3/10/2011

1

Lecture 10

Chi-Square Tests

Hypothesis Test

Two Population

Hypothesis Test

More than

Two Populations

Sample

Independent Sample

dependent

c MEANSc Proportions

Check the

conditions

If yes

Levene’s test

Equal Variance unequal Variance

STOP

Chi-square

Test

Non-parametric test

One-Way ANOVA

Post-hoc

(SPSS output)

ANOVA with SPSS

To perform ANOVA

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3/10/2011

2

Select “Post Hoc”

to perform “Multiple Comparisons-

Tukey Procedure

Select “Tukey”

Click continue

Click “OK” ANOVA

Breaking Strength

Sumof

Mean

SPSS OUTPUT

Sum

of

Squares df

Mean

Square FSig.

Between

Groups 329.389 2 164.694 11.366 .000

Within

Groups 478.167 33 14.490

Total807.556 35

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3/10/2011

3

Multiple Comparisons

Dependent Variable: Breaking Strength

Tukey HSD

(I) Machines (J) Machines

Mean

Differen

ce (I-J)

Std. Error Sig.

95% Confidence Interval

Lower Bound Upper Bound

1.00 2.00 7.333(*) 1.554 .000 3.52 11.15

3.00 4.583

(

*

)

1.554 .016 .77 8.40

()

2.00 1.00 -

7.333(*) 1.554 .000 -11.15 -3.52

3.00 -2.750 1.554 .195 -6.56 1.06

3.00 1.00 -

4.583(*) 1.554 .016 -8.40 -.77

2.00 2.750 1.554 .195 -1.06 6.56

* The mean difference is significant at the .05 level.

Breaking Strength

Tukey HSD

Machines N

Subset for alpha = .05

12

2.00 12 105.75

3.00 12 108.50

1.00 12 113.08

Sig. .195 1.000

Means for groups in homogeneous subsets are displayed.

a Uses Harmonic Mean Sample Size = 12.000.

Multiple Comparisons

Dependent Variable: Breaking Strength

Tukey HSD

(I) Machines (J) Machines

Mean

Differen

ce (I-J)

Std. Error Sig.

95% Confidence Interval

Lower Bound Upper Bound

1.00 2.00 7.333(*) 1.554 .000 3.52 11.15

3.00 4.583

(

*

)

1.554 .016 .77 8.40

How do we change the

Labelling?

()

2.00 1.00 -

7.333(*) 1.554 .000 -11.15 -3.52

3.00 -2.750 1.554 .195 -6.56 1.06

3.00 1.00 -

4.583(*) 1.554 .016 -8.40 -.77

2.00 2.750 1.554 .195 -1.06 6.56

* The mean difference is significant at the .05 level.

Select “values”

Go to “variable view”

Hypothesis Test

Two Population

Hypothesis Test

More than

Two Populations

Sample

Independent Sample

dependent

c MEANSc Proportions

Check the

conditions

If yes

Levene’s test

Equal Variance unequal Variance

STOP

Chi-square

Test

Non-parametric test

One-Way ANOVA

Post-hoc

(SPSS output)

Chi-Square Tests

A. Goodness-of-fit Tests

B. Contingency Analysis

1. 2 x 2 Contingency table

2. 2 x c contingency table: Chi-Square Test

for the Differences Among More Than

Two Proportions.

3. r x c contingency table: Chi-Square Test

of Independence

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