Chapter 1

Statistics

is the science of collecting, organizing, summarizing, presenting, analyzing, and interpreting numerical information from data to assist in making more effective decisions.

Descriptive Statistics

Area of statistics concerned with the organization, summarization, and presentation of data in an informative manner.

Inferential Statistics

Concerned with making statements/claim something about a population from a sample taken from that population

Aka “inductive statistics or statistical inference”

Population

• Entire set or totality of individuals or objects of interest

• All individuals of interest

• N

Sample

• a part or subset of the population of interest

• some selected individuals

• n

Parameter

represents important aspect of population which is a metric

Statistic

metric that depicts a feature of a sample taken from the target population

Variables

• Characteristics/attributes of individuals being measured.

• Can also be described as the operational definition or measurable representation of a construct

Data gathering

Fundamental requirement to conduct statistical analysis and to make decisions

Individual

Unit of analysis in a certain study which can be in the form of people, places, or objects.

Construct

• Concept, idea, abstract thing, or attribute that exists in our human brain, is not directly observable, is founded on specific ideas, and theoretically represents real objects and processes.

• can be represented by a variety of variables

• Conceptual definition of variable

Quantitative Variable

Variable is reported numerically

Qualitative Variable

also called an attribute (consist of demographic variables) , which is a non numeric characteristic of individuals

Discrete Variable

expressed, measured, or represented by whole numbers only with definite gaps between values

Continuous Variable

Can have any value within a specific range

Dummy Variable

• a numeric variable that represents categorical data mentioned under qualitative variables

• constructed in order to process and make sense of qualitative variables

• aka indicator, design variable, contrast, one hot coding, and binary basis variable

• are dichotomous quantitative variables

Latent Variables

• indirectly observed or inferred using other variables that can be directly observed.

• also known as hidden variables

• represent abstract concepts like behavioral states, mental states, or data structures.

1. Nominal

2. Ordinal

3. Interval

4. Ratio

Four levels of measurement of a variable

Nominal

• applied to data that consists of categories

• there is no order or sequence to the categorization, nor is there a prescribed criteria by which data can be sequenced.

• That is, they are observations of a qualitative variable that can be counted and classified.

• Mutually exclusive and exhaustive

Mutually Exclusive

Observation for an individual can only be classified into a single category

Exhaustive

observation for an individual must be classified in one of the categories

Ordinal

• applied to the data that can be ranked or sequenced in order

• cannot distinguish the magnitude of the difference between the values of data. That is, there is no meaning in the differences between the values of data.

Interval

• applied to data that can be ranked or sequenced (i.e., includes the characteristics of ordinal data), but differences between data values are constant and have meaning

• does not have absolute zero, zero does not mean absence of variable

Ratio

applied to data that can be ordered, and differences between data values and ratios of data values have meaning (i.e., includes the characteristics of interval data), and data have a true zero

Parametric

• are based on assumptions about the distribution of the underlying population where the sample was sourced, (Hoskin, n.d.). It is assumed that the population from which the sample data originates may be adequately represented by a probability distribution with a predetermined set of parameters. The most common assumption is that data approximates a normal distribution.

• interval/ratio

Nonparametric Statistics

• do not require assumptions about an underlying population distribution (Hoskin, n.d.). It does not rely solely on any particular probability distributions. Both distribution-free and uncertain distribution data can be used with it.

• Used in nominal and ordinal

Cross Section

data is gathered by observing numerous subjects, such as individuals, households, firms, countries, or regions, at one point in time (i.e., time is fixed).

Time Series

data is collected from one entity, such as individuals, households, firms, countries, or regions, and is sequenced according to time. It is a sequence taken at successive equally spaced time periods (i.e., a sequence of discrete-time data).

Panel Data

• is a type of data that combines the nature of cross-section and time series.

• it is a multidimensional data that involves measurement of cross-section entities over time. That is, it captures observations for the same subjects each time.

• It is also called longitudinal data. However, what distinguishes longitudinal data is that it is gathered through a series of repeated observations of the same entities for a longer period of time. It is used for monitoring trends across time by collecting data from the same respondents in several waves over long time periods.

• collected sequentially from same subjects across time