SlideShare a Scribd company logo
1 of 2
Download to read offline
CHI-SQUARE TEST EXPLANATION 
Let’s say you want to know if there is a difference in the proportion of men and women who are left handed and 
let’s say in your sample 10% of men and 5% of women were left -handed. 
How it’s Calculated (Without the gory details) 
1. You collect the data. For example, you ask 120 men and 140 women which hand they use and get this: 
ACTUAL DATA Left-handed Right-handed 
Men 12 108 
Women 7 133 
2. Calculate what numbers of left and right-handers we would expect IF men and women were the same. 
In this case, IF men and women were equally left and right handed, we would have expected these numbers in 
our sample of 260 people (Ask if you want to know how this is done): 
EXPECTED IF NO DIFFERENCE Left-handed Right-handed 
Men 8.77 111.23 
Women 10.23 129.77 
3. The computer calculates a Chi-square (pronounced Ki-square) value. The Chi-square value is a single number 
that adds up all the differences between our actual data and the data expected if there is no difference. If the 
actual data and expected data (if no difference) are identical, the Chi -square value is 0. A bigger difference will 
give a bigger Chi-square value. 
4. Look up the Chi-square value in a table to see if it is big enough to indicate a significant difference in 
handedness of males and females. 
Interpretation 
Greater differences between expected and actual data produce a larger Chi -square value. The larger the Chi-square 
value, the greater the probability that there really is a significant difference. 
With a 2 by 2 table like this (If you have more than 4 cells of data in your table, see your instructor): 
If the Chi-square value is greater than or equal to the critical value 
There is a significant difference between the groups we are studying. That is, the difference between actual data 
and the expected data (that assumes the groups aren’t different) is probably too great to be attributed to chance. 
So we conclude that our sample supports the hypothesis of a difference. 
If the Chi-square value is less than the critical value 
There is no significant difference. The amount of difference between expected and actual data is likely just due to 
chance. Thus, we conclude that our sample does not support the hypothesis of a difference. 
In this example, the critical value is 3.8. The Chi-square value was 2.383, which is less than 3.8. Thus, there is 
no significant difference in handedness between men and women in our sample. We conclude that based on this 
sample, men and women in general seem equally likely to be left or right handed. 
**Warning** 
We have not proven anything!!! These first samples might be atypical. Repeated sampling may show a 
significant difference, or eliminate the difference we thought we saw. Because of this uncertainty, we can only 
say that the hypothesis was supported or not supported.
Graphing Categorical Data that you analyze with the Chi -Square Statistic 
Let’s say you want to know if there is a difference in the proportion of men and women who are left handed and 
you collect this data: 
ACTUAL DATA Left-handed Right-handed 
Men 12 108 
Women 7 133 
Calculate the % of men that are left-handed and right handed in your study: 
12 / 120 total men = 0.10 X 10 = 10% of men were left -handed 
108 / 120 = 0.90 X 100 = 90% of men were right-handed 
Do the same for women: 
7 / 140 total women = 0.05 X 100 = 5% left handed 
133 / 140 = 0.95 X 100 = 95% right-handed 
Plot these percents as bars: 
Percent 
Lef t 
Hand ed 
30 
20 
10 
Men Women 
Or plot as stacked bars: 
10 0 
Percent 
50 
Or plot as a pie diagram. 
Lef t- handed 
Rig ht -handed 
Men Women

More Related Content

Similar to Chi sq explanation

Page 266LEARNING OBJECTIVES· Explain how researchers use inf.docx
Page 266LEARNING OBJECTIVES· Explain how researchers use inf.docxPage 266LEARNING OBJECTIVES· Explain how researchers use inf.docx
Page 266LEARNING OBJECTIVES· Explain how researchers use inf.docxkarlhennesey
 
Chapter8 introduction to hypothesis testing
Chapter8 introduction to hypothesis testingChapter8 introduction to hypothesis testing
Chapter8 introduction to hypothesis testingBOmebratu
 
Steps in hypothesis.pptx
Steps in hypothesis.pptxSteps in hypothesis.pptx
Steps in hypothesis.pptxYashwanth Rm
 
Data Analysis for Graduate Studies Summary
Data Analysis for Graduate Studies SummaryData Analysis for Graduate Studies Summary
Data Analysis for Graduate Studies SummaryKelvinNMhina
 
Topic Learning TeamNumber of Pages 2 (Double Spaced)Num.docx
Topic Learning TeamNumber of Pages 2 (Double Spaced)Num.docxTopic Learning TeamNumber of Pages 2 (Double Spaced)Num.docx
Topic Learning TeamNumber of Pages 2 (Double Spaced)Num.docxAASTHA76
 
Chi-Square Test of Independence
Chi-Square Test of IndependenceChi-Square Test of Independence
Chi-Square Test of IndependenceKen Plummer
 
Math class 8 data handling
Math class 8 data handling Math class 8 data handling
Math class 8 data handling HimakshiKava
 
Frequency Tables - Statistics
Frequency Tables - StatisticsFrequency Tables - Statistics
Frequency Tables - Statisticsmscartersmaths
 
Determination and Analysis of Sample size
Determination and Analysis of Sample sizeDetermination and Analysis of Sample size
Determination and Analysis of Sample sizeSudipto Krishna Dutta
 
How to calculate power in statistics
How to calculate power in statisticsHow to calculate power in statistics
How to calculate power in statisticsStat Analytica
 
data handling class 8
data handling class 8data handling class 8
data handling class 8HimakshiKava
 
analysing_data_using_spss.pdf
analysing_data_using_spss.pdfanalysing_data_using_spss.pdf
analysing_data_using_spss.pdfDrAnilKannur1
 
Analysis Of Data Using SPSS
Analysis Of Data Using SPSSAnalysis Of Data Using SPSS
Analysis Of Data Using SPSSBrittany Brown
 
Lesson 2 Statistics Benefits, Risks, and MeasurementsAssignmen.docx
Lesson 2 Statistics Benefits, Risks, and MeasurementsAssignmen.docxLesson 2 Statistics Benefits, Risks, and MeasurementsAssignmen.docx
Lesson 2 Statistics Benefits, Risks, and MeasurementsAssignmen.docxSHIVA101531
 

Similar to Chi sq explanation (20)

Page 266LEARNING OBJECTIVES· Explain how researchers use inf.docx
Page 266LEARNING OBJECTIVES· Explain how researchers use inf.docxPage 266LEARNING OBJECTIVES· Explain how researchers use inf.docx
Page 266LEARNING OBJECTIVES· Explain how researchers use inf.docx
 
40007 chapter8
40007 chapter840007 chapter8
40007 chapter8
 
Chapter8 introduction to hypothesis testing
Chapter8 introduction to hypothesis testingChapter8 introduction to hypothesis testing
Chapter8 introduction to hypothesis testing
 
Hypothesis test
Hypothesis testHypothesis test
Hypothesis test
 
Hypothesis testing - Primer
Hypothesis testing - PrimerHypothesis testing - Primer
Hypothesis testing - Primer
 
Steps in hypothesis.pptx
Steps in hypothesis.pptxSteps in hypothesis.pptx
Steps in hypothesis.pptx
 
Data Analysis for Graduate Studies Summary
Data Analysis for Graduate Studies SummaryData Analysis for Graduate Studies Summary
Data Analysis for Graduate Studies Summary
 
Topic Learning TeamNumber of Pages 2 (Double Spaced)Num.docx
Topic Learning TeamNumber of Pages 2 (Double Spaced)Num.docxTopic Learning TeamNumber of Pages 2 (Double Spaced)Num.docx
Topic Learning TeamNumber of Pages 2 (Double Spaced)Num.docx
 
Chi-Square Test of Independence
Chi-Square Test of IndependenceChi-Square Test of Independence
Chi-Square Test of Independence
 
Prob ^0 Stats Proj 1
Prob ^0 Stats Proj 1Prob ^0 Stats Proj 1
Prob ^0 Stats Proj 1
 
Math class 8 data handling
Math class 8 data handling Math class 8 data handling
Math class 8 data handling
 
Frequency Tables - Statistics
Frequency Tables - StatisticsFrequency Tables - Statistics
Frequency Tables - Statistics
 
Hypothesis testing
Hypothesis testingHypothesis testing
Hypothesis testing
 
Determination and Analysis of Sample size
Determination and Analysis of Sample sizeDetermination and Analysis of Sample size
Determination and Analysis of Sample size
 
How to calculate power in statistics
How to calculate power in statisticsHow to calculate power in statistics
How to calculate power in statistics
 
data handling class 8
data handling class 8data handling class 8
data handling class 8
 
analysing_data_using_spss.pdf
analysing_data_using_spss.pdfanalysing_data_using_spss.pdf
analysing_data_using_spss.pdf
 
analysing_data_using_spss.pdf
analysing_data_using_spss.pdfanalysing_data_using_spss.pdf
analysing_data_using_spss.pdf
 
Analysis Of Data Using SPSS
Analysis Of Data Using SPSSAnalysis Of Data Using SPSS
Analysis Of Data Using SPSS
 
Lesson 2 Statistics Benefits, Risks, and MeasurementsAssignmen.docx
Lesson 2 Statistics Benefits, Risks, and MeasurementsAssignmen.docxLesson 2 Statistics Benefits, Risks, and MeasurementsAssignmen.docx
Lesson 2 Statistics Benefits, Risks, and MeasurementsAssignmen.docx
 

More from Chinnannan Periasamy (15)

MCT
MCTMCT
MCT
 
Inventory notes
Inventory notesInventory notes
Inventory notes
 
Qtmd syllabus
Qtmd syllabusQtmd syllabus
Qtmd syllabus
 
Ec 15 101 advanced engineering mathematics
Ec 15 101 advanced engineering mathematicsEc 15 101 advanced engineering mathematics
Ec 15 101 advanced engineering mathematics
 
Fourier transform
Fourier transformFourier transform
Fourier transform
 
Avg q lenth
Avg q lenthAvg q lenth
Avg q lenth
 
Parametric test
Parametric testParametric test
Parametric test
 
HYPOTHESES STEPS
HYPOTHESES STEPSHYPOTHESES STEPS
HYPOTHESES STEPS
 
11.00 technology ok
11.00 technology ok11.00 technology ok
11.00 technology ok
 
segmentation
segmentationsegmentation
segmentation
 
1.11 functions of money ppt-ok
1.11 functions of money ppt-ok1.11 functions of money ppt-ok
1.11 functions of money ppt-ok
 
Listening
ListeningListening
Listening
 
decision
decisiondecision
decision
 
M tech regulations
M tech regulationsM tech regulations
M tech regulations
 
1.iib ppt
1.iib ppt1.iib ppt
1.iib ppt
 

Recently uploaded

Long journey of Ruby standard library at RubyConf AU 2024
Long journey of Ruby standard library at RubyConf AU 2024Long journey of Ruby standard library at RubyConf AU 2024
Long journey of Ruby standard library at RubyConf AU 2024Hiroshi SHIBATA
 
QCon London: Mastering long-running processes in modern architectures
QCon London: Mastering long-running processes in modern architecturesQCon London: Mastering long-running processes in modern architectures
QCon London: Mastering long-running processes in modern architecturesBernd Ruecker
 
A Journey Into the Emotions of Software Developers
A Journey Into the Emotions of Software DevelopersA Journey Into the Emotions of Software Developers
A Journey Into the Emotions of Software DevelopersNicole Novielli
 
MuleSoft Online Meetup Group - B2B Crash Course: Release SparkNotes
MuleSoft Online Meetup Group - B2B Crash Course: Release SparkNotesMuleSoft Online Meetup Group - B2B Crash Course: Release SparkNotes
MuleSoft Online Meetup Group - B2B Crash Course: Release SparkNotesManik S Magar
 
The Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptx
The Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptxThe Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptx
The Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptxLoriGlavin3
 
Abdul Kader Baba- Managing Cybersecurity Risks and Compliance Requirements i...
Abdul Kader Baba- Managing Cybersecurity Risks  and Compliance Requirements i...Abdul Kader Baba- Managing Cybersecurity Risks  and Compliance Requirements i...
Abdul Kader Baba- Managing Cybersecurity Risks and Compliance Requirements i...itnewsafrica
 
Modern Roaming for Notes and Nomad – Cheaper Faster Better Stronger
Modern Roaming for Notes and Nomad – Cheaper Faster Better StrongerModern Roaming for Notes and Nomad – Cheaper Faster Better Stronger
Modern Roaming for Notes and Nomad – Cheaper Faster Better Strongerpanagenda
 
Generative AI - Gitex v1Generative AI - Gitex v1.pptx
Generative AI - Gitex v1Generative AI - Gitex v1.pptxGenerative AI - Gitex v1Generative AI - Gitex v1.pptx
Generative AI - Gitex v1Generative AI - Gitex v1.pptxfnnc6jmgwh
 
The State of Passkeys with FIDO Alliance.pptx
The State of Passkeys with FIDO Alliance.pptxThe State of Passkeys with FIDO Alliance.pptx
The State of Passkeys with FIDO Alliance.pptxLoriGlavin3
 
Transcript: New from BookNet Canada for 2024: BNC SalesData and LibraryData -...
Transcript: New from BookNet Canada for 2024: BNC SalesData and LibraryData -...Transcript: New from BookNet Canada for 2024: BNC SalesData and LibraryData -...
Transcript: New from BookNet Canada for 2024: BNC SalesData and LibraryData -...BookNet Canada
 
[Webinar] SpiraTest - Setting New Standards in Quality Assurance
[Webinar] SpiraTest - Setting New Standards in Quality Assurance[Webinar] SpiraTest - Setting New Standards in Quality Assurance
[Webinar] SpiraTest - Setting New Standards in Quality AssuranceInflectra
 
Digital Identity is Under Attack: FIDO Paris Seminar.pptx
Digital Identity is Under Attack: FIDO Paris Seminar.pptxDigital Identity is Under Attack: FIDO Paris Seminar.pptx
Digital Identity is Under Attack: FIDO Paris Seminar.pptxLoriGlavin3
 
Data governance with Unity Catalog Presentation
Data governance with Unity Catalog PresentationData governance with Unity Catalog Presentation
Data governance with Unity Catalog PresentationKnoldus Inc.
 
How to Effectively Monitor SD-WAN and SASE Environments with ThousandEyes
How to Effectively Monitor SD-WAN and SASE Environments with ThousandEyesHow to Effectively Monitor SD-WAN and SASE Environments with ThousandEyes
How to Effectively Monitor SD-WAN and SASE Environments with ThousandEyesThousandEyes
 
Glenn Lazarus- Why Your Observability Strategy Needs Security Observability
Glenn Lazarus- Why Your Observability Strategy Needs Security ObservabilityGlenn Lazarus- Why Your Observability Strategy Needs Security Observability
Glenn Lazarus- Why Your Observability Strategy Needs Security Observabilityitnewsafrica
 
Email Marketing Automation for Bonterra Impact Management (fka Social Solutio...
Email Marketing Automation for Bonterra Impact Management (fka Social Solutio...Email Marketing Automation for Bonterra Impact Management (fka Social Solutio...
Email Marketing Automation for Bonterra Impact Management (fka Social Solutio...Jeffrey Haguewood
 
A Framework for Development in the AI Age
A Framework for Development in the AI AgeA Framework for Development in the AI Age
A Framework for Development in the AI AgeCprime
 
Decarbonising Buildings: Making a net-zero built environment a reality
Decarbonising Buildings: Making a net-zero built environment a realityDecarbonising Buildings: Making a net-zero built environment a reality
Decarbonising Buildings: Making a net-zero built environment a realityIES VE
 
All These Sophisticated Attacks, Can We Really Detect Them - PDF
All These Sophisticated Attacks, Can We Really Detect Them - PDFAll These Sophisticated Attacks, Can We Really Detect Them - PDF
All These Sophisticated Attacks, Can We Really Detect Them - PDFMichael Gough
 
Connecting the Dots for Information Discovery.pdf
Connecting the Dots for Information Discovery.pdfConnecting the Dots for Information Discovery.pdf
Connecting the Dots for Information Discovery.pdfNeo4j
 

Recently uploaded (20)

Long journey of Ruby standard library at RubyConf AU 2024
Long journey of Ruby standard library at RubyConf AU 2024Long journey of Ruby standard library at RubyConf AU 2024
Long journey of Ruby standard library at RubyConf AU 2024
 
QCon London: Mastering long-running processes in modern architectures
QCon London: Mastering long-running processes in modern architecturesQCon London: Mastering long-running processes in modern architectures
QCon London: Mastering long-running processes in modern architectures
 
A Journey Into the Emotions of Software Developers
A Journey Into the Emotions of Software DevelopersA Journey Into the Emotions of Software Developers
A Journey Into the Emotions of Software Developers
 
MuleSoft Online Meetup Group - B2B Crash Course: Release SparkNotes
MuleSoft Online Meetup Group - B2B Crash Course: Release SparkNotesMuleSoft Online Meetup Group - B2B Crash Course: Release SparkNotes
MuleSoft Online Meetup Group - B2B Crash Course: Release SparkNotes
 
The Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptx
The Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptxThe Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptx
The Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptx
 
Abdul Kader Baba- Managing Cybersecurity Risks and Compliance Requirements i...
Abdul Kader Baba- Managing Cybersecurity Risks  and Compliance Requirements i...Abdul Kader Baba- Managing Cybersecurity Risks  and Compliance Requirements i...
Abdul Kader Baba- Managing Cybersecurity Risks and Compliance Requirements i...
 
Modern Roaming for Notes and Nomad – Cheaper Faster Better Stronger
Modern Roaming for Notes and Nomad – Cheaper Faster Better StrongerModern Roaming for Notes and Nomad – Cheaper Faster Better Stronger
Modern Roaming for Notes and Nomad – Cheaper Faster Better Stronger
 
Generative AI - Gitex v1Generative AI - Gitex v1.pptx
Generative AI - Gitex v1Generative AI - Gitex v1.pptxGenerative AI - Gitex v1Generative AI - Gitex v1.pptx
Generative AI - Gitex v1Generative AI - Gitex v1.pptx
 
The State of Passkeys with FIDO Alliance.pptx
The State of Passkeys with FIDO Alliance.pptxThe State of Passkeys with FIDO Alliance.pptx
The State of Passkeys with FIDO Alliance.pptx
 
Transcript: New from BookNet Canada for 2024: BNC SalesData and LibraryData -...
Transcript: New from BookNet Canada for 2024: BNC SalesData and LibraryData -...Transcript: New from BookNet Canada for 2024: BNC SalesData and LibraryData -...
Transcript: New from BookNet Canada for 2024: BNC SalesData and LibraryData -...
 
[Webinar] SpiraTest - Setting New Standards in Quality Assurance
[Webinar] SpiraTest - Setting New Standards in Quality Assurance[Webinar] SpiraTest - Setting New Standards in Quality Assurance
[Webinar] SpiraTest - Setting New Standards in Quality Assurance
 
Digital Identity is Under Attack: FIDO Paris Seminar.pptx
Digital Identity is Under Attack: FIDO Paris Seminar.pptxDigital Identity is Under Attack: FIDO Paris Seminar.pptx
Digital Identity is Under Attack: FIDO Paris Seminar.pptx
 
Data governance with Unity Catalog Presentation
Data governance with Unity Catalog PresentationData governance with Unity Catalog Presentation
Data governance with Unity Catalog Presentation
 
How to Effectively Monitor SD-WAN and SASE Environments with ThousandEyes
How to Effectively Monitor SD-WAN and SASE Environments with ThousandEyesHow to Effectively Monitor SD-WAN and SASE Environments with ThousandEyes
How to Effectively Monitor SD-WAN and SASE Environments with ThousandEyes
 
Glenn Lazarus- Why Your Observability Strategy Needs Security Observability
Glenn Lazarus- Why Your Observability Strategy Needs Security ObservabilityGlenn Lazarus- Why Your Observability Strategy Needs Security Observability
Glenn Lazarus- Why Your Observability Strategy Needs Security Observability
 
Email Marketing Automation for Bonterra Impact Management (fka Social Solutio...
Email Marketing Automation for Bonterra Impact Management (fka Social Solutio...Email Marketing Automation for Bonterra Impact Management (fka Social Solutio...
Email Marketing Automation for Bonterra Impact Management (fka Social Solutio...
 
A Framework for Development in the AI Age
A Framework for Development in the AI AgeA Framework for Development in the AI Age
A Framework for Development in the AI Age
 
Decarbonising Buildings: Making a net-zero built environment a reality
Decarbonising Buildings: Making a net-zero built environment a realityDecarbonising Buildings: Making a net-zero built environment a reality
Decarbonising Buildings: Making a net-zero built environment a reality
 
All These Sophisticated Attacks, Can We Really Detect Them - PDF
All These Sophisticated Attacks, Can We Really Detect Them - PDFAll These Sophisticated Attacks, Can We Really Detect Them - PDF
All These Sophisticated Attacks, Can We Really Detect Them - PDF
 
Connecting the Dots for Information Discovery.pdf
Connecting the Dots for Information Discovery.pdfConnecting the Dots for Information Discovery.pdf
Connecting the Dots for Information Discovery.pdf
 

Chi sq explanation

  • 1. CHI-SQUARE TEST EXPLANATION Let’s say you want to know if there is a difference in the proportion of men and women who are left handed and let’s say in your sample 10% of men and 5% of women were left -handed. How it’s Calculated (Without the gory details) 1. You collect the data. For example, you ask 120 men and 140 women which hand they use and get this: ACTUAL DATA Left-handed Right-handed Men 12 108 Women 7 133 2. Calculate what numbers of left and right-handers we would expect IF men and women were the same. In this case, IF men and women were equally left and right handed, we would have expected these numbers in our sample of 260 people (Ask if you want to know how this is done): EXPECTED IF NO DIFFERENCE Left-handed Right-handed Men 8.77 111.23 Women 10.23 129.77 3. The computer calculates a Chi-square (pronounced Ki-square) value. The Chi-square value is a single number that adds up all the differences between our actual data and the data expected if there is no difference. If the actual data and expected data (if no difference) are identical, the Chi -square value is 0. A bigger difference will give a bigger Chi-square value. 4. Look up the Chi-square value in a table to see if it is big enough to indicate a significant difference in handedness of males and females. Interpretation Greater differences between expected and actual data produce a larger Chi -square value. The larger the Chi-square value, the greater the probability that there really is a significant difference. With a 2 by 2 table like this (If you have more than 4 cells of data in your table, see your instructor): If the Chi-square value is greater than or equal to the critical value There is a significant difference between the groups we are studying. That is, the difference between actual data and the expected data (that assumes the groups aren’t different) is probably too great to be attributed to chance. So we conclude that our sample supports the hypothesis of a difference. If the Chi-square value is less than the critical value There is no significant difference. The amount of difference between expected and actual data is likely just due to chance. Thus, we conclude that our sample does not support the hypothesis of a difference. In this example, the critical value is 3.8. The Chi-square value was 2.383, which is less than 3.8. Thus, there is no significant difference in handedness between men and women in our sample. We conclude that based on this sample, men and women in general seem equally likely to be left or right handed. **Warning** We have not proven anything!!! These first samples might be atypical. Repeated sampling may show a significant difference, or eliminate the difference we thought we saw. Because of this uncertainty, we can only say that the hypothesis was supported or not supported.
  • 2. Graphing Categorical Data that you analyze with the Chi -Square Statistic Let’s say you want to know if there is a difference in the proportion of men and women who are left handed and you collect this data: ACTUAL DATA Left-handed Right-handed Men 12 108 Women 7 133 Calculate the % of men that are left-handed and right handed in your study: 12 / 120 total men = 0.10 X 10 = 10% of men were left -handed 108 / 120 = 0.90 X 100 = 90% of men were right-handed Do the same for women: 7 / 140 total women = 0.05 X 100 = 5% left handed 133 / 140 = 0.95 X 100 = 95% right-handed Plot these percents as bars: Percent Lef t Hand ed 30 20 10 Men Women Or plot as stacked bars: 10 0 Percent 50 Or plot as a pie diagram. Lef t- handed Rig ht -handed Men Women