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K sample problemsand non-parametric tests
K sample problemsand non-parametric tests
Two-Sample T-test (unpaired)
K-Sample
Equal variances?
If NOT!!!
K-Sample Output Descriptives
Embarasing Measurement
10 4,0100 1,69801 ,53696 2,7953 5,2247 1,10 6,50
10 5,4900 1,10599 ,34975 4,6988 6,2812 3,70 7,30
20 4,7500 1,58795 ,35508 4,0068 5,4932 1,10 7,30
Before
After
Total
N Mean Std. Deviation Std. Error Lower Bound Upper Bound
95% Confidence Interval forMean
Minimum Maximum
Test of Homogeneity of Variances
Embarasing Measurement
1,597 1 18 ,222
LeveneStatistic df1 df2 Sig.
ANOVA
Embarasing Measurement
10,952 1 10,952 5,334 ,033
36,958 18 2,053
47,910 19
Between Groups
Within Groups
Total
Sum ofSquares df Mean Square F Sig.
P-value
A Small Trick (Post Hoc)
Warnings
Post hoc tests are not performed for Embarasing Measurement because there arefewer than three groups.
OK OK, I’ll use another data set
1 2 3
Specno
9
10
11
12
13
14
15
95%
CI A
ng
le
Multiple Comparisons
Dependent Variable: Angle
Bonferroni
-,195 ,285 1,000 -,89 ,50
4,004* ,307 ,000 3,25 4,76
,195 ,285 1,000 -,50 ,89
4,199* ,281 ,000 3,51 4,89
-4,004* ,307 ,000 -4,76 -3,25
-4,199* ,281 ,000 -4,89 -3,51
(J) Specno2
3
1
3
1
2
(I) Specno1
2
3
MeanDifference
(I-J) Std. Error Sig. Lower Bound Upper Bound
95% Confidence Interval
The mean difference is significant at the .05 level.*.
Normal data?
• How do I check the assumption of normality?
• You already know Q-Q plots
• Kolmogorov-Smirnov (K-S) test
Normal distributed?
OutputOne-Sample Kolmogorov-Smirnov Test
64
39,83
33,751
,173
,173
-,165
1,382
,044
N
Mean
Std. Deviation
Normal Parameters a,b
Absolute
Positive
Negative
Most ExtremeDifferences
Kolmogorov-Smirnov Z
Asymp. Sig. (2-tailed)
TimeintervalbetweenKiama
Blowholeeruptions
Test distribution is Normal.a.
Calculated from data.b.
Data are
not normal
But QQ-plots are better!!
But QQ-plots are better!!
Non-Normal Data
1,00 1,50 2,00 2,50 3,00 3,50 4,00 4,50 5,00
0 5 10 15 20
Observations
Ranks
Statistics on Ranks
Rank
1 4
2 6
3 7
5 10
8 12
9 13
11 16
14 17
15 19
18 20
Mean Ranks should be close
if the two distributions are located similarly
Mean Ranks should be close
if the two distributions are located similarly
8.6 12.4
How to do it in SPSS
Output
Descriptive Statistics
210 3,2366 1,11176 1,10 4,50 2,0000 3,6000 4,2000
210 1,59 ,493 1 2 1,00 2,00 2,00
Observation
City
N Mean Std. Deviation Minimum Maximum 25th 50th (Median) 75th
Percentiles
Ranks
86 93,31 8025,00
124 113,95 14130,00
210
CityAalborg
Århus
Total
ObservationN Mean Rank Sum of Ranks
Test Statisticsa
4284,000
8025,000
-2,426
,015
Mann-Whitney U
Wilcoxon W
Z
Asymp. Sig. (2-tailed)
Observation
Grouping Variable: Citya.
Mann-Whitney Test
K-samples test
Output
Ranks
86 85,87
124 119,11
115 268,00
325
CityAalborg
Århus
Randers
Total
NumberN Mean Rank
Kruskal-Wallis Test
Test Statisticsa,b
229,298
2
,000
Chi-Square
df
Asymp. Sig.
Number
Kruskal Wallis Testa.
Grouping Variable: Cityb.
Overview (normal samples)
One sampleOne sample
Two samples (paired)Two samples (paired)
K samplesK samples
Two samples (unpaired)Two samples (unpaired)
Overview (non normal samples)
One sampleOne sample
Two samples (paired)Two samples (paired)
K samplesK samples
Two samples (unpaired)Two samples (unpaired)
