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7/31/2019 Onboarding Training - I (1)

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Introduction to Statistics - IMari Sudha


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Outline

Glossary

Levels of Measurement

Sampling

Organizing Data Statistics


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Glossary

Population Group of individuals under study

Sample A finite subset of statistical individuals in a population

Parameter A value, usually unknown (and which therefore has to be estimated), used to

represent a certain population characteristic. For example, the population meanis a parameter that is often used to indicate the average value of a quantity.Denoted by Greek letters e.g., ,

Statistic A quantity that is calculated from a sample of data; Possible to draw more than

one sample from the same population - the value of a statistic will in general varyfrom sample to sample. Often assigned Roman letters (e.g. m and s)


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Glossary (cont.) Sample Size

No. of individuals in a sample

Population Frame List of sampling units from which the sample is selected (directories, maps,

registered voters, list(s), etc.)

Statistical Inference Makes use of information from a sample to draw conclusions (inferences) about

the population from which the sample was taken

Experiment Any process or study which results in the collection of data, the outcome of which

is unknown


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Glossary (cont.) Random Process

An experiment, trial, or observation that can be repeated numerous times under

the same conditions; outcome of which are independent and identicallydistributed. It is in no ways affected by any previous outcome and cannot bepredicted with certainty

Random Variable A variable whose value results from a measurement on some type of random

process e.g., the tossing of a coin Can be classified as eitherdiscrete(a random variable that may assume either a

finite number of values or an infinite sequence of values) or as continuous(avariable that may assume any numerical value in an interval or collection ofintervals

Independent Variables

Variables that are manipulated and whose effects are measured and compared;also known as treatments; may include price levels, advertising themes etc.,


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Glossary (cont.) Experimental/Test Unit

Individuals, organizations, or other entities whose response to the independentvariables or treatments is examined; may include consumers, stores, orgeographic areas

Dependent Variables Variables that measure the effect of the independent variables on the test units;

may include sales, profits, and market share

Extraneous Variables Variables other than the independent variables that affect the response on the

test units; can confound the dependent variable measures such that it weakensor invalidates the results of the experiment

Includes store size, store location, and competitive effort

Raw Data Data collected in original form


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Glossary (cont.) Frequency

Variables that measure the effect of the independent variables on the test units;may include sales, profits, and market share

Frequency Distribution The organization of raw data in table form with classes and frequencies


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Measurement Scales

Variables differ in how well they can be measured, i.e., inhow much measurable information their measurement scale can provide

There is obviously some measurement error involved inevery measurement, which determines the amount ofinformation that we can obtain

Another factor that determines the amount of informationthat can be provided by a variable is its type/level ofmeasurement scale


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Outline

Glossary


Sampling



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Data obtained from measurement classified usingnumbers (In order to determine the way we are going to measure thevariables)

Classification can be done with different levels of

precision or levels of measurement Important to know the LOM we are working on partly

determines the arithmetic and statistical operations thatcan be carried out on them


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Levels of Measurement (cont.)

Four types of Levels of Measurement

They, in ascending order of precision are:

- Nominal

- Ordinal

- Interval

- Ratio


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Nominal Levels of Measurement (cont.)

Numbers are used to classify data words or letterwould be equally appropriate

Variables assessed on a nominal scale are calledcategoricalvariables

Examples include- Religion (Protestant Catholic, Hebrew, Buddhist, etc)

- Race (Caucasian, African-American, Hispanic, Asian, etc)

- Linguistic Group

- Marital Status (Married, Single, Divorced)

- Credit Card Numbers, Bank Account Numbers, Employee ID


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Nominal (cont.) Simple and widely used when relationship between two

variables is to be studied Nominal Scale numbers are no more than labels; used

specifically to identify different categories of responses

E.g.,

What is your gender?

[ ] Male[ ] Female


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Nominal (cont.) E.g.,A survey of retail stores done on two dimensions -

way of maintaining stocks and daily turnover.How do you stock items at present?

[ ] By product category[ ] At a centralized store[ ] Department wise

[ ] Single warehouseDaily turnover of consumer is?

[ ] Between 100 200[ ] Between 200 300[ ] Above 300


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Ordinal Levels of Measurement (cont.)

Simplest attitude measuring scale used in Marketing

Research Values given to measurements can be ordered

There is a rough quantitative sense to theirmeasurement, but the differences between scores are

not necessarily equal Examples Shoe size

Shoes are assigned a number to represent the size, larger numbers mean

bigger shoes (show an ordered relationship between numbered items) we

know that a shoe size of 8 is bigger than a shoe size of 4. What you cant saythough is that a shoe size of 8 is twice as big as a shoe size of 4


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Ordinal (cont.)

E.g., Results of a horse race, which say only whichhorses arrived first, second, third, etc. but include noinformation about times

Textual labels can be instead of numbers to represent

the category responses


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Ordinal (cont.)

E.g.1, Rank the following attributes (1 5), on theirimportance in a microwave oven

1. Company Name

2. Functions

3. Price

4. Comfort5. Design

The most important attribute is ranked 1 by the respondents and the leastimportant is ranked 5. Instead of numbers, letters or symbols too can beused to rate in a ordinal scale. Such scale makes no attempt to measure thedegree of favorability of different rankings


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Ordinal (cont.)

If there are 4 different types of fertilizers and if they areordered on the basis of quality as Grade A, Grade B, GradeC, Grade D is again an Ordinal Scale

If there are 5 different brands of Talcum Powder and if a

respondent ranks them based on say, Freshness into Rank1 having maximum Freshness Rank 2 the second maximumFreshness, and so on, an Ordinal Scale results


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Interval Levels of Measurement (cont.)

Measurements are classified, ordered with equal distancesbetween each interval on the scale (right along the scalefrom low end to high end i.e., )

Does not have an absolute zero; zero is arbitrary withfurther numbers placed at equal interval

Also termed as Rating Scales

E.g.,Temperature in centigrade: distance between 96 and 98oC is the sameas between 100 and 102 oC; measurement of 100oC does not mean that thetemperature is 10 times hotter than something measuring 10oC even though the

value given on the scale is 10 times as large


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Interval Levels of Measurement (cont.)

E.g., How do you rate your present refrigerator for thefollowing qualities

Tells us that position 5 on the scale is above position 4 and also thedistance from 5 to 4 is same as distance from 4 to 3

Does not permit conclusion that position 4 is twice as strong asposition 2 because no zero position has been established

Company Name

Less

Known 1 2 3 4 5

Well

Known

Functions Few 1 2 3 4 5 Many

Price Low 1 2 3 4 5 High

Design Poor 1 2 3 4 5 Good

Overall SatisfactionVery Dis-Satisfied 1 2 3 4 5

VerySatisfied


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Interval (cont.)

E.g.2, Calendar years are an interval scale. The arbitrary 0(or 1 depending on your viewpoint) was assigned whenChrist was born and time before this is labeled BC

E.g.3, Difference between the following values is measured

by a fixed scale- Money

- People

- Education (in years)


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Ratio Levels of Measurement (cont.) Has a natural zero point and further numbers are placed

at equally appearing Values given to measurements canbe ordered

Divisions between the points on the scale have the samedistance between them and numbers on the scale areranked according to size

Not widely used in Marketing Research unless a BaseValue is available for comparison

For example scales for measuring physical quantitieslike length, weight, etc.


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Ratio (cont.) Data on certain demographic or descriptive attributes, if

they are obtained through open-ended questions, willhave ratio-scale properties E.g.,

What is your annual income before taxes? ______ $How far is the Theater from your home ? ______ miles

Answers to these questions have a natural, unambiguous startingpoint, namely zero. Since starting point is not chosen arbitrarily,computing and interpreting ratio makes sense. For example we cansay that a respondent with an annual income of $ 40,000 earnstwice as much as one with an annual income of $ 20,000


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Nominal: Mode is frequently used for response category Ordinal: The central tendency can be represented by its

mode or its median, but the mean cannot be defined

Interval: Can be represented by its mode, its median, orits arithmetic mean. Statistical dispersion can bemeasured by range, inter-quartile range, and standarddeviation.


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Scale Type Mathematicalstructure Permissible Statistics

Admissible ScaleTransformation Mathematical structure

Nominal (also denoted as

categorical or discrete)Mode, chi square One to One (equality(=))

Standard set structure

(unordered)

Ordinal Median, percentileMonotonic increasing

(order(


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OK to compute Nominal Ordinal Interval Ratio

Frequency Distribution Yes Yes Yes Yes

Median and Percentiles No Yes Yes Yes

Add or Substract No No Yes Yes

Mean, Standard Deviation,Standard Error of the Mean No No Yes Yes

Ratio or Coefficient of Variation No No No Yes


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Outline

Glossary


Sampling



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Sampling Depends upon the nature of the data and type of enquiry

Procedure for selecting a sample- Decide on the target population/audience

- Identification of population frame

- Selection of sampling procedure/technique

- Decide the sample size

- Execute the Sampling Process (Select the sample individuals)

The nature of selecting a sample can be broadly classifiedunder three heads:- Non-Probability Sampling

- Probability Sampling

- Mixed Sampling


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Sampling (cont.)

Procedure for selecting a sample

- Decide on the target population/audience- Identification of population frame

- Selection of sampling procedure/technique

- Decide the sample size- Execute the Sampling Process (Select the sample individuals)


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Sampling (cont.)

Non-Probability Sampling- Every individual in the population does not have equal chance of being

selected

- Suffers from drawbacks of favoritism and nepotism depending upon

beliefs and prejudice of investigator- Statistically valid statements cannot be made about the precision of the

estimates (i.e. predictive value is weak)

- Methods of Non-Prob. Sampling: 1. Convenience Sampling2. Judgment Sampling

3. Quota Sampling

4. Snowball Sampling


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Sampling (cont.) Mixed Sampling

- Samples selected partly according to some laws of chance and partly

according to a fixed sampling rule

- No assignment of probabilities


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Sampling (cont.) Probability Sampling

- Every individual in the population has an equal chance of being selected

- No assignment of probabilities

- Different types of Probability Sampling:

I. Where each individual has an equal chance of being selected

II. Sampling units have different probabilities of being selected

III.Probability of selection of an individual is proportional to the sample size- Forms of Probability Sampling:

I. Simple Random Sampling

II. Stratified Simple Random Sampling

III.Systematic Sampling

IV.Cluster Sampling (simple and multistage)


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Outline

Glossary


Sampling



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Organizing Data

The first step in the analysis of the data is organizing thecollected numbers

A frequency distribution is a tool for organizing data

The first step in drawing a frequency distribution is to

construct a frequency table

A frequency table is a way of organizing the data by listingevery possible score (including those not actually obtained in the sample)as a column of numbers and the frequency of occurrence of

each score as another


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Organizing Data (cont.): Frequency Distribution

Contingency Table- Frequency tables of two variables presented simultaneously

Information contained in the frequency table may betransformed to a graphical or pictorial form, like:

I. Histograms

II. Absolute Frequency Polygons

III. Relative Frequency Polygons

IV. Absolute Cumulative Frequency Polygons

V. Relative Cumulative Polygons

VI. Box PlotsVII. Pie Charts etc.,


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Data Analysis

The steps in the analysis of the data include:- Data must be accurately scored and systematically organized to facilitate

data analysis

I. Scoring: assigning a total to each participants instrument

II. Tabulating: the mechanics of organizing the data

III. Coding: assigning numerals (e.g., ID) to data

IV. Performing both the initial and more detailed analysis


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Outline

Glossary


Sampling



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Statistics

Descriptive Statistics Gives numerical and graphic

procedures to summarize acollection of data in a clear andunderstandable way

Inferential Statistics Provides procedures to draw

inferences about a populationfrom a sample


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An unsophisticatedforecaster uses

statistics as a drunken

man uses lamp-posts -for support rather thanfor illumination ~

Andrew Lang

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