STATISTICALMETHODS I

 STATISTICALMETHODS I

 

Prof. Elizabeth M. Role, Ph. D.

 

Prof. Elizabeth M. Role, Ph. D.

“It is not the capability you now possessor ever will have that will give you success; it is that which the Lord

will do for you.”

“It is not the capability you now possessor ever will have that will give you success; it is that which the Lord

will do for you.”

Ellen G. White

Theoretical Statistics

Applied Statistics

Types of

Statistics

Theoretical (Mathematical) Statistics• deals with the development, derivation, and proof of statistical theorems, formulas, rules, and laws.

Applied Statistics•Involves the applications of statistical theorems, formulas, rules, and laws to solve real-world problems.

APPLIED STATISTICS

CollectionCollectionPresentationPresentation

InterpretationInterpretationAnalysisAnalysis

Inferential Statistics

Descriptive Statistics

DIVISIONS OF APPLIED STATISTICS

Prob

ability

Descriptive Statistics•Consists of methods for organizing, displaying, and describing, data by using tables, graphs, and summary measures.

Inferential Statistics•Consists of methods that use sample results to help make decisions or predictions about a population.

  Census  Census

TERMINOLOGIES  TERMINOLOGIES 

PopulationPopulation SampleSample

Random SampleRandom Sample

Representative Sample

Representative Sample

Sample SurveySample Survey

Statistics Statistics

  Survey  Survey   Element  Element

Non-random SampleNon-random Sample

  Data  Data   Variable  Variable

Population is the collection of all elements whose characteristics are being studied.

Sample is a portion of the population of interest.

Element is a specific subject or object included in a sample or population.

Data is the collection of observations or measurements (value/score for an element) on a variable.

Data

Cross-section

Time-series

Cross-section data are collected on different elements at the same point in time or for the same period of time.

Time-series data give the values of the same variable for the same element at different points in time or for different periods of time.

Sources of DataExperiment

Survey

Experiment is the collection of data under controlled or modified environment.

Survey is the collection of data on the elements of a population or sample.

Census is a survey that includes all members of the population.

Luke 2The Birth of Jesus

1In those days Caesar Augustus issued a decree that a census should be taken of the entire

Roman world. 2(This was the first census that took place while Quirinius was governor of Syria.) 3And everyone went to his own town to register.

Sample survey is a survey that includes elements of a sample.

Representative sample is a sample that contains the same characteristics as the corresponding population.

Random sample is a sample drawn in such a way that each element of the population has some chance of being included in the sample.

Simple random sample is a sample drawn in such a way that each element of the population has the same chance of being selected for the sample.

Casting Lots

Casting the lot settles disputes and keeps strong

opponents apart.

Proverbs 18:18

The lot is cast into the lap, but its every decision is from the Lord.

Proverbs 16:33

Sampling with replacement

w/o replacement

With replacement – each element is put back in the population before the next element is selected.

Without replacement – occurs when the selected element is not replaced in the population.

Variable Types

Quantitative

Qualitative

Quantitative variable is a variable that can be measured numerically.

Variable is a characteristic under study that assumes different values for different elements.

QuantitativeContinuous

Discrete

Discrete variable is a variable whose values are countable.

Continuous variable can assume any numerical value over a certain interval.

Qualitative (categorical) variable cannot assume numerical values but is classified into two or more categories.

Levels of MeasurementLevels of MeasurementRatio

Interval

Ordinal

Nominal

Quantitative Qualitative