**Introduction to Statistics**

Statistics...

statistics has two main definitions:

1. Statistics in singular sense and,

2. statistics in plural sense

Types of Statistics

There are two types of Statistics:

1. Parametric statistics

2. Nonparametric statistics

Branches of Statistics

There are two main branches of statisitcs:

1. Descriptive Statistics

2. Inferential statistics

Plural sense...

statistics is a set of numerical characteristics.

Singular sense...

it is a branch of science that deals the processes of collecting, organizing, presentation, analysis, and interpretation of data.

Fields of Statistics

The field of statistics is divided into:

Mathematical statistics

Applied statistics

Mathematical Statistics

this deals with the development of theories that serve as a basis for statistical methods.

Applied Statistics

this refers to the application of statistical methods to solve real life problems as well as the development of new statistical methods motivated by real problems.

Descriptive statistics

This refers to the methods of summarazing and presenting data in the form which will make them easier to interpret.

This includes the following:

Tables/graphs

Measures of Central Tendency

Measures of Position/Variability

Inferential statistics

It refers to the process of drawing and making decision on the population on the evidence obtained from a sample.

This includes:

Estimation

Hypothesis Testing

Parametric statistics

It is a statisical approach that assumes random sample from a normal distribution and involves testing of hypothesis about the population mean.

This includes:

z test/ t test

ANOVA and etc.

Nonparametric statistics

It is a statistical approach with no underlying data distribution assumed and involves hypothesis testing about a population median.

This includes:

sign test

Wilcoxon-signed test

Mann-Whitney and etc.

Variables

A variable is any characteristics, number, or quantity that can be measured or counted. A variable may also be called a data item.

Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye colour and vehicle type are examples of variables.

Population VS Sample

Parameter VS Statistic

Population

Parameter

Statistic

A parameter is a numerical characteristic of a population.

it is a numerical characteristic of a sample.

Sample

A population is a group of phenomena that have something in common. The term often refers to a group of people, as in the example:

All basal ganglia cells from a particular rhesus monkey.

A sample is a smaller group of members of a population selected to represent the population.

Types of Variables

Qualitative Variable

Categorical variables have values that describe a 'quality' or 'characteristic' of a data unit, like 'what type' or 'which category'. Categorical variables fall into mutually exclusive and exhaustive categories.

Therefore, categorical variables are qualitative variables and tend to be represented by a non-numeric value.

Types of Quantitative Variable

Discrete

Quantitative Variable

Continuous

Numeric variables have values that describe a measurable quantity as a number, like 'how many' or 'how much'.

Therefore numeric variables are quantitative variables.

A discrete variable is a numeric variable. Observations can take a value based on a count from a set of distinct whole values.

A discrete variable cannot take the value of a fraction between one value and the next closest value.

A continuous variable is a numeric variable. Observations can take any value between a certain set of real numbers.

The value given to an observation for a continuous variable can include values as small as the instrument of measurement allows.

Illustration

Illustration

Inferential statistics enables you to make an educated guess about a population parameter based on a statistic computed from a sample randomly drawn from that population .

More examples

Measurement Scales

There are four measurement scales for data analysis:

Nominal

Ordinal

Interval

Ratio

Measurement scales

Nominal

Examples

Measurement scales

When measuring using a nominal scale, one simply names or categorizes responses.

The essential point about nominal scales is that they do not imply any ordering among the responses.

Gender,

handedness,

favorite color,

and religion

Ordinal

Examples

Measurement Scales

The items in this scale are ordered, ranging from least to most.

Unlike nominal scales, ordinal scales allow comparisons of the degree to which two subjects possess the dependent variable.

satisfaction scale

year level

educational attainment

Military positions

Interval

Interval scales are numerical scales in which intervals have the same interpretation throughout

Interval scales are not perfect, however. In particular, they do not have a true zero point.

Examples

Temperature

General Weighted Average

Measurement scales

Ratio

The ratio scale of measurement is the most informative scale.

it is an interval scale with the additional property that its zero position indicates the absence of the quantity being measured

Examples

Temperature

money