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5/21/2016 1 www.utm.my innovative entrepreneurial global Non Parametric 1 www.utm.my innovative entrepreneurial global Goal Parametric Non parametric Describe one group Mean, SD Median, interquartile range Compare one group to a hypothetical value One-sample t-test Wilcoxon test Compare two unpaired groups Unpaired t test Mann-Whitney test Compare two paired groups Paired t test Wilcoxon test Compare three or more unmatched groups One-way ANOVA Kruskal-Wallis test Compare three or more matched groups Repeated-measures ANOVA Friedman test Quantify association between two variables Pearson correlation Spearman correlation 2 www.utm.my innovative entrepreneurial global 3 Chi-square Test

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Page 1: 1 Non Parametric - Universiti Teknologi Malaysia€¦ · Compare two paired groups Paired t test Wilcoxon test Compare three or more unmatched groups One-way ANOVA Kruskal-Wallis

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Non Parametric 1

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Goal Parametric Non parametric

Describe one group Mean, SD Median, interquartile

range

Compare one group to a hypothetical value

One-sample t-test Wilcoxon test

Compare two unpaired groups Unpaired t test Mann-Whitney test

Compare two paired groups Paired t test Wilcoxon test

Compare three or more unmatched groups

One-way ANOVA Kruskal-Wallis test

Compare three or more matched groups

Repeated-measures ANOVA Friedman test

Quantify association between two variables

Pearson correlation Spearman correlation

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Chi-square Test

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Nonparametric Tests

Non-parametric hypothesis tests (distribution free test) using the chi-square statistic:

1. the chi-square test for goodness of fit

2. the chi-square test for independence.

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Nonparametric Tests 5

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The Chi-Square Test for Goodness-of-Fit

• The chi-square test for goodness-of-fit uses frequency data from a sample to test hypotheses about the shape or proportions of a population.

• The data, called observed frequencies, simply count how many individuals from the sample are in each category. (eg. How many choose Likert scale no. 4)

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• The null hypothesis specifies the proportion of the population that should be in each category.

• The proportions from the null hypothesis are used to compute expected frequencies that describe how the sample would appear if it were in perfect agreement with the null hypothesis.

The Chi-Square Test for Goodness-of-Fit 7

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How to compare?

8

21

12

3

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Nominal Data 9

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EXAMPLE- Goodness-of-Fit

YES NO

GROUP A 16 34

GROUP B 7 43

Dependent variables

Independent variables

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Example- Goodness-of-Fit

Lake view Sea view River view Town view

18 17 7 8

A survey of 50 respondent to choose preferable view of their future houses.

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Goodness-of-Fit

1. State the hypothesis

Ho: No preference for any specific view

H1: One or more specific view is preferred

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Goodness-of-Fit

1. State the hypothesis

Ho: No preference for any specific view

H1: One or more specific view is preferred

Lake view Sea view River view Town view

25% 25% 25% 25%

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Goodness-of-Fit

Lake view

Sea view

River view

Town view

Observed frequency 18 17 7 8

Expected frequency 12.5 12.5 12.5 12.5

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Goodness-of-Fit

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Goodness-of-Fit

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Goodness-of-Fit

4. Make decision Reject hypothesis Null

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CHI SQUARE

Goodness-of-Fit

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Lake view Sea view River view Town view

18 17 7 8

Data Structure On Spss

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SPSS Output

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Decision

The respondent showed significant

preference among the four views.

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The Chi-Square Test for Independence

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The Chi-Square Test for Independence

The second chi-square test, the chi-square test for independence, can be used and interpreted in two different ways:

a) Testing hypotheses about the relationship between two variables in a population, or

b) Testing hypotheses about differences between proportions for two or more populations.

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A frequency distribution showing willingness to use mental health service according to gender for a sample of 150

Willingness to use Mental Health Service

Probably No Maybe Probably yes

Male 17 32 11

Female 13 43 34

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Ho : In the general population, there is no

relationship between gender and

willingness to use mental health service.

The Chi-Square Test for Independence Version 1:

Ho : In the general population, the distribution of reported willingness to use

mental health service is the same for male and female.

Version 2

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A frequency distribution showing willingness to use mental health service according to gender for a sample of 150

Willingness to use Mental Health Service

Probably No Maybe Probably yes

Male 17 32 11 60

Female 13 43 34 90

30 75 45 N=150

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Willingness to use Mental Health Service

Probably No Maybe Probably yes

Male 17 (12) 32 (30) 11 (18) 60

Female 13 (18) 43 (45) 34 (27) 90

30 75 45 N=150

20% 50% 30%

=30/150*100

=75/150*100

=30% from 90 =45/150*100 =30% from 60

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Willingness to use Mental Health Service

Probably No Maybe Probably yes

Male 17 (12) 32 (30) 11 (18) 60

Female 13 (18) 43 (45) 34 (27) 90

30 75 45 N=150

20% 50% 30%

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The Chi-Square Test for Independence

Ho : In the general population, there is no

relationship between gender and

willingness to use mental health service.

H1: In the general population, there is a consistent predictable relationship between gender and willingness to use mental model service.

Version 1:

1

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Compute

2

R=Row C=Column

= (2-1)(3-1)

3

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Reject H0

Or

There is a significant relationship

between gender and willingness to use

mental model service.

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Table 5.99 Calculation

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SPSS

CHI SQUARE

for Independence

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SPSS

Willingness to use Mental Health Service

Probably No Maybe Probably yes

Male 17 32 11

Female 13 43 34

1 2 3

1

2

1 1 17

1 2 32

1 3 11

2 1 13

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SPSS

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Statistical Tests for Ordinal Data

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Tests for Ordinal Data

• B4 this four statistical techniques that have been developed specifically for use with ordinal data; that is, data where the measurement procedure simply arranges the subjects into a rank-ordered sequence.

• The statistical methods presented in this chapter can be used when the original data consist of ordinal measurements (ranks), or when the original data come from an interval or ratio scale but are converted to ranks because they do not satisfy the assumptions of a standard parametric test such as the t statistic.

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Tests for Ordinal Data (cont.)

Four statistical methods are introduced:

1. The Mann-Whitney test

2. The Wilcoxon test.

3. The Kruskal-Wallis test

4. The Friedman test.

Goal Parametric Non parametric

Compare one group to a hypothetical value One-sample t-test Wilcoxon test

Compare two unpaired groups Unpaired t test Mann-Whitney test

Compare two paired groups Paired t test Wilcoxon test

Compare three or more unmatched groups One-way ANOVA Kruskal-Wallis test

Compare three or more matched groups Repeated-measures ANOVA

Friedman test

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Tests for Ordinal Data (cont.)

???

The Wilcoxon test

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Tests for Ordinal Data (cont.)

Test evaluates the difference between two treatments or two populations using data from an independent-measures design; that is, two separate samples.

The Mann-Whitney test

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Tests for Ordinal Data (cont.)

Test evaluates the difference between two treatment conditions using data from a repeated-measures design; that is, the same sample is tested/measured in both treatment conditions.

The Wilcoxon test

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Tests for Ordinal Data (cont.)

Test evaluates the differences between three or more treatments for studies using the same group of participants in all treatments (a repeated-measures study).

The Friedman test

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Tests for Ordinal Data (cont.)

The Kruskal-Wallis test evaluates the differences between three or more treatments (or populations) using a separate sample for each treatment condition.

The Kruskal-Wallis test

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The Kruskal-Wallis Test

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The Kruskal-Wallis Test

• The Kruskal-Wallis test can be viewed as an alternative to a single-factor, independent-measures analysis of variance ANOVA.

• The test uses data from three or more separate samples to evaluate differences among three or more treatment conditions.

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The Kruskal-Wallis Test (cont.)

• The test requires that you are able to rank order the individuals but does not require numerical scores.

• The null hypothesis for the Kruskal-Wallis test simply states that there are no systematic or consistent differences among the treatments being compared.

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• Ho: There is no tendency for the rank in any treatment condition to be systematically higher or lower than the ranks in any other treatment condition. There are no differences among the three treatment.

• H1: The rank in at least one treatment condition are systematically higher (or lower) than the ranks in another condition. There are differences among the treatment.

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TREATMENTS

X Y Z

8 1 11 2 7 5 4 6 9

10 3 12 14 13 15

Data collected after three treatments independently and were ranked as bellow

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TREATMENTS

X Y Z

8 1 11 N=15

2 7 5 4 6 9

10 3 12 14 13 15

T1 =38 T2 =30 T3 =52

n1 =5 n2 =5 n3 =5

Data collected after three treatments independently and were ranked as bellow

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Compute

2

3

Locate the critical region

1 Hypothesis?

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Table 5.99

Calculation 2.48

4 Fail Reject H0

Or

There is NO significant relationship

between three treatments group.

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conclusion

• The H value for these data is not in the critical region. Therefore, we fail to reject Ho and conclude that the data are not sufficient to show any significant differences among the three treatment.

4

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GROUP

A B C

14 2 26 3 14 8

21 9 14 5 12 19

16 5 20

Example: Original DATA NUMERIC Score 60

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Original Numeric Score Ordinal Rank

2 1 1 3 2 2

5 3 3.5

5 4 3.5 8 5 5 9 6 6

12 7 7

14 8 9

14 9 9 14 10 9 16 11 11 19 12 12

20 13 13

21 14 14 26 15 15

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Original DATA NUMERIC Score

Rank Data

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GROUP

A B C

9 1 15 N=15

2 9 5 14 6 9 3.5 7 12 11 3.5 13

T1 =39.5 T2 =26.5 T3 =54

n1 =5 n2 =5 n3 =5

Data collected after three treatments independently and were ranked as bellow

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conclusion

The H value for these data is not in the critical region. Therefore, we fail to reject Ho and

conclude that the data are not sufficient to show any significant differences among the

three treatment.

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