Basic Concepts, Definitions, Sampling Techniques and Probabilities

data set

data set

a collection of data values

data value or datum

Each value in the data set is called a __ or a _______

data

facts, figures and information collected on some characteristics of a population or sample

qualitative or quantitative data

Data can be classified as

Population

refers to the totality of objects, persons, places, things used in a particular study.

Sample

any subset of population or few members of a population

investigator

The person who plans and conducts the statistical investigation independently or with the help of others

respondent

The person who answers/responds to the set of questions

enumerator

The person who collects data by conducting an enquiry or an investigation

Categorical data

A type of data that is used to group information with similar characteristics, also called qualitative data

numerical data

A type of data that expresses information in the form of numbers, also called quantitative data

Nominal Scale

classifies data into mutually exclusive (non-overlapping), exhausting categories in which no order or ranking can be imposed on the data

Ordinal Scale

classifies data into categories that can be ranked; however, precise differences between the ranks do not exist.

Interval Scale

ranks data, and precise differences between units of measure do exist; however, there is no meaningful zero.

Rational Scale

possesses all the characteristics of an interval measurement, and there exist a true zero

Primary data

is collected firsthand by a researcher (organization, person, authority, agency or party etc) through experiments, surveys, questionnaires, focus groups, conducting interviews and taking (required) measurements.

Secondary data

is readily available (collected by someone else) and is available to the public through publications, journals and newspapers.

Variable

is a measure or characteristic or property of a population or sample that may have a number of different values.

Variable

It is the characteristic or property that is measured, controlled, or manipulated in research.

Constant

is a characteristic or property of a population or sample which is common to all members of the group.

Retrospective

cohort studies are a type of observational research in which the investigator looks back in time at archived or self-report data.

Observational studies

process or population is observed and disturbed as little as possible, and the quantities of interests are recorded.

Design of experiments

is defined as a branch of applied statistics that deals with planning, conducting, analyzing, and interpreting controlled tests to evaluate the factors that control the value of a parameter or group of parameters.

• Retrospective

• Observational studies

• Design of Experiments

The three basic methods of collecting data

Sampling

The process of selecting just a small group of cases from out of a large group

1. Impracticable

2. Budget

3. Time

4. needed quickly

WHY THERE IS A NEED TO SAMPLE?

n=N/(1+Ne^2)

Slovin’s Formula

Andrew fisher formula

(1+CL)/2

Confidence level to Z-score Formula

Probabilistic Sampling

In every element of our sample the probability of them has the same weight. EPS (Equal Probability of Sampling)

Stratified Sampling

a method of sampling that involves the division of a population into smaller sub-groups known as strata.

Random Sampling

a subset of a statistical population in which each member of the subset has an equal probability of being chosen. Meant to be an unbiased representation of a group.

Systematic Sampling

a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval

Cluster Sampling

a probability sampling technique where researchers divide the population into multiple groups for research. Researchers then select random groups with a simple random or systematic random sampling technique for data collection and data analysis.

Non-Probabilistic Sampling

also called judgment or subjective sampling. This method is convenient and economical but the inferences made based on the findings are not so reliable

Convenience Sampling

taken from a group of people easy to contact or to reach. For a example, standing at a mall or a grocery store and asking people to answer questions.

Purposive Sampling

also known as judgmental, selective, or subjective sampling, is a form of non-probability sampling in which researchers rely on their own judgement

Quota Sampling

a sampling methodology wherein data is collected from a homogenous group. You continue sampling for each cell until you get the desired number and then stop

Snowball Sampling

is a recruitment technique in which research participants are asked to assist researchers in identifying other potential subjects.

Probability

the likelihood or chance of an event occurring

E(number of ways achieving success)/S(total number)

Probability Formula

Experiment

used to describe any process that generates a set of data

Event

consists of a set of possible outcomes of a probability experiment. Can be one outcome (simple event) or more than one outcome (compound event)

Sample space

the set of all possible outcomes or results of a random experiment.

element

Each outcome in the sample space

1. Convenience Sampling

2. Purposive Sampling

3. Quota Sampling

4. Snowball Sampling

Non-Probabilistic Sampling

1. Stratified Sampling

2. Random Sampling

3. Systematic Sampling

4. Cluster Sampling

Probabilistic Sampling

Null space

a subset of the sample space that contains no elements and is denoted by the symbol  Æ. It is also called empty space.

Intersection of Events ( A ∩ B)

the event containing all elements that are common to A and B

1.      Mutually Exclusive Events ( A ∩ B = O/ )

they have no elements in common

Union of Events ( A ∪ B )

containing all the elements that belong to A or to B or to both

Compliment of an Event (A ∩ C)’

• t A with respect to S is

• the set of all elements of S that are not in A and is denoted by A’

Statistical Unit

the items on which measurements are taken