Chapter 1 Introd to Statistics

7/31/2019 Chapter 1 Introd to Statistics

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CHAPTER 1 : INTRODUCTION TOSTATISTICS

1.1 Definition

1.2 Types of Statistics1.3 Important StatisticalTerminologies

1.4 Types of Variables and Data

1.5 Sources of Data


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Objectives

At the end of this chapter, you will be able to:

Definestatistics and basic statistical

terminologies correctly Classify statistics into two types with

examples

Differentiate and classify types of data interms of measurement level, form, andrepresentation.

Identify data sources and data collection

methods used in research.M4003 INTRODUCTION HELEN TEH


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1.1 What is statistics?

Statistics is the science of

collecting summarizing

organizing

analyzing

displaying

numerical data for the purpose of makinga more informed conclusion and decision.

interpreting

M4003 INTRODUCTION HELEN TEH


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1.2 Types of Statistics

Types of Statistics

Descriptive Statistics Inferential Statistics


Is the type of statistics used todescribe datanumerically

(mean, standard deviation) or

graphically (line graph, piechart) in forms that easilyunderstood and used.

Is the type of statisticsusedto make statements and

draw conclusions about apopulation using informationobtained from a sample andbased on probability theory.

2 types


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Mode = value that occurs most

frequently in a data set.

For example, for the sample

[1, 3, 6, 6, 6, 6, 7, 7, 12, 12, 17]

the mode is 6.

1.2.1 Descriptive Statistics


n

xxxxxMean

n

...

, 321

Standard deviation, = shows

how much the set of data varies

from the "average (mean)


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1.2.2 Inferential Statistics

Examples of statistical tests such as:

hypothesis testing (standard normal test, Z test;

t-test to compare two means, ANOVA to compare 3 oror more means, Chi square test, etc)

test of relationship between two variables (correlation Pearson, r; and Spearman, )

prediction test (regression) Others which you will not be learning in this course

include multiple regression, Mann-Whitney U test,Kruskal-Wallis test, factor analysis and etc.



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X1X2 X3X4 X5

X7 X9X10

X11X12

X13X14

X15 X16 X17

X18

X19X20

X21X22

X23

X24 X25X26

X27X28

X29 X30

X34

X31 X32

X37

X36X35

X33

X38

X39

X40

1.3 Statistical Terminologies

Population

Sample A Sample CX8

Parameter(, 2), N=40

Statistic

cc

sx ,


Statistic

bb

sx ,

Statistic

aasx ,

X6

Sampling unit

n=10

n=10

n=10 Sample B

Population : Entire group of people or objects which is being

studied (set of all measurement of interest). Example:

all registered voters, all students in a college.

Sample: A small group which is selected from the population

of interest (a subset of the population). A good sample

is a random sample (fair i.e. equal chance of being

selected and representative of the population).

Sampling Unit: Each population unit that may be sampled.

Variable: Characteristic or attribute of a population being

studied Example: height, weight, length, gender, taste,

aroma, colour etc.


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Unit/ Case/Element

Height (cm)

Ali 160

Guna 162

Swee Lin 157

Aida 155

Prakash 167

Variable

Value obtained froma variable

ObservationUnit/ Case

Also known asrespondents/ elements.

They are objects or sourcesof information.

Populationcharacteristic/ attribute

being studied




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Population : Entiregroup of people or objects which is being

studied (set of all measurement of interest). Example:

all registered voters, all students in a college.

Sample: A small group which is selected from the population

(a subset of the population). A good sample is a

random sample (fair and representative of the

population).

Sampling Unit: Each population unit that may be sampled.

Variable: Characteristic or attribute of a population that is

being studied Example: height, weight, length, gender,

taste, aroma, colour etc.


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Think and do ...

Identify the population, sample and variable inthe research statements below:

1. A research was carried out to determine the effectiveness of a

new teaching approach (Outcome-based education, OBE)introduced in 2009 for all diploma programs in Malaysianpolytechnics. The perspectives of 450 students and 85 lecturerswere obtained through surveys.

2. A sensory evaluation was conducted to determine the bestformulation for chicken nuggets. A panel of 30 consumers werechosen randomly from among those who visited Carrefour at EastCoast Mall between 12.00 2.00 pm on Sunday.



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Identify the population, sample and variable in theresearch statements below:

population

1. A research was carried out to determine theeffectiveness of a new teaching approach

(Outcome-based education, OBE) introduced in 2009for all diploma programs in Malaysian polytechnics.The perspectives of 450 students and 85 lecturerswere obtained through surveys.


sample

variable

All students and all lecturers in Malaysianpolytechnics who followed or taught using theOBE approach


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Identify the population, sample and variable in theresearch statements below:

2. A sensory evaluation using hedonic testing was conducted todetermine the best formulation for chicken nuggets based onfour attributes taste, aroma, texture and colour; and overall

acceptance of the product. An untrained panel of 30consumers were chosen randomly from among those whovisited Carrefour at East Coast Mall between 12.00 2.00 pmon Sunday.


variables sample population


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1.4 Variable

Qualitative Quantitative

Expresses quality or category,

also called categorical variable Nominal scale (name)

Examples: gender, hair colour,

religious affiliation, state of

birth, favourite singer, grade of

cocoa, ethnic background etc. Can be coded to appear

numeric but values are

meaningless.

Can be measured on a numeric

scale Numerically meaningful

Examples: number of children

in a family, amount of bacteria

in a culture (cfu), weight of

chillies in kilogram, height, etc.



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1.4.1 Qualitative Variable


The variable Gender

Female = F or 1

Male = M or 2

1 1 2

+

Numericallymeaningless!

Suppose you addthe values from a

qualitative variable.

Would the value bemeaningful?

=+


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1.4.1 Qualitative Variable


The variable number of babies in a nursery

1 1 2

+ =

Numerically

meaningful!

Suppose you addvalues from aquantitative

variable. Would thevalue obtained be

meaningful?


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Quantitative Qualitative

Exercise 1.1:

1. Give 5 examples for quantitative variables and qualitative

variables.


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Exercise 1.1:

2. List whether the following is quantitative variable or qualitative

variable:

a. Lifetime of a light bulb in hours

b. Final results from the judges

c. Religion of an individual

d. The concentration of sugar in a fruit juice

e. Aroma of flowers

f. Monthly telephone bill

g. Dividend paid to investment with Amanah Saham Bumiputerah. Temperature of a region


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1.4.2 Quantitative Variable

Discrete quantitativevariable

Continuous quantitativevariable

Finite or countablenumber (whole numbers)

Counts/ frequencies

Example: the number of

bedrooms in a house,number of apples in the

basket, etc.

Infinite number of possiblevalues

Usually obtained by

measurement

Example: the weight ofpotatoes in a bag, duration

taken to bake a cake,

temperature. Brix, etc.



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Exercise 1.1:

3. State whether the following statement is either discrete variable or

continuous variable:

a. Number of phone calls every 2 hours.

b. Number of goals that scored by a player in a tournament

c. The amount of petrol used by a car in 4 days.

d. Weight of a letter.

e. Number of seeds in an orange.f. Speed of a car.

g. Number of passengers in a plane.

h. Time needed to run 100 meters.

i. Volume of fruit juice in a bottle.j. Height of a student.

k. Number of children in a family.

l. Lifetime of a light bulb.


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1.5 Statistics and Research

To describe the population or phenomenon being studied


Researchers and scientists frequently use statistics to analyze their

results.

To determine the right statistical methods or procedures to

analyze and understand the data better (and more accurately)

To help confirm or reject a hypothesis and to make informed

and more valid decisions

Gathering information (data) from a sample is cheaper and

more manageable (feasible)


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Of the 47,263 students

eligible to participate inMonash ExperienceQuestionnaire 2005, therewere 16,116 returns, resultingin an overall response rate of

34.1%.

King, M. & Nair, C. S. (2006).The student experience:

Quality never dies. InProceedings of the AustralianUniversities Quality Forum2006. AUQA: 96100


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For example, a yes or no

questionnaire produces

categorical data. For such data,

frequency counts and

percentages are some descriptive

statistics often used.

A questionnaire with a 9-point

hedonic scale or a 10-interval

scoring test used in sensory

evaluation produce ordinal data.

As the number of intervals usedis more than 5, the data is often

analysed as interval data.

Comparison of formulations

would use statistical procedures

such as t-tests and ANOVA.

Design type of test

T-test, t

ANOVA, F

Pearson, r

Spearman,

y = mx + c


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... The optimal conditions to obtain the highest yield of acid-

soluble collagen from the skin of grass carp (Ctenopharyngodonidella) were ... The predicted yield of acid-soluble collagen was19.3 0.5% which was in agreement with the actual value(p

Chapter 1 Introd to Statistics

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