Statistics Key Definations

DEFINITIONS OF STATISTICS

"Statistics is the branch of the scientific method which deals with the data, particularly the collection, analysis, interpretation, presentation, and organization of data." - Ronald A. Fisher
"Statistics is the science of estimates and probabilities." - W. Edwards Deming
"Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data." - John Tukey
"Statistics is the science of learning from data, and of measuring, controlling and communicating uncertainty." - Peter J. Diggle

DATA IN STATISTICS

In statistics, data refers to a collection of facts, figures, or information that can be analyzed and used to make informed decisions. There are several different definitions of data in statistics, here are a few examples:

• "Data are the values of qualitative or quantitative variables, belonging to a set of items" - L. Leemis, "A Course in Probability Theory"
• "Data are the facts, figures, and other evidence from which conclusions can be drawn" - J.K. Pearson, "The Grammar of Science"
• "Data are the values of a variable that are observed or recorded" - D.S. Moore, "The Basic Practice of Statistics"
• "Data is a set of observations or measurements, often numerical, that is collected, recorded and analyzed in order to draw conclusions" - M.H. Kutner, et al., "Applied Linear Statistical Models"

In summary, data is a set of observations or measurements that can be analyzed using statistical methods to draw conclusions.

DATA AND ITS TYPES 

There are four main types of data used in statistics:

i. Numerical data: 

This type of data can be either continuous or discrete. Continuous data can take any value within a certain range, such as weight or height. Discrete data can only take certain values, such as the number of children in a household.

Examples: 

• Temperature measurements in Celsius or Fahrenheit
• Height and weight of individuals
• Number of items sold in a store
• Distance between two points

ii. Categorical data: 

This type of data is used to classify or categorize observations into groups or classes. It can be further divided into nominal and ordinal data. Nominal data has no inherent order and examples include color, gender, and brand. Ordinal data has an order, such as rankings, education levels, and social economic status.

Examples: 

• Gender (male or female)
• Eye color (brown, blue, green, etc.)
• Political affiliation (Democrat, Republican, Independent)
• Type of pet (dog, cat, fish, etc.)

iii. Time series data: 

This type of data is collected over time and is often used to analyze trends and patterns. Examples include stock prices, temperature, and population.

Examples: 

• Monthly sales of a company
• Daily temperature recordings over a year
• Weekly stock prices
• Hourly electricity usage

iv. Spatial data: 

This type of data is collected in relation to a specific location. Examples include population density, weather patterns, and crime rates by geographical location.

Examples: 

• Latitude and longitude coordinates of a location
• Elevation of a specific point
• Number of crimes committed in a specific neighborhood
• Population density of a city or region.

SCALE OF MEASUREMENT 

It's important to note that these types of data are not mutually exclusive, and a data set may include elements of more than one type.

In statistics, the scale of measurement refers to the level of measurement or measurement level of the data, which describes the level of detail and the nature of the information that the data can provide. There are four main scales of measurement: nominal, ordinal, interval, and ratio.

(i) Nominal scale: 

This is the lowest level of measurement, and it only provides a way of identifying or labeling the data. Nominal data does not have any inherent order or structure, and it cannot be meaningfully quantified. Examples include: Gender (Male/Female), Eye color (brown, blue, green), Religion (Christian, Muslim, Hindu)

(ii)Ordinal scale: 

This scale is one step higher than the nominal, and it provides a way of ordering or ranking the data. Ordinal data can be arranged in a meaningful order, but the differences between values are not meaningful. Examples include: the Likert scale (strongly agree, agree, disagree, strongly disagree), Education level (less than high school, high school, some college, college graduate)

(iii)Interval scale: 

This scale provides a way of measuring the distance between values, but it does not have a true zero point. This means that zero does not represent the absence of the variable being measured. Examples include: Temperature in Celsius or Fahrenheit, time measured in seconds or minutes

(iv)Ratio scale: 

This scale is the highest level of measurement, and it provides a way of measuring the distance between values and a true zero point. This means that zero represents the absence of the variable being measured. Examples include: Weight, height, income, population

It's important to note that the scale of measurement determines which statistical methods can be used to analyze the data.