1 non parametric - universiti teknologi malaysia€¦ · compare two paired groups paired t test...
TRANSCRIPT
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
5/21/2016
2
www.utm.my innovative ● entrepreneurial ● global
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.
4
www.utm.my innovative ● entrepreneurial ● global
Nonparametric Tests 5
www.utm.my innovative ● entrepreneurial ● global
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)
6
5/21/2016
3
www.utm.my innovative ● entrepreneurial ● global
• 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
www.utm.my innovative ● entrepreneurial ● global
How to compare?
8
21
12
3
4
www.utm.my innovative ● entrepreneurial ● global
Nominal Data 9
5/21/2016
4
www.utm.my innovative ● entrepreneurial ● global
EXAMPLE- Goodness-of-Fit
YES NO
GROUP A 16 34
GROUP B 7 43
Dependent variables
Independent variables
10
www.utm.my innovative ● entrepreneurial ● global
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.
11
www.utm.my innovative ● entrepreneurial ● global
Goodness-of-Fit
1. State the hypothesis
Ho: No preference for any specific view
H1: One or more specific view is preferred
12
5/21/2016
5
www.utm.my innovative ● entrepreneurial ● global
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%
13
www.utm.my innovative ● entrepreneurial ● global
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
14
www.utm.my innovative ● entrepreneurial ● global
Goodness-of-Fit
15
5/21/2016
6
www.utm.my innovative ● entrepreneurial ● global
Goodness-of-Fit
16
www.utm.my innovative ● entrepreneurial ● global
Goodness-of-Fit
4. Make decision Reject hypothesis Null
17
www.utm.my innovative ● entrepreneurial ● global
CHI SQUARE
Goodness-of-Fit
18
5/21/2016
7
www.utm.my innovative ● entrepreneurial ● global
19
Lake view Sea view River view Town view
18 17 7 8
Data Structure On Spss
www.utm.my innovative ● entrepreneurial ● global
20
www.utm.my innovative ● entrepreneurial ● global
21
5/21/2016
8
www.utm.my innovative ● entrepreneurial ● global
22
www.utm.my innovative ● entrepreneurial ● global
SPSS Output
23
www.utm.my innovative ● entrepreneurial ● global
Decision
The respondent showed significant
preference among the four views.
24
5/21/2016
9
www.utm.my innovative ● entrepreneurial ● global
25
The Chi-Square Test for Independence
www.utm.my innovative ● entrepreneurial ● global
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.
26
www.utm.my innovative ● entrepreneurial ● global
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
27
5/21/2016
10
www.utm.my innovative ● entrepreneurial ● global
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
28
www.utm.my innovative ● entrepreneurial ● global
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
29
www.utm.my innovative ● entrepreneurial ● global
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
30
5/21/2016
11
www.utm.my innovative ● entrepreneurial ● global
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%
31
www.utm.my innovative ● entrepreneurial ● global
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
32
www.utm.my innovative ● entrepreneurial ● global
Compute
2
R=Row C=Column
= (2-1)(3-1)
3
33
5/21/2016
12
www.utm.my innovative ● entrepreneurial ● global
34
Reject H0
Or
There is a significant relationship
between gender and willingness to use
mental model service.
4
Table 5.99 Calculation
8.23
www.utm.my innovative ● entrepreneurial ● global
SPSS
CHI SQUARE
for Independence
35
www.utm.my innovative ● entrepreneurial ● global
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
…
36
5/21/2016
13
www.utm.my innovative ● entrepreneurial ● global
SPSS
37
www.utm.my innovative ● entrepreneurial ● global
38
www.utm.my innovative ● entrepreneurial ● global
39
5/21/2016
14
www.utm.my innovative ● entrepreneurial ● global
40
www.utm.my innovative ● entrepreneurial ● global
41
www.utm.my innovative ● entrepreneurial ● global
42
5/21/2016
15
www.utm.my innovative ● entrepreneurial ● global
Statistical Tests for Ordinal Data
43
www.utm.my innovative ● entrepreneurial ● global
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.
44
www.utm.my innovative ● entrepreneurial ● global
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
45
5/21/2016
16
www.utm.my innovative ● entrepreneurial ● global
Tests for Ordinal Data (cont.)
???
The Wilcoxon test
46
www.utm.my innovative ● entrepreneurial ● global
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
47
www.utm.my innovative ● entrepreneurial ● global
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
48
5/21/2016
17
www.utm.my innovative ● entrepreneurial ● global
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
49
www.utm.my innovative ● entrepreneurial ● global
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
50
www.utm.my innovative ● entrepreneurial ● global
The Kruskal-Wallis Test
51
5/21/2016
18
www.utm.my innovative ● entrepreneurial ● global
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.
52
www.utm.my innovative ● entrepreneurial ● global
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.
53
www.utm.my innovative ● entrepreneurial ● global
• 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.
54
5/21/2016
19
www.utm.my innovative ● entrepreneurial ● global
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
55
www.utm.my innovative ● entrepreneurial ● global
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
56
www.utm.my innovative ● entrepreneurial ● global
Compute
2
3
Locate the critical region
1 Hypothesis?
57
5/21/2016
20
www.utm.my innovative ● entrepreneurial ● global
58
Table 5.99
Calculation 2.48
4 Fail Reject H0
Or
There is NO significant relationship
between three treatments group.
www.utm.my innovative ● entrepreneurial ● global
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
59
www.utm.my innovative ● entrepreneurial ● global
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
5/21/2016
21
www.utm.my innovative ● entrepreneurial ● global
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
61
www.utm.my innovative ● entrepreneurial ● global
62
Original DATA NUMERIC Score
Rank Data
www.utm.my innovative ● entrepreneurial ● global
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
63
5/21/2016
22
www.utm.my innovative ● entrepreneurial ● global
64
www.utm.my innovative ● entrepreneurial ● global
65
www.utm.my innovative ● entrepreneurial ● global
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.
66
5/21/2016
23
www.utm.my innovative ● entrepreneurial ● global
67