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Stata 2, Bivariate

Hein Stigum

Presentation, data and programs at:

http://folk.uio.no/heins/

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Datatypes

• Categorical data– Nominal: married/ single/ divorced– Ordinal: small/ medium/ large

• Numerical data– Discrete: number of children– Continuous: weight

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Data type

Normal data

MeansT-testLinear regression

MediansNon-par tests

Freq tableCross, ChisquareLogistic regression

CategoricalNumerical

Yes No

Data type dictates type of analysis

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Continuous symmetric outcome

Example:

Birth weight

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Distribution0

.000

2.0

004

.000

6.0

008

Den

sity

0 2000 4000 6000weight

0.0

002

.000

4.0

006

.000

8D

ensi

ty2000 3000 4000 5000 6000

weight

kdensity weight drop if weight<2000kdensity weight

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Central tendency and dispersion

Mean and standard deviation:

Mean with confidence interval:

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Compare groups, equal variance?• Equal • Not equal

2 0 2 4 2 0 2 4

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2 independent samples

Are birth weights the same for boys and girls?

2000 3000 4000 5000 6000Birth weight

2000

3000

4000

5000

6000

Birt

h w

eigh

t

Boys Girlssex

Scatterplot Density plot

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2 independent samples test

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K independent samples

• Is birth weight the same over parity?

Scatterplot Density plot

2000

3000

4000

5000

6000

Birt

h w

eigh

t

0 1 2-7Parity

2000 3000 4000 5000 6000Birth weight, g

012+

Equal means? Linear effect?Outliers?

Equal variances?

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K independent samples test

equal means?

Equal variances?

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Continuous by continuous • Does birth weight depend on gestational age?

Scatterplot Scatterplot, outlier dropped

2000

3000

4000

5000

6000

Birt

h w

eigh

t

200 300 400 500 600 700Gestational age

2000

3000

4000

5000

Birt

h w

eigh

t

200 220 240 260 280 300Gestational age

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Continuous by continuous tests

• Cut gestational age up in groups, then use T-test or ANOVA

or

• Use linear regression with 1 covariate

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Test situations

• 2 independent samples• ttest weight, by(sex)

• K independent samples• oneway weight parity

• By continuous• regress weight gestAge

• 2 dependent samples (Paired)• ttest weight_last_year = weight_today

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Continuous skewed outcome

Example:

Number of sexual partners

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Distributionkdensity partners if partners<=50

25%50% 75% 95%0.0

2.0

4.0

6.0

8.1

11 4 9 20 50Partners

N=394

Distribution of number of lifetime partners

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Central tendency and dispersion

Median and percentiles:

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2 independent samplesDo males and females have the same number of partners?

Scatterplot Density plot

0 10 20 30 40 50partners

050

100

150

200

Par

tner

s

Males FemalesGender

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2 independent samples test

equal medians?

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20

050

100

150

200

Par

tner

s

18-29 30-44 45-60agegr3

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K independent samplesDo partners vary with age?

Scatterplot (partners<20) Density plot (partners<20)

0 5 10 15 20Partners

Age:18-2930-4445-60

05

1015

20P

artn

ers

18-29 30-44 45-60agegr3

Scatterplot

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K independent samples test

equal medians?

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Table of tests

ProportionsNormal Skewed

1 sample One sample T-test Kolmogorov-Smirnov Binomial2 independent samples Independent sample T-test Mann-Whitney U Chi-squareK independent samples ANOVA Kruskal-Wallis Chi-square2 dependent samples Paired sample T-test Wilcoxon signed rank test Mc-Nemar (2x2)

Numerical data

Categorical ordered: use nonparametric tests

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Categorical data

Example:

Being bullied

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Frequency and proportionFrequency:

Proportion with CI:

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Proportion, confidence interval

proportion:

standard error:

confidence interval:

nxp x=”disease”

n=total number

)(2)(

)1()(

pseppCI

npppse

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Crosstables

equal proportions?

Are boys bullied as much as girls?

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Ordered categories, trend

.1.1

5.2

.25

Pro

porti

on b

ullie

d

2-6 y 7-12 y 13-17 yAge group

Does bullied vary with age?twoway (fpfitci bullied agegr) ///

(lfit bullied agegr)

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Ordered categories, trend

Trend?

equal proportions?

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Table of tests

ProportionsNormal Skewed

1 sample One sample T-test Kolmogorov-Smirnov Binomial2 independent samples Independent sample T-test Mann-Whitney U Chi-squareK independent samples ANOVA Kruskal-Wallis Chi-square2 dependent samples Paired sample T-test Wilcoxon signed rank test Mc-Nemar (2x2)

Numerical data

Categorical ordered: use nonparametric tests