lesson 06 chapter 9 two samples test and chapter 11 chi square test
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Inductive StatisticsInductive Statistics
Dr. Ning DING
n.ding@pl.hanze.nl
I.007 IBS, Hanze
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Table of Contents
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests~Basics~Independent Sample Test
~Large Samples~Small Samples
~Dependent Sample Test
~Differences between Proportions~Two-tailed Test~One-tailed Test
Chapter 11: Chi-Square ~Basics~Contingency Table 2-row~Contingency Table 3-row
Chapter 9 Testing Hypotheses: Two-Sample Tests: Basics-Independent
σ is known:σ is known:
σ is unknown:σ is unknown:
H0H1
Two-tailedtest
One-tailedtest
n <30 & σ is unknownn <30 & σ is unknown
Chapter 9 Testing Hypotheses: Two-Sample Tests: Practice
Ch 9 No. 9-9 P.466
Step 1: Formulate hypothesesStep 1: Formulate hypotheses
9-99-9
Step 2: Find the Pooled Estimate of σ2Step 2: Find the Pooled Estimate of σ2
Step 3: Calculate the standard errorStep 3: Calculate the standard error
Step 4: Visualize and Find the t scoresStep 4: Visualize and Find the t scores
Gender Mean Standard Deviation
Sample size
Female 12.8 1.0667 10Male 11.625 1.4107 8
One-tailed Test
df = 16 area=0.10 t=1.746t=1.746
Review:Chapter 5
Chapter 6 Chapter 7
Chapter 8 Testing Hypothesis~Test for Mean* when σ is known* when σ is unknown AND n=<30~Test for Proportion
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics
~Independent Sample Test~Large Samples~Small Samples
~Dependent Sample Test
Chapter 9 Testing Hypotheses: Two-Sample Tests: Dependent Samples
9.2 Dependent SamplesReview:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 9 Testing Hypotheses: Two-Sample Tests: Dependent Samples
9.2 Dependent Samples
Ch 9 Example P.468
Will the participant lose more than 17 pounds after the weight-reducing program? The survey data is:
Step 1: Formulate Hypotheses Step 1: Formulate Hypotheses
One-tailed Test
Example:Example:Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 9 Testing Hypotheses: Two-Sample Tests: Dependent Samples
9.2 Dependent Samples
Ch 9 Example P.468
Step 2: Calculate the estimated standard deviation of the population differenceStep 2: Calculate the estimated standard deviation of the population difference
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 9 Testing Hypotheses: Two-Sample Tests: Dependent Samples
9.2 Dependent Samples
Ch 9 Example P.468
Step 3: Find the Standard Error of the population differenceStep 3: Find the Standard Error of the population difference
Step 4: Calculate the t valueStep 4: Calculate the t value
Step 5: Visualize and get the t valuesStep 5: Visualize and get the t values
df = 10-1=9 area = 0.10
t=1.833t=1.833
One-tailed Test
reject H0
significant difference
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 9 Testing Hypotheses: Two-Sample Tests: Practice
Ch 9 No. 9-15 P.474
Step 4: Visalize and Calculate the t valuesStep 4: Visalize and Calculate the t values
t=1.895t=1.895
9-159-15
Step 3: Find the Standard Error of the population differenceStep 3: Find the Standard Error of the population difference
Step 1: Formulate Hypotheses Step 1: Formulate Hypotheses
Step 2: Calculate the estimated standard deviation of the population differenceStep 2: Calculate the estimated standard deviation of the population difference
One-tailed Test
df=7 area=0.10 reject H0
sig difference
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 9 Testing Hypotheses: Two-Sample Tests: Proportion
Example:Example:
Ch 9 Example P.476
You are testing whether the two drugs cause different blood-pressure levels. The data is as below:
Step 1: Formulate HypothesesStep 1: Formulate Hypotheses
Step 3: Calculate the Standard Error of Proportion DifferenceStep 3: Calculate the Standard Error of Proportion Difference
Step 2: Calculate the Estimated Proportion DifferenceStep 2: Calculate the Estimated Proportion Difference
Two-tailed Test
Two-tailed Test
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Step 4: Visualize and get the z valuesStep 4: Visualize and get the z values
-1.96 +1.96
Accept H0
No significant difference
Chapter 9 Testing Hypotheses: Two-Sample Tests: Proportion
Ch 9 Example P.476
Two-tailed Test
Two-tailed Test
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 9 Testing Hypotheses: Two-Sample Tests: Proportion
Step 1: Formulate HypothesesStep 1: Formulate Hypotheses
Step 3: Calculate the Standard Error of Proportion DifferenceStep 3: Calculate the Standard Error of Proportion Difference
Step 2: Calculate the Estimated Proportion DifferenceStep 2: Calculate the Estimated Proportion Difference
One-tailed Test
One-tailed Test
Example:Example:
Ch 9 Example P.480
You are testing whether personal-appearance method causes fewer tax mistakes than mail method. The data is as below:
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Step 4: Visualize and get the z valuesStep 4: Visualize and get the z values
One-tailed α=0.15 P=0.35 z= -1.04
Accept H0
No significant difference
Chapter 9 Testing Hypotheses: Two-Sample Tests: Proportion
Ch 9 Example P.480
One-tailed Test
One-tailed Test
-1.04
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 9 Testing Hypotheses: Two-Sample Tests: Practice9-209-20
Ch 9 No. 9-20 P.483
Step 1: Formulate HypothesesStep 1: Formulate Hypotheses
Step 3: Calculate the Standard Error of Proportion DifferenceStep 3: Calculate the Standard Error of Proportion Difference
Step 2: Calculate the Estimated Proportion DifferenceStep 2: Calculate the Estimated Proportion Difference
Step 4: Visualize and get the z valuesStep 4: Visualize and get the z values
z= -1.28z= -1.28
reject H0 sig difference
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 9 Testing Hypotheses: Two-Sample Tests: Practice9-219-21
Step 1: Formulate HypothesesStep 1: Formulate Hypotheses
Step 3: Calculate the Standard Error of Proportion DifferenceStep 3: Calculate the Standard Error of Proportion Difference
Step 2: Calculate the Estimated Proportion DifferenceStep 2: Calculate the Estimated Proportion Difference
Ch 9 No. 9-21 P.483
Step 4: Visualize and get the z valuesStep 4: Visualize and get the z values
accept H0 no sig difference
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 11 Chi-Square Test-Basics
Contingency Table (Cross break table)
Male Female TotalJunior high school 40 60 100Senior high school 60 40 100Total 100 100 200
Rows * Columns == 2*2 tableRows * Columns == 2*2 table
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 11 Chi-Square Test-Basics
Contingency Table (Cross break table)
Male Female TotalJunior high school 40 60 100Senior high school 60 40 100Total 100 100 200
Rows * Columns == 2*2 tableRows * Columns == 2*2 table
Male Female TotalJunior high school 40(50) 60(50) 100Senior high school 60(50) 40(50) 100Total 100 100 200
Expected and Observed ValuesExpected and Observed Values
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 11 Chi-Square Test-Basics
Contingency Table (Cross break table)
1*1=11*1=1
Male Female TotalJunior high school 40 60 100Senior high school 60 40 100Total 100 100 200
Social Science
Nature Science
Sports
Junior high school 40 60 20Senior high school 60 40 40University 50 30 120
2*2=42*2=4
Degree of freedom= (row-1)*(column-1)Degree of freedom= (row-1)*(column-1) 2*2 table2*2 table
3*3 table3*3 table
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 11 Chi-Square Test–Calculate χ2
for 2-row Table
Step 1: Calculate the expected valuesStep 1: Calculate the expected values
Ch 11 Example P.570
Example:Example:Our employees’ attitude toward job-performance reviews. There are two review methods, the present one or the new one. Is the attitude dependent on geography? The survey looks like below:
Chapter 11 Chi-Square Test–Calculate χ2
for 2-row TableStep 2: Calculate the χ2Step 2: Calculate the χ2
2.7644
Ch 11 Example P.570
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Step 3: Find the critical χ2Step 3: Find the critical χ2
Chapter 11 Chi-Square Test–Calculate χ2
for 2-row Table
α = 0.10 2*4 df= 3 χ2=6.251
10%Acceptance
Region
χ2=2.7644
Accept H0
No sig difference among groups
Ch 11 Example P.570
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 11 Chi-Square Test–Calculate χ2
for 3-row TableFor a national health insurance program, you believes that lengths of stays in hospitals are dependent on the types of health insurance that people have. The random data from the survey is as below:
Ch 11 Example P.575
Step 1: Formulate the hypothesesStep 1: Formulate the hypotheses
H0: length of stay and insurance types are independent
H1: length of stay depends on insurance types
α=0.01
Days in HospitalCost Cover <5 5-10 >10 Total<25% 40 75 65 18025-50% 30 45 75 150>50% 40 100 190 330Total 110 220 330 660
Example:Example:
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 11 Chi-Square Test–Calculate χ2
for 3-row Table
Days in HospitalCost Cover <5 5-10 >10 Total<25% 40 75 65 18025-50% 30 45 75 150>50% 40 100 190 330Total 110 220 330 660
For a national health insurance program, you believes that lengths of stays in hospitals are dependent on the types of health insurance that people have. The random data from the survey is as below: Example:Example:
Ch 11 Example P.575
Step 2: Calculate the Expected Frequency For Any CellStep 2: Calculate the Expected Frequency For Any Cell
RT
CT
(30) (60)
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 11 Chi-Square Test–Calculate χ2
for 3-row Table
Ch 11 Example P.575
Step 3: Calculate the Chi-SquareStep 3: Calculate the Chi-Square
Days in Hospital
Cost Cover<5 5-10 >10 Total
<25% 40(30) 75(60) 65(90) 18025-50% 30(25) 45(50) 75(75) 150>50% 40(55) 100(110) 190(165) 330
Total 110 220 330 660
Example:Example:
For a national health insurance program, you believes that lengths of stays in hospitals are dependent on the types of health insurance that people have. The random data from the survey is as below:
3.33
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 11 Chi-Square Test–Calculate χ2
for 3-row Table
Ch 11 Example P.575
Step 3: Calculate the Chi-SquareStep 3: Calculate the Chi-Square
Days in Hospital
Cost Cover<5 5-10 >10 Total
<25% 40(30) 75(60) 65(90) 18025-50% 30(25) 45(50) 75(75) 150>50% 40(55) 100(110) 190(165) 330
Total 110 220 330 660
Example:Example:
For a national health insurance program, you believes that lengths of stays in hospitals are dependent on the types of health insurance that people have. The random data from the survey is as below:
3.33 3.75 6.94
1.00
4.09
0.500.91
0.003.79
=3.33+3.75+6.94+1.00+0.50+0.00+4.09+0.91+3.79=24.32
Chi-Square χ2 =24.32Chi-Square χ2 =24.32
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 11 Chi-Square Test–Calculate χ2
for 3-row Table
Ch 11 Example P.575
Step 4: Find the critical Chi-SquareStep 4: Find the critical Chi-Square
For a national health insurance program, you believes that lengths of stays in hospitals are dependent on the types of health insurance that people have. The random data from the survey is as below:
Chi-Square χ2 =24.32Chi-Square χ2 =24.32
Days in HospitalCost Cover <5 5-10 >10 Total<25% 40 75 65 18025-50% 30 45 75 150>50% 40 100 190 330Total 110 220 330 660
Example:Example:
1%
Acceptance Region
α = 0.01 3*3 df= 4
χ2 =13.277 Reject H0
dependent on each other
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 11 Chi-Square Test–Calculate χ2
for 3-row Table: Practice
Ch 11 No. 11-9/10 P.582
11-9/1011-9/10 Economy Weekly Chip SalesHigh Medium Low Total
At peak 20 7 3 30At Through 30 40 30 100Rising 20 8 2 30Falling 30 5 5 40Total 100 60 40 200
Step 1: Formulate the hypothesesStep 1: Formulate the hypotheses
Step 2: Calculate the Expected Frequency For Any CellStep 2: Calculate the Expected Frequency For Any Cell
Step 3: Calculate the Chi-SquareStep 3: Calculate the Chi-Square
Step 4: Find the critical Chi-SquareStep 4: Find the critical Chi-Square
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 11 Chi-Square Test–Calculate χ2
for 3-row Table: Practice
Ch 11 No. 11-9/10 P.582
11-9/1011-9/10 Economy Weekly Chip SalesHigh Medium Low Total
At peak 20 7 3 30At Through 30 40 30 100Rising 20 8 2 30Falling 30 5 5 40Total 100 60 40 200
Step 1: Formulate the hypothesesStep 1: Formulate the hypotheses
H0: Sales and economy are independent
H1: sales depends on economy
α=0.10
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 11 Chi-Square Test–Calculate χ2
for 3-row Table: Practice
Ch 11 No. 11-9/10 P.582
11-9/1011-9/10 Economy Weekly Chip SalesHigh Medium Low Total
At peak 20 7 3 30At Through 30 40 30 100Rising 20 8 2 30Falling 30 5 5 40Total 100 60 40 200
Step 2: Calculate the Expected Frequency For Any CellStep 2: Calculate the Expected Frequency For Any Cell
Economy Weekly Chip SalesHigh Medium Low Total
At peak 20 (15) 7 (9) 3 (6) 30
At Through 30 (50) 40 (30) 30 (20) 100Rising 20 (15) 8 (9) 2 (6) 30Falling 30 (20) 5 (12) 5 (8) 40Total 100 60 40 200
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Chapter 11 Chi-Square Test–Calculate χ2
for 3-row Table: Practice
Ch 11 No. 11-9/10 P.582
11-9/1011-9/10
Step 3: Calculate the Chi-SquareStep 3: Calculate the Chi-Square
= 34.60
10%
Acceptance Region
α = 0.10 4*3df= 6
χ2 =10.645
Chi-Square χ2 =34.60Chi-Square χ2 =34.60
Reject H0
dependent on each other
Economy Weekly Chip SalesHigh Medium Low Total
At peak 20 (15) 7 (9) 3 (6) 30
At Through 30 (50) 40 (30) 30 (20) 100Rising 20 (15) 8 (9) 2 (6) 30Falling 30 (20) 5 (12) 5 (8) 40Total 100 60 40 200
Economy Weekly Chip SalesHigh Medium Low Total
At peak 1.67 0.44 1.50 30At Through 8.00 3.33 5.00 100Rising 1.67 0.11 2.67 30Falling 5.00 4.08 1.13 40Total 100 60 40 200
Step 4: Find the critical Chi-SquareStep 4: Find the critical Chi-Square
Review:
Chapter 9: Testing Hypotheses: Two-Sample Tests
~Basics~Independent
Sample Test~Large
Samples~Small
Samples~Dependent
Sample Test
~Differences between Proportions
~Two-tailed Test
~One-tailed Test
Chapter 11: Chi-Square
~Basics~Contingency
Table 2-row~Contingency
Table 3-row
Table of Contents
Review:Chapter 8 Testing Hypothesis
Chapter 9: Testing Hypotheses: Two-Sample Tests~Basics~Independent Sample Test
~Large Samples~Small Samples
~Dependent Sample Test
~Differences between Proportions~Two-tailed Test~One-tailed Test
Chapter 11: Chi-Square ~Basics~Contingency Table 2-row~Contingency Table 3-row
The Normal DistributionSPSS Tips
The data can be downloaded from:
Blackboard – Inductive Statsitics STA2—SPSS--Week 6 Chi-Square.sav
The Normal DistributionSPSS TipsAPPLE shop in Groningen wants to know whether our IBS students have an intention to buy an iPad and whether their interest depends on their nationalities. They have interviewed 64 Year TWO students and the data can be downloaded from Blackboard—STA2—SPSS –Chi square.sav.
The Normal DistributionSPSS TipsStep 1: Analyze Descriptive Statistics Crosstabs…
Step 1: Analyze Descriptive Statistics Crosstabs…
The Normal DistributionSPSS Tips
Step 2: Move the variable to “Rows” and “Columns” respectively.
Click on “Statistics” and choose: Chi-square.
Step 2: Move the variable to “Rows” and “Columns” respectively.
Click on “Statistics” and choose: Chi-square.
The Normal DistributionSPSS Tips Step 3:Click on “Cells” and choose: Observed and Expected.
Step 3:Click on “Cells” and choose: Observed and Expected.
The Normal DistributionSPSS Tips
Now you get the output!But how to interpret it?Now you get the output!But how to interpret it?
The Normal DistributionSPSS Tips
• In our example, the cross break table (Table 1) has shown the observed and expected values of the frequency concerning those who are willing to buy an iPad.
Table 1: Nationality and Intention to buy an iPad
The Normal DistributionSPSS Tips
Now you get the output!But how to interpret it?Now you get the output!But how to interpret it?
importantimportant
The Normal DistributionSPSS Tips
• We can reject at the .05 level the null hypothesis that population proportions are equal across the three categories, X2(3, N =64) = 0.645, p=.886.
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