Tables and Non Parametric Tests

Tables and Non Parametric Tests

Lecture 5

Compare Means Menu

Compare Means OutputGroup Statistics

10 2,40 1,275 ,403

10 2,85 1,247 ,394

Group1

2

ObservationN Mean Std. Deviation

Std. ErrorMean

Independent Samples Test

,004 ,949 -,793 18 ,438 -,447 ,564 -1,632 ,738

-,793 17,991 ,438 -,447 ,564 -1,632 ,738

Equal variancesassumed

Equal variancesnot assumed

ObservationF Sig.

Levene's Test forEquality of Variances

t df Sig. (2-tailed)Mean

DifferenceStd. ErrorDifference Lower Upper

95% ConfidenceInterval of the

Difference

t-test for Equality of Means

”Service package””Service package”

”Important package””Important package”

Non-normal Data

0 5 10 15

Observed Value

0

3

6

9

12

15

Exp

ect

ed

No

rmal

Va

lue

Normal Q-Q Plot of Not Normal

-10 0 10 20

Observed Value

-10

0

10

20

Ex

pe

cte

d N

orm

al V

alu

e

Normal Q-Q Plot of Not Normal Either

Log-normal dataLog-normal data

Transform DataTransform Data

Compare the means of the transformed (normal) data

Compare the means of the transformed (normal) data

Binomial dataBinomial data

Really non-normal data

Really non-normal data

Binomial Data

Are the proportions of Turks in Aalborg and Århus the same?

Non-Turks

Turks

Aalborg 465 35

Århus 358 42

Are the proportions significantly different?

Non-Turks

Turks

Aalborg 465 35

Århus 358 42

7.0%7.0%

10.5%10.5%

Compare 3.5% (= 10.5 – 7.0%)

with suitable SE.

Compare 3.5% (= 10.5 – 7.0%)

with suitable SE.

Another Approach

Non-Turks

Turks

Aalborg 465 35

Århus 358 42

Non-Turks

Turks

Aalborg 457 43

Århus 366 34

ObservedObserved ExpectedExpected

In total 77 turks in a 900 sample, i.e. 8.6%

In total 77 turks in a 900 sample, i.e. 8.6%

We expect 34 turks in

Århus (8.6% of 400) We expect 34 turks in

Århus (8.6% of 400)

Same proportion in Aalborg and Århus?

Non-Turks

Turks

Aalborg 465 35

Århus 358 42

Non-Turks

Turks

Aalborg 457 43

Århus 366 34

ObservedObserved ExpectedExpected

Observed and expected should be

close

Observed and expected should be

close

How to do it in SPSS

…or data could be organized in 900 rows

…or data could be organized in 900 rows

Cross-Tabs

City * Etnicity Crosstabulation

Count

465 35 500

358 42 400

823 77 900

Aalborg

Århus

City

Total

Non-Turk Turk

Etnicity

Total

Tricks

City * Etnicity Crosstabulation

465 35 500

457,2 42,8 500,0

93,0% 7,0% 100,0%

358 42 400

365,8 34,2 400,0

89,5% 10,5% 100,0%

823 77 900

823,0 77,0 900,0

91,4% 8,6% 100,0%

Count

Expected Count

% within City

Count

Expected Count

% within City

Count

Expected Count

% within City

Aalborg

Århus

City

Total

Non-Turk Turk

Etnicity

Total

Output

Chi-Square Tests

3,480b 1 ,062

3,047 1 ,081

3,454 1 ,063

,072 ,041

3,476 1 ,062

900

Pearson Chi-Square

Continuity Correctiona

Likelihood Ratio

Fisher's Exact Test

Linear-by-LinearAssociation

N of Valid Cases

Value dfAsymp. Sig.

(2-sided)Exact Sig.(2-sided)

Exact Sig.(1-sided)

Computed only for a 2x2 tablea.

0 cells (,0%) have expected count less than 5. The minimum expected count is34,22.

b.

Expected values

Expected values

ProportionsProportions

P-valueP-value

Test Statistic

Test Statistic

Binomial

One-SampleOne-Sample Two-SampleTwo-Sample K-SampleK-Sample

Is proportion equal to 10%

Proportions in Aalborg and

Århus are equal

Proportions in Aalborg, Randers, Vester Hjermislev

and Århus are equal

Cross-Tabs handles two or

more cities (categories)

Cross-Tabs handles two or

more cities (categories)

1. Calculate proportion and 95% CI

2. Is 10% in the CI?

1. Calculate proportion and 95% CI

2. Is 10% in the CI?

…or use SPSS as I will show

later

…or use SPSS as I will show

later

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

OutputDescriptive 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 ”Service package””Service package”

”Interesting package”

”Interesting package”

”Important package””Important package”

One-Sample (Symmetry or Location)

Kiama Blowhole Data

• Highly skew distribution

• Average approx 40 sec

• Rarely above 100 sec

Median equal to 40 sec?

Only above 100 sec in 1% of the eruptions?

Normal distributed ?

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.

One-Sample Kolmogorov-Smirnov Test 2

64

7

169

,464

,464

-,016

3,708

,000

N

Minimum

Maximum

Uniform Parametersa,b

Absolute

Positive

Negative

Most ExtremeDifferences

Kolmogorov-Smirnov Z

Asymp. Sig. (2-tailed)

TimeintervalbetweenKiama

Blowholeeruptions

Test distribution is Uniform.a.

Calculated from data.b.

Data are

Not Normal

Not Uniform

But QQ-plots are better!!

But QQ-plots are better!!

Location of medianMedian equal to 40

sec?

Only above 100 sec in 1% of the eruptions?

Median equal to 40 sec?

Output

Descriptive Statistics

64 39,83 33,751 7 169 14,25 28,00 60,00Timeintervalbetween KiamaBlowhole eruptions

N Mean Std. Deviation Minimum Maximum 25th 50th (Median) 75th

Percentiles

NPar Tests

Binomial Test

<= 40 41 ,64 ,50 ,033a

> 40 23 ,36

64 1,00

Group 1

Group 2

Total

Timeintervalbetween KiamaBlowhole eruptions

Category NObserved

Prop. Test Prop.Asymp. Sig.

(2-tailed)

Based on Z Approximation.a.

NOPE!Median equal to 40 sec?

Only above 100 sec in 1% of the eruptions?

Binomial Test

<= 100 62 ,97 ,01 ,000a

> 100 2 ,03

64 1,00

Group 1

Group 2

Total

Timeintervalbetween KiamaBlowhole eruptions

Category NObserved

Prop. Test Prop.Asymp. Sig.

(1-tailed)

Based on Z Approximation.a.

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.

”Important package””Important package”

”Service package””Service package”

Overview (normal samples)

One sampleOne sample

Two samples (paired)Two samples (paired)

K samplesK samples

Two samples (unpaired)Two samples (unpaired)

Overview (binomial 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)