Intro to Stat-PDF

8/14/2019 Intro to Stat-PDF

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STATISTICSSTATISTICS

the science of collecting, organizing,the science of collecting, organizing,presenting, analyzing, and interpretingpresenting, analyzing, and interpreting

data to assist in making more effectivedata to assist in making more effective

decisions.decisions.


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WHY STUDY STATISTICS?

3 Reasons:

1.) Data are everywhere

2.) Statistical techniques are used to

make many decisions that affect ourlives (examples: Medicine, Water

quality, teaching methodologies, etc.)


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3.)No matter what your future line of

work, you will make decisions that

involve data.


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WHAT IS MEANT BY

STATISTICS?


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Numerical

Information

Examples:

1Average starting salary ofcollege graduates

2Average number of Fords

sold per month at Ford

Cagayan

3Percentage of

undergraduates attending

CU who will attend graduate

school

4The number of deaths due

to alcoholism last year

5etc.

Statistics

Graphical Information

Examples:

+1000

0

-1000

86 87 88 89 90 91 92

Net Income of PAL


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TYPES OF STATISTICS

Descriptive Statistics is a scientific

method of dealing with data. It is

the collection, organization,

presentation and interpretation of

numerical data. Statistics are also

quantities calculated fromobservations.


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Inferential Statistics involves the

interpretation of values resulting

from the descriptive techniques. It

also involves making inferences,

conclusions, or decisions about

the population of which thesample is a part, again using

sample results. The objective of

inferential statistics is to draw

inferences from a small group(sample) to a large group

(population) and to do so with a

well defined degree of confidence.


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VARIABLES AND

MEASUREMENTVariable. Characteristics or phenomenon

which may take on different values.The set values that the variable cantake is called its domain.

Example: weight, grades, income, age, jobperformance

Constant. Characteristics which assumeonly one value.


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Quantitative or Numerical Variable.Variables which are expressednumerically in terms of magnitude.

Example: height, income

Qualitative or Categorical Variables.Variables expressed in quality or kind.

Example: sex, color, type of school


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Continuous Variable. One which assumesall values between two points in acontinuous scale.

Example: weight, income

Discrete Variable. One which can onlyassume a finite number of values most

frequently integers.

Example: number of respondents in astudy


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Observation. Numerical recording ofinformation on a variable.

Example: variable weight

110 lbs. 100 lbs. 135 lbs.

9.85 lbs. 112.78 lbs.

Data. A collection of observations.


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Scales of Measurement

1. Nominal or Classificatory Scale

Numbers are used as codes simply toclassify an object, persons orcharacteristics into certain categories(Equivalence).

Example : Red = 0Blue = 1

Green = 2


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2. Ordinal or Ranking Scale

Numbers are used as codes, categoriesare not just different but be put in order(Equivalence, or)

Example: poor = 0

Midclass = 1

Rich = 2


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3. Interval Scale

Has all the characteristics of ordinal scaleand nominal scale and in addition, the

distance between 2 points on the scale isknown. However, the zero point isartificial. (Equivalence, or, differencebetween two points can be compared)

Example: 320 C, 900F (Variable-Temperature)


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4.) Ratio Scale

Has all the characteristics of the interval

scale and in addition has a true zero point.

Example: weight, height


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DATA COLLECTION

Primary Data. Gathered by the Researcher.

Secondary Data. Using data of other

sources

Census. Complete enumeration in whichevery member of the population is

included.

Sample Survey. Survey of a portion of thepopulation.


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Elements in a Survey Design:

1. Set of Objectives

2. Sampling Design

3. Data of gathering plan

4. Plan for analysis of collected data


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Sampling Procedures

1. Probability Sampling. A samplingmethod, which makes use of the

knowledge of the characteristics of theindividual element in the population

and thus, the chance that, each element

has of being drawn as sample.


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2. Non Probability Sampling. Asampling method which does not specify theprobability of selection of the elements in thepopulation.

Examples:

a.) accidents or haphazard samples items which come inhandy are taken as samples.

- TV commercial of a certain product where a buyer in asuperstore is interviewed

b.)judgment or purposive sampling sample is selected withthe researchers subjective judgment.

c.) quota sampling - purposive sampling with the addedspecification that sample is proport ioned to the population.


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Probability Sampling Techniques:

1. Random Sampling. Process of selectinga sample wherein every element in the

sampled population is given an equal non zero chance of entering the sample.

2. Systematic Random Sampling.

Sampling wherein every kth

unit isincluded after a random start is taken forthe sample.


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3. Stratif ied Sampling. Population isdivided into homogenous groups of strata

and selection is done within each strata.

4. Multi Stage Sampling. Sampling donein several stages.


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Sampling Techniques

SLOUVINS FORMULA

N

n = ---------------

1 + Ne2 where N = population

n = no. of sample

e = margin in of error or level of signi ficance

(0.01, 0.05, 0.001)

Example:

N = 100,000

e = 0.05

n = ?

100,000

n = ----------------------------- =398

1 + 100,000 (0.05)2


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Proportionate Sampling: (sampling Proportionate to Size)

Men 3,000 X

Women 20,000 Y

________________________________________

N = 23,000 n = 393

23, 000

n = ----------------------- = 393

1 + 23,000 (0.05)2

X 393

---------- = ---------- ; X = 51

3000 23,000

Y 393

---------- = -----------; Y = 342

20,000 23,000

or Y = 393 51 = 342

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