
Central tendency
Central tendencyCentral tendency
Central tendency
 
Analysis of variance
Analysis of varianceAnalysis of variance
Analysis of variance
 

Recently uploaded

Learn How Data Science Changes Our World
Learn How Data Science Changes Our WorldLearn How Data Science Changes Our World
Learn How Data Science Changes Our WorldEduminds Learning
 
RABBIT: A CLI tool for identifying bots based on their GitHub events.
RABBIT: A CLI tool for identifying bots based on their GitHub events.RABBIT: A CLI tool for identifying bots based on their GitHub events.
RABBIT: A CLI tool for identifying bots based on their GitHub events.natarajan8993
 
Identifying Appropriate Test Statistics Involving Population Mean
Identifying Appropriate Test Statistics Involving Population MeanIdentifying Appropriate Test Statistics Involving Population Mean
Identifying Appropriate Test Statistics Involving Population MeanMYRABACSAFRA2
 
Bank Loan Approval Analysis: A Comprehensive Data Analysis Project
Bank Loan Approval Analysis: A Comprehensive Data Analysis ProjectBank Loan Approval Analysis: A Comprehensive Data Analysis Project
Bank Loan Approval Analysis: A Comprehensive Data Analysis ProjectBoston Institute of Analytics
 
专业一比一美国俄亥俄大学毕业证成绩单pdf电子版制作修改
专业一比一美国俄亥俄大学毕业证成绩单pdf电子版制作修改专业一比一美国俄亥俄大学毕业证成绩单pdf电子版制作修改
专业一比一美国俄亥俄大学毕业证成绩单pdf电子版制作修改yuu sss
 
FAIR, FAIRsharing, FAIR Cookbook and ELIXIR - Sansone SA - Boston 2024
FAIR, FAIRsharing, FAIR Cookbook and ELIXIR - Sansone SA - Boston 2024FAIR, FAIRsharing, FAIR Cookbook and ELIXIR - Sansone SA - Boston 2024
FAIR, FAIRsharing, FAIR Cookbook and ELIXIR - Sansone SA - Boston 2024Susanna-Assunta Sansone
 
Student profile product demonstration on grades, ability, well-being and mind...
Student profile product demonstration on grades, ability, well-being and mind...Student profile product demonstration on grades, ability, well-being and mind...
Student profile product demonstration on grades, ability, well-being and mind...Seán Kennedy
 
Conf42-LLM_Adding Generative AI to Real-Time Streaming Pipelines
Conf42-LLM_Adding Generative AI to Real-Time Streaming PipelinesConf42-LLM_Adding Generative AI to Real-Time Streaming Pipelines
Conf42-LLM_Adding Generative AI to Real-Time Streaming PipelinesTimothy Spann
 
SMOTE and K-Fold Cross Validation-Presentation.pptx
SMOTE and K-Fold Cross Validation-Presentation.pptxSMOTE and K-Fold Cross Validation-Presentation.pptx
SMOTE and K-Fold Cross Validation-Presentation.pptxHaritikaChhatwal1
 
Thiophen Mechanism khhjjjjjjjhhhhhhhhhhh
Thiophen Mechanism khhjjjjjjjhhhhhhhhhhhThiophen Mechanism khhjjjjjjjhhhhhhhhhhh
Thiophen Mechanism khhjjjjjjjhhhhhhhhhhhYasamin16
 
Minimizing AI Hallucinations/Confabulations and the Path towards AGI with Exa...
Minimizing AI Hallucinations/Confabulations and the Path towards AGI with Exa...Minimizing AI Hallucinations/Confabulations and the Path towards AGI with Exa...
Minimizing AI Hallucinations/Confabulations and the Path towards AGI with Exa...Thomas Poetter
 
Principles and Practices of Data Visualization
Principles and Practices of Data VisualizationPrinciples and Practices of Data Visualization
Principles and Practices of Data VisualizationKianJazayeri1
 
NO1 Certified Black Magic Specialist Expert Amil baba in Lahore Islamabad Raw...
NO1 Certified Black Magic Specialist Expert Amil baba in Lahore Islamabad Raw...NO1 Certified Black Magic Specialist Expert Amil baba in Lahore Islamabad Raw...
NO1 Certified Black Magic Specialist Expert Amil baba in Lahore Islamabad Raw...Amil Baba Dawood bangali
 
modul pembelajaran robotic Workshop _ by Slidesgo.pptx
modul pembelajaran robotic Workshop _ by Slidesgo.pptxmodul pembelajaran robotic Workshop _ by Slidesgo.pptx
modul pembelajaran robotic Workshop _ by Slidesgo.pptxaleedritatuxx
 
Cyber awareness ppt on the recorded data
Cyber awareness ppt on the recorded dataCyber awareness ppt on the recorded data
Cyber awareness ppt on the recorded dataTecnoIncentive
 
Decoding the Heart: Student Presentation on Heart Attack Prediction with Data...
Decoding the Heart: Student Presentation on Heart Attack Prediction with Data...Decoding the Heart: Student Presentation on Heart Attack Prediction with Data...
Decoding the Heart: Student Presentation on Heart Attack Prediction with Data...Boston Institute of Analytics
 
INTRODUCTION TO Natural language processing
INTRODUCTION TO Natural language processingINTRODUCTION TO Natural language processing
INTRODUCTION TO Natural language processingsocarem879
 
Generative AI for Social Good at Open Data Science East 2024
Generative AI for Social Good at Open Data Science East 2024Generative AI for Social Good at Open Data Science East 2024
Generative AI for Social Good at Open Data Science East 2024Colleen Farrelly
 
Decoding Patterns: Customer Churn Prediction Data Analysis Project
Decoding Patterns: Customer Churn Prediction Data Analysis ProjectDecoding Patterns: Customer Churn Prediction Data Analysis Project
Decoding Patterns: Customer Churn Prediction Data Analysis ProjectBoston Institute of Analytics
 

Recently uploaded (20)

Learn How Data Science Changes Our World
Learn How Data Science Changes Our WorldLearn How Data Science Changes Our World
Learn How Data Science Changes Our World
 
RABBIT: A CLI tool for identifying bots based on their GitHub events.
RABBIT: A CLI tool for identifying bots based on their GitHub events.RABBIT: A CLI tool for identifying bots based on their GitHub events.
RABBIT: A CLI tool for identifying bots based on their GitHub events.
 
Identifying Appropriate Test Statistics Involving Population Mean
Identifying Appropriate Test Statistics Involving Population MeanIdentifying Appropriate Test Statistics Involving Population Mean
Identifying Appropriate Test Statistics Involving Population Mean
 
Bank Loan Approval Analysis: A Comprehensive Data Analysis Project
Bank Loan Approval Analysis: A Comprehensive Data Analysis ProjectBank Loan Approval Analysis: A Comprehensive Data Analysis Project
Bank Loan Approval Analysis: A Comprehensive Data Analysis Project
 
专业一比一美国俄亥俄大学毕业证成绩单pdf电子版制作修改
专业一比一美国俄亥俄大学毕业证成绩单pdf电子版制作修改专业一比一美国俄亥俄大学毕业证成绩单pdf电子版制作修改
专业一比一美国俄亥俄大学毕业证成绩单pdf电子版制作修改
 
FAIR, FAIRsharing, FAIR Cookbook and ELIXIR - Sansone SA - Boston 2024
FAIR, FAIRsharing, FAIR Cookbook and ELIXIR - Sansone SA - Boston 2024FAIR, FAIRsharing, FAIR Cookbook and ELIXIR - Sansone SA - Boston 2024
FAIR, FAIRsharing, FAIR Cookbook and ELIXIR - Sansone SA - Boston 2024
 
Student profile product demonstration on grades, ability, well-being and mind...
Student profile product demonstration on grades, ability, well-being and mind...Student profile product demonstration on grades, ability, well-being and mind...
Student profile product demonstration on grades, ability, well-being and mind...
 
Conf42-LLM_Adding Generative AI to Real-Time Streaming Pipelines
Conf42-LLM_Adding Generative AI to Real-Time Streaming PipelinesConf42-LLM_Adding Generative AI to Real-Time Streaming Pipelines
Conf42-LLM_Adding Generative AI to Real-Time Streaming Pipelines
 
SMOTE and K-Fold Cross Validation-Presentation.pptx
SMOTE and K-Fold Cross Validation-Presentation.pptxSMOTE and K-Fold Cross Validation-Presentation.pptx
SMOTE and K-Fold Cross Validation-Presentation.pptx
 
Thiophen Mechanism khhjjjjjjjhhhhhhhhhhh
Thiophen Mechanism khhjjjjjjjhhhhhhhhhhhThiophen Mechanism khhjjjjjjjhhhhhhhhhhh
Thiophen Mechanism khhjjjjjjjhhhhhhhhhhh
 
Minimizing AI Hallucinations/Confabulations and the Path towards AGI with Exa...
Minimizing AI Hallucinations/Confabulations and the Path towards AGI with Exa...Minimizing AI Hallucinations/Confabulations and the Path towards AGI with Exa...
Minimizing AI Hallucinations/Confabulations and the Path towards AGI with Exa...
 
Principles and Practices of Data Visualization
Principles and Practices of Data VisualizationPrinciples and Practices of Data Visualization
Principles and Practices of Data Visualization
 
NO1 Certified Black Magic Specialist Expert Amil baba in Lahore Islamabad Raw...
NO1 Certified Black Magic Specialist Expert Amil baba in Lahore Islamabad Raw...NO1 Certified Black Magic Specialist Expert Amil baba in Lahore Islamabad Raw...
NO1 Certified Black Magic Specialist Expert Amil baba in Lahore Islamabad Raw...
 
modul pembelajaran robotic Workshop _ by Slidesgo.pptx
modul pembelajaran robotic Workshop _ by Slidesgo.pptxmodul pembelajaran robotic Workshop _ by Slidesgo.pptx
modul pembelajaran robotic Workshop _ by Slidesgo.pptx
 
Cyber awareness ppt on the recorded data
Cyber awareness ppt on the recorded dataCyber awareness ppt on the recorded data
Cyber awareness ppt on the recorded data
 
Decoding the Heart: Student Presentation on Heart Attack Prediction with Data...
Decoding the Heart: Student Presentation on Heart Attack Prediction with Data...Decoding the Heart: Student Presentation on Heart Attack Prediction with Data...
Decoding the Heart: Student Presentation on Heart Attack Prediction with Data...
 
INTRODUCTION TO Natural language processing
INTRODUCTION TO Natural language processingINTRODUCTION TO Natural language processing
INTRODUCTION TO Natural language processing
 
Generative AI for Social Good at Open Data Science East 2024
Generative AI for Social Good at Open Data Science East 2024Generative AI for Social Good at Open Data Science East 2024
Generative AI for Social Good at Open Data Science East 2024
 
Data Analysis Project: Stroke Prediction
Data Analysis Project: Stroke PredictionData Analysis Project: Stroke Prediction
Data Analysis Project: Stroke Prediction
 
Decoding Patterns: Customer Churn Prediction Data Analysis Project
Decoding Patterns: Customer Churn Prediction Data Analysis ProjectDecoding Patterns: Customer Churn Prediction Data Analysis Project
Decoding Patterns: Customer Churn Prediction Data Analysis Project
 

Chi square

  • 1. © aSup-2007 CHI SQUARE    1 The CHI SQUARE Statistic Tests for Goodness of Fit and Independence
  • 2. © aSup-2007 CHI SQUARE    2 Preview  Color is known to affect human moods and emotion. Sitting in a pale-blue room is more calming than sitting in a bright-red room  Based on the known influence of color, Hill and Barton (2005) hypothesized that the color of uniform may influence the outcome of physical sports contest  The study does not produce a numerical score for each participant. Each participant is simply classified into two categories (winning or losing)
  • 3. © aSup-2007 CHI SQUARE    3 Preview  The data consist of frequencies or proportions describing how many individuals are in each category  This study want to use a hypothesis test to evaluate data. The null hypothesis would state that color has no effect on the outcome of the contest  Statistical technique have been developed specifically to analyze and interpret data consisting of frequencies or proportions  CHI SQUARE
  • 4. © aSup-2007 CHI SQUARE    4 PARAMETRIC AND NONPARAMETRIC STATISTICAL TESTS  The tests that concern parameter and require assumptions about parameter are called parametric tests  Another general characteristic of parametric tests is that they require a numerical score for each individual in the sample. In terms of measurement scales, parametric tests require data from an interval or a ratio scale
  • 5. © aSup-2007 CHI SQUARE    5 PARAMETRIC AND NONPARAMETRIC STATISTICAL TESTS  Often, researcher are confronted with experimental situation that do not conform to the requirements of parametric tests. In this situations, it may not be appropriate to use a parametric test because may lead to an erroneous interpretation of the data  Fortunately, there are several hypothesis testing techniques that provide alternatives to parametric test that called nonparametric tests
  • 6. © aSup-2007 CHI SQUARE    6 NONPARAMETRIC TEST  Nonparametric tests sometimes are called distribution free tests  One of the most obvious differences between parametric and nonparametric tests is the type of data they use  All the parametric tests required numerical scores. For nonparametric, the subjects are usually just classified into categories
  • 7. © aSup-2007 CHI SQUARE    7 NONPARAMETRIC TEST  Notice that these classification involve measurement on nominal or ordinal scales, and they do not produce numerical values that can be used to calculate mean and variance  Nonparametric tests generally are not as sensitive as parametric test; nonparametric tests are more likely to fail in detecting a real difference between two treatments
  • 8. © aSup-2007 CHI SQUARE    8 THE CHI SQUARE TEST FOR GOODNESS OF FIT … uses sample data to test hypotheses about the shape or proportions of a population distribution. The test determines how well the obtained sample proportions fit the population proportions specified by the null hypothesis
  • 9. © aSup-2007 CHI SQUARE    9 THE NULL HYPOTHESIS FOR THE GOODNESS OF FIT  For the chi-square test of goodness of fit, the null hypothesis specifies the proportion (or percentage) of the population in each category  Generally H0 will fall into one of the following categories: ○ No preference H0 states that the population is divided equally among the categories ○ No difference from a Known population H0 states that the proportion for one population are not different from the proportion that are known to exist for another population
  • 10. © aSup-2007 CHI SQUARE    10 THE DATA FOR THE GOODNESS OF FIT TEST  Select a sample of n individuals and count how many are in each category  The resulting values are called observed frequency (fo)  A sample of n = 40 participants was given a personality questionnaire and classified into one of three personality categories: A, B, or C Category A Category B Category C 15 19 6
  • 11. © aSup-2007 CHI SQUARE    11 EXPECTED FREQUENCIES  The general goal of the chi-square test for goodness of fit is to compare the data (the observed frequencies) with the null hypothesis  The problem is to determine how well the data fit the distribution specified in H0 – hence name goodness of fit  Suppose, for example, the null hypothesis states that the population is distributed into three categories with the following proportion Category A Category B Category C 25% 50% 25%
  • 12. © aSup-2007 CHI SQUARE    12 EXPECTED FREQUENCIES To find the exact frequency expected for each category, multiply the same size (n) by the proportion (or percentage) from the null hypothesis 25% of 40 = 10 individual in category A 50% of 40 = 20 individual in category B 25% of 40 = 10 individual in category C
  • 13. © aSup-2007 CHI SQUARE    13 THE CHI-SQUARE STATISTIC  The general purpose of any hypothesis test is to determine whether the sample data support or refute a hypothesis about population  In the chi-square test for goodness of fit, the sample expressed as a set of observe frequencies (fovalues) and the null hypothesis is used to generate a set of expected frequencies (fe values)
  • 14. © aSup-2007 CHI SQUARE    14 THE CHI-SQUARE STATISTIC  The chi-square statistic simply measures ho well the data (fo) fit the hypothesis (fe)  The symbol for the chi-square statistic is χ2  The formula for the chi-square statistic is χ2 = ∑ (fo – fe)2 fe
  • 15. © aSup-2007 CHI SQUARE    15 A researcher has developed three different design for a computer keyboard. A sample of n = 60 participants is obtained, and each individual tests all three keyboard and identifies his or her favorite. The frequency distribution of preference is: Design A = 23, Design B = 12, Design C = 25. Use a chi-square test for goodness of fit with α = .05 to determine whether there are significant preferences among three design LEARNING CHECK
  • 16. © aSup-2007 CHI SQUARE    16 Dari https://twitter.com/#!/palangmerah diketahui bahwa persentase golongan darah di Indonesia adalah: A : 25,48%, B : 26,68%, O : 40,77 %, AB : 6,6 % Golongan darah di kelas kita? Apakah berbeda dengan data PMI? LEARNING CHECK
  • 17. © aSup-2007 CHI SQUARE    17 THE CHI-SQUARE TEST FOR INDEPENDENCE  The chi-square may also be used to test whether there is a relationship between two variables  For example, a group of students could be classified in term of personality (introvert, extrovert) and in terms of color preferences (red, white, green, or blue). RED WHITE GREEN BLUE ∑ INTRO 10 3 15 22 50 EXTRO 90 17 25 18 150 100 20 40 40 200
  • 18. © aSup-2007 CHI SQUARE    18 OBSERVED AND EXPECTED FREQUENCIES fo RED WHITE GREEN BLUE ∑ INTRO 10 3 15 22 50 EXTRO 90 17 25 18 150 ∑ 100 20 40 40 200 fe RED WHITE GREEN BLUE ∑ INTRO 50 EXTRO 150 ∑ 100 20 40 40 200
  • 19. © aSup-2007 CHI SQUARE    19 OBSERVED AND EXPECTED FREQUENCIES fo RED WHITE GREEN BLUE ∑ INTRO 10 3 15 22 50 EXTRO 90 17 25 18 150 ∑ 100 20 40 40 200 fe RED WHITE GREEN BLUE ∑ INTRO 25 5 10 10 50 EXTRO 75 15 30 30 150 ∑ 100 20 40 40 200
  • 20. © aSup-2007 CHI SQUARE    20 OBSERVED AND EXPECTED FREQUENCIES fo R W G B ∑ INTRO 10 3 15 22 50 EXTRO 90 17 25 18 150 ∑ 100 20 40 40 200 (fo– fe)2 R W G B INTRO EXTRO fe R W G B ∑ INTRO 25 5 10 10 50 EXTRO 75 15 30 30 150 ∑ 100 20 40 40 200
  • 21. © aSup-2007 CHI SQUARE    21 OBSERVED AND EXPECTED FREQUENCIES fo R W G B ∑ INTRO 10 3 15 22 50 EXTRO 90 17 25 18 150 ∑ 100 20 40 40 200 (fo– fe)2 R W G B INTRO (-15)2 (-2)2 (5)2 (12)2 EXTRO (15)2 (-2)2 (-5)2 (-12)2 fe R W G B ∑ INTRO 25 5 10 10 50 EXTRO 75 15 30 30 150 ∑ 100 20 40 40 200
  • 22. © aSup-2007 CHI SQUARE    22 OBSERVED AND EXPECTED FREQUENCIES (fo– fe)2 /fe R W G B INTRO EXTRO fe R W G B INTRO 25 5 10 10 EXTRO 75 15 30 30 (fo– fe)2 R W G B INTRO 225 4 25 144 EXTRO 225 4 25 144
  • 23. © aSup-2007 CHI SQUARE    23 OBSERVED AND EXPECTED FREQUENCIES (fo– fe)2 /fe R W G B INTRO 9 0,8 2,5 14,4 EXTRO 3 0,267 0,833 4,8 fe R W G B INTRO 25 5 10 10 EXTRO 75 15 30 30 (fo– fe)2 R W G B INTRO 225 4 25 144 EXTRO 225 4 25 144
  • 24. © aSup-2007 CHI SQUARE    24 THE CHI-SQUARE STATISTIC χ2 = ∑ (fo – fe)2 fe χ2 = 35,6 df = (C-1) (R-1) = (3) (1) = 3 χ2 critical at α = .05 is 7,81