k sample problems and non-parametric tests. two-sample t-test (unpaired)

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)