1. Presentation, data and programs at:
Stata 2, Bivariate
Hein Stigum
Presentation, data and programs at:
Timing:
Intro and continuous symmetrical: min
Skewed, categorical and regression (not survival): 60 min 8:30-9:30
Groups min 9:30-10:45
Plenary min 10:45.11:30
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2. Datatypes Categorical data Numerical data
Nominal: married/ single/ divorced
Ordinal: small/ medium/ large
Numerical data
Discrete: number of children
Continuous: weight
Coding 1, 2, 3, is 2 twice as much as 1
1. Set of methods for categorical data
proportion married
1. Set of methods for numerical data
average weight
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3. Data type dictates type of analysis
Start with continuous data
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4. Continuous symmetric outcome
Example:
Birth weight
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5. Distribution kdensity weight drop if weight<2000 kdensity weight
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6. Central tendency and dispersion
Mean and standard deviation:
Mean with confidence interval:
Std Dev for Data
Std Err for Estimate
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7. Compare groups, equal variance?
Not equal
Compare boys and girls
Fokus om means or fokus on low tail gives opposite results!!
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8. 2 independent samples Are birth weights the same for boys and girls?
Density plot
Scatterplot
Scatter to see linear/no-linear effect, look for outliers
Density to see equal variance
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9. 2 independent samples test
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10. K independent samples Is birth weight the same over parity?
Density plot
Scatterplot
Scatter to see linear/no-linear effect, look for outliers
Density to see equal variance
Equal means? Linear effect?
Outliers?
Equal variances?
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11. K independent samples test
equal means?
Equal variances?
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12. Continuous by continuous
Does birth weight depend on gestational age?
Scatterplot
Scatterplot, outlier dropped
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13. 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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14. Test situations 2 independent samples K 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
1: ttest weight=10
4: ttest weight0=weight1 (assumes paired test)
Equal/unequal
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15. Continuous skewed outcome
Example:
Number of sexual partners
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16. Distribution kdensity partners if partners<=50 Dec-18 Dec-18 H.S.
Lower 75% fractile here than on next page because partner>50 are dropped here
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17. Central tendency and dispersion
Median and percentiles:
cci binomial exact; conservative confidence interval
normal normal, based on observed centiles
meansd normal, based on mean and standard deviation
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18. 2 independent samples
Do males and females have the same number of partners?
Scatterplot
Density plot
Scatter to see linear/no-linear effect, look for outliers
Density to see equal variance
Unequal variance! Test somewhat problematic
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19. 2 independent samples test
equal medians?
Could also use T-test since the “difference in means” is probably normal from 400 observations, even thou the underlying distribution are quite skewed.
T-test gives p=0.0000
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20. K independent samples Do partners vary with age? Scatterplot
Scatterplot (partners<20)
Density plot (partners<20)
Scatter to see linear/no-linear effect, look for outliers
Problems with unequal variance
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21. K independent samples test
equal medians?
Probably a cohort effect rather than an age effect
Oneway anova gives p=0.48, and Bartlett’s test for equal var gives p=0.000, that is clearly unequal variances. Group sizes also somewhat different.
Both tests (K-Wallis and anova) shaky. Regroup to 2 groups, or remove outlier
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22. Table of tests Categorical ordered: use nonparametric tests Dec-18
Mann-Whithey U=Wilcoxon rank sum
Categorical ordered: use nonparametric tests
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23. Example: Being bullied
Categorical data
Example:
Being bullied
Shown flowchart p3
Boys more or less than girls (2 sided test)
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24. Frequency and proportion
Proportion with CI:
Proportion:
May standardize, adjust for clusters, use bootstrap or jacknife est
May weigth if stratified sample
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25. Proportion, confidence interval
x=”disease”
n=total number
proportion:
standard error:
confidence interval:
How much increase n to get half the standard error?
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26. Crosstables Are boys bullied as much as girls? equal proportions?
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27. Ordered categories, trend
Does bullied vary with age?
twoway (fpfitci bullied agegr) ///
(lfit bullied agegr)
Could also have used age as countinuous.
Have not shown the data as two rugs.
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28. Ordered categories, trend
equal proportions?
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29. Table of tests Categorical ordered: use nonparametric tests Dec-18
Mann-Whithey U=Wilcoxon rank sum
For matched CC data:
Mc-Nemar for 2*2 tables
symmetry for K*K tables (outcome with more than 2 categories)
Categorical ordered: use nonparametric tests
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