Summarising Data, Assignments of Statistics

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Types of data Qualitative Data Quantitative Data

Summarising Data

Mark Lunt

Centre for Epidemiology Versus Arthritis University of Manchester

Types of data Qualitative Data Quantitative Data

Summarising Data

Today we will consider Different types of data Appropriate ways to summarise these data Graphical Summary Numerical Summary

Types of data Qualitative Data Quantitative Data

Examples of Types of Data

Nominal Blood group; Hair colour.

Ordinal Strongly agree, agree, disagree, strongly disagree.

Discrete Number of children.

Continuous Birthweight.

Types of data Qualitative Data Quantitative Data

Caveats with Data Types

Distinction between nominal and ordinal variables can be subjective: e.g. vertebral fracture types: Wedge, Concavity, Biconcavity, Crush. Could argue that a crush is worse than a biconcavity which is worse than a concavity... , but this is not self-evident. Distinction between ordinal and discrete variables can be subjective: e.g. cancer staging I, II, III, IV: sounds discrete, but better treated as ordinal. Continuous variables generally measured to a fixed level of precision, which makes them discrete. Not a problem, provide there are enough levels.

Types of data Qualitative Data Quantitative Data

Summarizing Qualitative Data

Count the number of subjects in each group. The count is commonly refered to as the frequency The proportion in each group is referred to as the relative frequency Stata command to produce a tabulation is tabulate varname

Types of data Qualitative Data Quantitative Data

Numerical Summary of Qualitative Data

region | Freq. Percent Cum. ------------+----------------------------------- Canada | 422 22.84 22. USA | 541 29.27 52. Mexico | 223 12.07 64. Europe | 493 26.68 90. Asia | 169 9.15 100. ------------+----------------------------------- Total | 1,848 100.

Types of data Qualitative Data Quantitative Data

Bar Chart

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Frequency

Canada USA Mexico Europe Asia region

Types of data Qualitative Data Quantitative Data

Graphical Summary Numerical Summary Alternative graphical summary

Summarizing Quantitative Data

Simplest method: treat as qualitative data. Divide observations into groups May be unnecessary for discrete data. Look at the frequency distribution of these groups Can use table or diagram.

Types of data Qualitative Data Quantitative Data

Graphical Summary Numerical Summary Alternative graphical summary

How Many Groups?

Impossible to say. Depends on the number of observations: if individual groups are too small, results are meaningless. With discrete variables, exact positions of boundaries may be important. Tables need few groups, graphs can have more if sufficient numbers. May be decided for you in software.

Types of data Qualitative Data Quantitative Data

Graphical Summary Numerical Summary Alternative graphical summary

Histograms

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140 160 180 200 140 160 180 200

female male

Density

measured height (cm) Graphs by sex

Types of data Qualitative Data Quantitative Data

Graphical Summary Numerical Summary Alternative graphical summary

Bar charts and histograms in Stata

histogram varname produces a histogram Number of bars can by set by option bin() Width of a bar can be set by option width() histogram varname, discrete produces a bar chart What stata calls a bar chart is the mean of second variable subdivided by category, rather than a frequency.

Types of data Qualitative Data Quantitative Data

Graphical Summary Numerical Summary Alternative graphical summary

Numerical Summary of Quantitative Data

Need to know: (^1) What is a typical value (“location”) (^2) How much do the values vary (“scale”) Simplest distribution to summarize is the normal distribution Other summary statistics (skewness, kurtosis etc) thought of relative to normal distribution.

Types of data Qualitative Data Quantitative Data

Graphical Summary Numerical Summary Alternative graphical summary

Arithmetic Mean

“Add them up and divide by how many there are.”

¯x =

x 1 + x 2 +... + xn n = (Σni= 1 xi )/n

Types of data Qualitative Data Quantitative Data

Graphical Summary Numerical Summary Alternative graphical summary

Median

“Arrange in increasing order, pick the middle.” If an even number of observations, take mean of middle two. Ignores the precise magnitude of most observations Contains less “information” than mean May be useful if there are outliers Less easy to use mathematically.