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Multivariate Statistics

Types of Data

**Micro Data:**Individual Data of respondents like people, households or enterprises. The basic commodity for the statistican.**Macro or tabular data:**aggregate micro data, table cells**Meta data:**Data about data. Information about variables, sampling frame, questionnaire etc.

Multivariate Statistics

Metadata types

- Acting as identifiers and descriptors of the data, such as: dimensions of statistical cubes, variables, titles of tables, Nomenclatures (code lists)
- Always be associated with the data to allow their identification, retrieval and browsing

- Acting only as descriptors of the data, they don't help to actually identify the data
- Can be exchanged independently from the data they are related to, but are however often linked to them

Multivariate Statistics

Para data

- Data about the process by which the survey data were collected
- E.g.: day interviews were conducted, how long the interviews took or how many times there were contacts

Multivariate Statistics

Nominal scale

- Just name the attribute uniquely
- No ordering of the cases is implied
- Central tendency given by its mode; neither the mean nor the median can be defined

Multivariate Statistics

Ordinal scale

- Attributes can be rank-ordered
- Distances between attributes do not have any meaning
- Central tendency can be represented by its mode or its median, but the mean cannot be defined

Multivariate Statistics

Interval scale

- Distance between attributes does have a meaning, the interval between values is interpretable
- "zero point" of an interval scale is arbitrary and negative values can be used
- Central tendency can be represented by its mode, its median, or its arithmetic mean

Multivariate Statistics

Ratio measurement

- Always an absolute zero that is meaningful
- Possible to construct a meaningful fraction with a ratio variable
- All statistical measures can be used, as all necessary mathematical operations are defined

Multivariate Statistics

Types of variables

**Discrete or categorical variables:**Countable set of categories and often small, the elements are from the set of natural numbers (e.g. sex)**Continuous variables:**infinitely set of possible numbers (e.g. income)

Multivariate Statistics

Sampling

- Sample = selection of units of a given population
- Sampling fraction = share of the population that is selected
- Sample is called representative if the statistical values of interest are equal to the corresponding values based on the whole population

Multivariate Statistics

Advantages of sampling

- Considerably lower cost
- More practicable
- Shorter time for data producing and evaluation
- In general, higher accuracy of results

Multivariate Statistics

Cluster sampling

- Population is fragmented in many small subpopulations (=clusters)
- Only a fraction of the cluster is randomly drawn
- Every single unit of the drawn clusters end up in the sample

Multivariate Statistics

Stratified random samples

- Complete division of the population into disjoint groups
- Is called stratified random sampling if in every stratum an independent simple random sample is drawn

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