MODULE 1.1 Basic Concepts in Inferential Statistics

Statistics singular

• refers to a branch of science concerned with the collection, organization, presentation, analysis, and interpretation of sets of numerical figures.

• It refers to the science consisting of theory and methods for planning the collection of data to answer the research questions at hand, and then collecting the data, analyzing the data, and finally interpreting the results of the analysis.

Statistics plural

refers to a collection of numerical figures. For instance, the numbers that you hear and read from the news, such as the number of COVID-19 active cases, the unemployment rate, the inflation rate, the proportion of Filipinos who are satisfied with the government response to COVID-19, and even basketball statistics,

Population

• The entire collection of entities that we want information about, on which inferences are made.

• A collection or set of all individuals/entities whose characteristics are to be studies (Who?)

Universe

Set of all possible values of a variable.

Sample

The subset of the population we actually examine to gather information.

Parameters

• Summary measures from a population

• The population mean (μ) and the population standard deviation (σ) are examples of ___________.

• You would often find _________ to be denoted using Greek

  letters.

Statistics

• summary measures based on a sample

• The sample mean (x̅) and the sample standard deviation (s) are examples of ________.

Variables

• a characteristic or attribute that is measured for the unit under consideration.

• attribute or characteristic of interest measurable on each and every unit of the universe (what?)

Observation

The realized value of a variable that is measured and recorded for each unit

Data

The collection of observations on one or more variables

Quantitative and Qualitative

Variables can be classified into one of two categories:

Qualitative variable

• measures a characteristic that can be classified into one of a group of categories and cannot be measured on a natural numerical scale.

• could be represented in a database as numbers: for example, 1 if male, 0 if female. These two numerical values do not express quantity, amount, or magnitude. Zip code (say, 4030 for Los Baños, Laguna)

• Cannot perform arithmetic

Categorical data

Observations made on qualitative variables are sometimes referred to as

Quantitative variable

measures a characteristic that is recorded on a naturally occurring numerical scale; thus, performing arithmetic operations on this type of variable has a meaning.

discrete

A quantitative variable is said to be _______ if it can only take a finite or countable number of values.

continuous

a _______ quantitative variable takes infinitely many values at any point on a given interval. For example, the height (in centimeters) of a student can assume any value from the minimum possible height and the maximum possible height.

Nominal level

• Qualitative

• The lowest level gives names, and labels to various categories without a sense of order.

• Info obtained limited to frequency counts and percentages.

Ordinal level

• Qualitative

• There is order

• Info obtained limited to frequency counts and percentages

Interval level

• Has no absolute zero point. Zero still has meaning.

• Temp, IQ, EQ

• Add/subtract

Ratio

• Has absolute zero, meaning nothing.

• Add/subtract/multiply/divide

• No. of household members, height, weight.