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Statistics revisions: Theoretical basis



Chapter I: Statistical Thinking

Key definitions:

Population: all the elements of interest under study: N represents the Population size and, and a specific characteristic of a population is a parameter.

Sample: subset of a population: n represents the sample size, and the specific characteristic of a sample is a statistic.

Variable: acharacteristic of an item or individual; the numbers associated with that variable is the data.

Statistical Methods

Descriptive statistics: gathering, studying , summarizing and characterizing data with numerical tools(mean, variance, etc).

Inferential statistics: using the information from a sample to make decisions concerning the whole population. These are estimates, so may be lessaccurate than descriptive statistics.

Decision making process:

Gathering data( Using descriptive statistics to extract information( Using the knowledge obtained to make decisions.



Chapter 2: Data collection and survey method

Sources of data:

Primary: the data collector is the one analyzing

Secondary: analyzing data collected by a second source: data from journal, census,internet…

Source Categories

Data distributed by an organization

Designed experiment(strict control over the units)

Survey

Observational study(no control over the units).

Types of variables:

Quantitative: numerical data; this data may be discrete(counted items) or continuous(fragment able, measured characteristics).

Qualitative: studying categories

Types of data

Time seriesdata: values of a variable observed over time

Cross section data: values observed at a specific point in time

Levels of measurement:

Ordinal scale: classifying data in categories. Ranking implied.

Classifying data in categories: no ranking implied.

Interval scale:Ordered scale in which the difference between measurements is a set quantity but the data does not have a true zeropoint. For instance, a study of temperature between Celsius and farenheit: 0 degrees does not mean absence of temperature, just another temperature. The same way, 0 in a grade does not mean absence of grade, just a really bad grade.

Ratio scale: Ordered scale in which the difference between measurements is a set quantity: however, there is a true 0 point. A 0 in height means absence of height. A 0in age means absence of age, and a 0 in salary means absence of salary, not just another value for a salary/ for age/for height.

Sampling techniques:

|Sample: |
|Non probability Sample |
|(Judgment |
|(Convenience|
| |
|Probability Sample |
|(Simple random |
|(Stratified |
|(Systematic |
|(Cluster |Statistical sampling: how to build a probability sample?

- Simple random : every unit has an equal chance of being selected; selection with or without replacements.

- Stratified: you divide the population in strata according to a common characteristic and then select simple random units from each group.

- Systematic: divide the population between the size of sample we want andobtain a number k. Then randomly select an unit from the first group and then select the next one every k units.

- Cluster: Population divided in representative groups called clusters. Then carry a simple random selection of clusters that will build your sample.



Chapter 3: Describing data; tables and graphs

Data presentation:

The type of graph depends on the type of variable...