Tables and Non Parametric Tests

Tables and Non Parametric Tests

Lecture 5

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 proprotion 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

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 ?

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.