EOP Statistics CHAPTER 1

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1 Math Seminar 2 (First Year Statistics Seminar)

MATH SEMINAR 2A(Statistics)

Prof. Aryee

2 Why Statistics

Why Statistics

Any field of study that collects data,

summarizes and describes the information

collected, as well as interprets and draws

valid conclusions from the information

collected is a candidate for statistical

application


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3 Why Statistics

Why Statistics

Statistics provide us with the tools toanalyze data. Whether we want to detect

differences between groups of people,

events or activities, reorganize data to

identify hidden patterns, or to create

models in predicting outcomes of future

events, statistics provide us with a variety

of tools to achieve our goals.

4 Why Statistics

Why StatisticsThe following list of reasons for taking

statistics.

Statistics gives us a clearer understanding

of the world around us. It provides the

methods and techniques for developing

knowledge and for learning frominformation, thus forming the basis for

thinking and planning ahead.


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5 Why Statistics

Why Statistics

Statistics allow us to formulate questionsthat can be addressed by using data and

it provides the methods needed to

adequately describe, summarize, analyze,

interpret and draw valid conclusions from

the set of data to answer the questions.

6 Why Statistics

Why Statistics

Proper usage of statistics helps us to

critically interpret and evaluate claims as

well as to make informed decisions in the

face of uncertainty.

The tools of statistics are widely employedin many fields of study, including business,

communication, science, law, and so on.


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7 Why Statistics

Statistics, What Is It?

Everything dealing with the collection,analysis, interpretation, presentation,

and making valid conclusion of

numerical data belong to the domain of

statistics.

8 Statistics, What Is It?

Statistics, What Is It?Statistics is discipline which deals with:

a) Designing the data collection process and

experiments,

b) Preparing the data collected for analysis

and to aid understanding,

c) Analyzing and drawing conclusions from

data, and

d) Making estimates and predictions from

data.


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In general, statistics is a collection ofmethods for gathering, organizing,

summarizing, describing, analyzing,

interpreting, presenting, and making

valid conclusions of numerical data.

Often, data collected has inherent degree of variability

within them. Statistical techniques help us deal with this

variability and uncertainty in the data.



The American Statistical Association

described statistics as the science of

learning from data, and of measuring,

controlling, and communicating

uncertainty. In addition, they indicated

that statistics provide the navigation

essential for controlling the course of

scientific and societal advances.


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11 Statistics, two branches

Statistics, Two (2) branchesStatistics is grouped under two broad

categories,

1. Descriptive statistics, and

2. Inferential statistics.

12 Statistics, two branches

What is Descriptive Statistics

The purpose of descriptive statistics is to

make the collected data more easily

comprehensible and understandable.

In descriptive statistics, analysis of data is

directed entirely towards describing,

summarizing, and interpreting the basic

features or characteristics of the data

actually collected.


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13 What is Descriptive Statistics

What is Descriptive Statistics

The aim is to describe what is going onwithin the data or what the data

collected actually shows.

There is no intention to make conclusions

that extend beyond the data actually

collected.

14 What is Descriptive Statistics

What is Descriptive StatisticsDescriptive statistics techniques provide the

platform for reducing data. These techniques

include: Numerical counts or frequencies

Construction of tables and graphs

Computation of various descriptive measures

such as averages, percentages, and percentiles

Computation of variability measures such as

range, variance, and standard deviations


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15 Descriptive Statistics, Examples

Descriptive Statistics, Examples How much do Americans borrow/have

borrowed for college? As of Quarter 1 in2012, the average student loan balance

for all age groups is $24,301. About

one-quarter of borrowers owe more than

$28,000; 10% of borrowers owe more

than $54,000; 3% owe more than

$100,000; and less than 1%, or 167,000

people, owe more than $200,000.Source: http://libertystreeteconomics.newyorkfed.org/2012/03/grading-student-loans.html

16 Descriptive Statistics, Examples

Descriptive Statistics, Examples What is left? Not enough good men for

all the women available. The Daily News,

USA Weekend Section, printed these

statistics: 9 out of 10 on-the-job fatalities

are men, 5 out of 7 victims of traffic

accidents are men, 4 out of 5 homicide

victims are men, at least 4 out of 5suicides are men, 9 out of 10 HIV-related

deaths are men.Source: http://www.mendontlisten.com/StartingAgainPtrFr.html


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17 What is Inferential Statistics?

Inferential Statistics In inferential statistics, analysis of data is

directed towards generalizing,summarizing, predicting and making valid

conclusion about a larger set of data

from which the given sample was

collected and of which the given sample

forms just a part.

18 Inferential Statsitics

Inferential Statistics When we use statistical methods to draw

conclusions, make estimations, predictions,

and generalization about an entire set of

data by studying only part of the data, then

we are dealing with inferential statistics.

Inferential statistics allows us to use informationfrom a smaller group to make inferences about

a larger group from which the smaller group

was taken.


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19 Inferential Statistics

Inferential Statistics How many children die each year from child

abuse? Based on data reported by CPSagencies in 2001, it is estimated that

nationwide, 2,000 children died as a result of

abuse or neglect. Based on this number, five to

six children die each day as a result of child

abuse or neglect.

Source: http://www.preventchildabuse.com/abuse.htm

20 Statistics, what is a population and a sample

Population and Sample There are two very important underlying

concepts in inferential statistics.

These are the concepts of population and

sample. The paragraphs below explain these

concepts

A population is a complete collection of all

the set of units such as people, objects, events,transactions, animals, plants, or other things

whose characteristics a researcher is

interested in learning about.


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Population and SampleIdentify the population of interest to the researcher. In order to determine whether or not the cost of college

education is spiraling out of control, most analyst focus on the

cost of tuition as a yardstick to measure college education

cost. Other costs accompanying college education, such as

textbook cost, are rarely considered. A researcher wishes to

estimate the textbook cost of first-year students at Seton Hall

University. To do so, she randomly selected 300 first-year

students and found that their average textbook cost was $350

per semester.

Answer: The population of interest is all first-year Seton Hall university students.


A sample When a population is inaccessible or not

available (due to time or money constraint), or

we cannot get a complete set because it is

impractical or impossible to obtain a complete

set, we draw samples.

A sample is a collection of some (but not all) of

the elements of the population. Thus, a sample is a subset of the population.

It is usually selected to represent the

population from which it was drawn.


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A sample It is important to note that, different samples may

give us different portions of the same population. Asa result, if we already know the result of one sample

and then draw a second sample from the same

population we should not expect to have the exact

same replica of data in the first.

The difference in two or more samples drawn from

the same population is called sampling variation or

sampling error.

The sampling variation decreases as we increase thesize of our sample.


A sample


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A sample It is important to note that, different samples may

give us different portions of the same population. Asa result, if we already know the result of one sample

and then draw a second sample from the same

population we should not expect to have the exact

same replica of data in the first.

The difference in two or more samples drawn from

the same population is called sampling variation or

sampling error.

The sampling variation decreases as we increase thesize of our sample.

26 A RANDOM sample

A Random Sample The sample taken must be based on a selection

technique called random sampling. To use this

technique, each member of the population must

have an equal chance of being selected. A sample

resulting from a random sampling technique is

called a random sample.

A random sample is one in which every different

subset of a specified size from the population has

equal probability of being selected.

We can use a table of random numbers to select a

random sample.


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27 A unit of analysis

A unit of analysis or an element A unit of analysis or an element is a single entity

of the population from which information will becollected for analysis.

In a study, a statement about the population under

investigation must also state the object of interest,

that is, who (the entityperson, city, county, state,

school, organization) is being investigated.

A unit of analysis (also called an element) is a

single entity of the population from which

information will be collected for analysis.


A unit of analysis or an element In most studies, the units of analysis are the

smallest units that are independent of each other.

In identifying the units of analysis, you must answer

the question: what things are being compared or

examined by the researcher?

The things being compared or examined can be

at the level of an individual (say, students in a

college), or groups of individuals representing

different categories (such as undergraduate and

graduate students).


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A unit of analysis or an element A researcher may be interested in assessing the

patterns generated by the variation among thoseunits. In social science, the most typically chosen

unit of analysis is the individual person. For

instance, in a Gallop Poll, the unit of analysis is the

individual voter.

The population being studied or examined must be

clearly defined so that there is no ambiguity as to

whether or not an element is a member of the

population.


A unit of analysis or an element Mr. Jermic Smith, a pollster, is interested in finding

out what percentage of registered voters in the

country will vote for a particular presidential

candidate, Mr. John David. Jermic randomly

selected 3000 registered voters and ask them on

the phone who they will vote for. 1,680 (56%) of

the people polled informed him that they will vote

for Mr. David. What is the unit of analysis?

Answer: The unit of analysis is each individual

registered voter represented the population of

interest.


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31 What is a parameter

What is a parameter A parameter is a numerical descriptive

measure of a population. It is usually a singlevalue computed by using all the values in the

entire population.

The study in which all members of the

population are included in the study is called a

census.

32 Example of a parameter

Example of a parameter In an English class of 40 students, 24 of them had

participated in the English as a Second Language

Program which provide a coursework for

comprehensive language development for students

from other non-English speaking countries.

The statement "60% of the students in this English

class had participated in the English as a SecondLanguage Program" is a descriptive statement. The

population is the 40 students in this English class.

The 60% represents a parameter of interest.


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33 What is a statistic?

What is a statistic A statistic is a numerical descriptive measure of

a sample. It is usually a single numerical value

computed by using only the sample data, and

not the entire population.

Most statistical investigation leads to searching for the values of

population parameters that are of interest to the investigator. If

the population is not readily available, or we cannot get a

complete set because it is impractical or impossible to obtain a

complete set, we draw samples and then compute the necessary

descriptive statistic. We then make statistical inference about thepopulation parameter using the computed sample statistic.

34 What is a variable

What is a variable A parameter is a numerical descriptive

measure of a population. It is usually a single

value computed by using all the values in the

entire population.

The study in which all members of the

population are included in the study is called acensus.


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35 What is a variable

What is a variable A variable is usually a common characteristic that an

investigation focuses on after all the units of analysis

in the population or sample underlying the study havebeen identified.

A variable can also be thought of as the

characteristics of the units of analysis under

investigation that vary from one unit to another, taking

on different values, categories, or attributes.

A variable tells us what particular characteristic is

being studied or is of interest to the researcher.

Researchers focus on the empirical measurement ofthis characteristic.

36 What is the variable of interest?

What is the variable of interest? The reputations of many businesses can be

severely damaged by shipments of manufactured

items that contain a large percentage of

defectives. A manufacturer of alkaline batteries

wants to be reasonably certain whether fewerthan 5% of its batteries are defective. To do so,

300 batteries are randomly selected from a very

large shipment, each is tested and 10 defectivebatteries are found.

Answer: The variable of interest is the number

of defective batteries.


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37 Values of a variable

Values of a variable It is sometimes possible to confuse the difference

between the variables name and the differentcategories or attributes which the variable consist,

called the variables value. For example, gender

is a variable consisting two different categories

namely male and female.

In this example, male and female are values

we use to distinguish different people, however the

name of the variable is gender.


Values of a variable A variable may consist of two or more values.

Suppose a question on a survey asks each person

to choose the response that best reflects their

marital status: Are you Married, Widowed,

Divorced, Separated, or Never Married. In this

case, the name of the variable is marital status.

The five different categoriesMarried,

Widowed, Divorced, Separated, or Never

Marriedare the values of the variable.


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Values of a variable Some variables, such as height, weight, age, may take

on so many values. Others, such as gender, may takeon just a few values. Irrespective of how many values

a variable may take on, you can usually determine

the name of the variable by asking the question what

is this individuals ______?

For example, what is this individuals weight? So the

name of the variable is weight. Suppose the answer is

120 pounds. Then the value of this variable is 120

pounds. In this case, 120 pounds is just one of the

many values of this variable named weight.


Values of a variable Domestic Violence: Battered women who live in

poverty are often forced to choose between abusive

relationships and homelessness. In a study of 777

homeless parents (the majority of whom were mothers)

in ten U.S. cities, 22% said they had left their last

place of residence because of domestic violence

(Homes for the Homeless, 1998).

What is the population of interest in thisstudy?

Answer: The population of interest is all

homeless parents in the ten U.S. cities.


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relationships and homelessness. In a study of 777homeless parents (the majority of whom were mothers)




What is the variable of interest being study?

Answer: The variable of interest is the response of

each homeless parent as to whether or not the reason

for leaving their last place of residence because ofdomestic violence.




relationships and homelessness. In a study of 777

homeless parents (the majority of whom were mothers)




What is the size of the sample used? Answer: The 777 homeless parents (the

majority of whom were mothers) in the ten U.S.

cities.


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43 Social Research Design

Social Research Design Researchers in the social sciences study people,

and they are interested in understanding thebasic features and characteristics that mark the

people and groups in which the people live

and how and why these characteristics are

related.

Once they have an explanation, they offer

hypothesis about social relationships and collect

facts that can shed more light on socialbehaviors.

.

44 Social Research Design

Social Research Design Formulating of hypotheses usually begins with an

observation of a characteristic that differ or varies

across individuals or groups. Usually, the researcher

wants to understand the differences or variations

among the units of analysis.

For example, a researcher would like to know why

some students prefer to take professor A and others

prefer to take professor B, why some students

prefer to sit at the back of the classroom and others

prefer to sit in the front row, or why some people

voted for John Kerry and others voted for President

George Bush in the 2004 US presidential elections.


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45 What is a dependent Variable?

What is a dependent Variable? These why questions usually rush to our mind when

we observe differences between people. There are

two important lesions we can learn about these whyquestions.

First, it is always based on some characteristic that

varies. That is, it is always based on a variable.

The particular variable that constitutes our why

question is called the dependent variable. It is the

variable we want to understand, is usually view in a

particular wayas the effect of some unknown cause.


What is a dependent Variable? If we are interested in explaining why some students

prefer to sit at the back rows and others prefer to

sit in the front rows of the classroom, then seating

preference is the name of our dependent variable.

We are interested in two values of this variable:

back rows and the front rows of the classroom.


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What is a dependent Variable? Explanation in social science begins by observing a

characteristic that varies between subjects. The second

thing is that, each why question (the dependent

variable) implicitly request a causal explanation for

the observe differences. In order words, each why

question (or the dependent variable) is looking for

what causes the differences between the respondents

on this variable.

For example, what causes one student to take

professor A and another to take professor B?, or

what causes one student to sit at the front row andanother to sit in the back row of the classroom?

48 What is an independent Variable?

What is an independent Variable? Researchers use their creativity to come out with

explanations for these why questions.

These explanations involve identifying factors and

reasons why something happens in a particular way.

When researchers propose explanations to the why

questions, it usually involve a characteristic that varies

between subjects.

The variable that is proposed as an explanations tothe why questions is called the independent

variable.


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What is an independent Variable? In general, the variable that the researcher selects as

the causal factor in an explanation is calledindependent variable. The independent variable is

the variable the influences the behavior of other

variables.

The investigator can alter, manipulate or control the

independent variable.

In a study, the independent variable is the variable

the researchers identifies as being responsible for

influencing or producing effect or impart on othervariables.


What is an independent Variable? For example, a researcher may be interested in

explaining why some communities have higher crime

rates than others. When researchers propose an

explanation, it must be stated in such a way that

involves causation.

Explanation for differences in crime rates, for

example, may propose that the type of community,

whether urban or rural, plays a causal role. We mightmake a statement that prevalence of crime is higher in

the urban communities than in the rural communities.


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What is an independent Variable? As more and more rural communities are turned into

urban communities, due to increase population,

different type of people including criminals arebrought into the community, leading to an increase in

the crime rate.

Thus, this explanation proposes that the type of

community is associated to crime rates. So the type of

community, whether urban or rural, is the independent

variable.

52 Identify dependent and independent Variable

Identifying independent and dependent variables in the following hypothesis

Question 1: In comparing individuals, the mean number of hours spentwatching TV will be higher among newspaper readers than nonreaders.

Answer: Independent variablewhether or not an individual reads

newspaper. Dependent variablenumber of hours spent watching TV.

Question 2: In comparing candidates campaigning for elections, those who

spend more money on their campaigns are more likely to win than those

candidates who spend less money on their campaigns.

Answer: Independent variableamount of money spent on campaign.

Dependent variablewhether or not the candidate won the election.

Question 3: In comparing students, those who arrive late to class are morelikely to receive poor grades than those who arrive on time.

Answer: Independent variablewhether or not the student arrived late.

Dependent variablewhether or not the student received a poor grade.


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53 What is an Hypothesis?

What is an Hypothesis? When researchers propose an explanation to a

why question, the explanation must bedescribed in such a way that it can be tested

with an empirical data.

A hypothesis, therefore, is a testable

statement about the empirical relationship

between independent variable and the

dependent variable (or between cause and

effect).


What is an Hypothesis? For example, we might formulate the

hypothesis that students from richer communities

have higher SAT scores than those from poorer

communities.


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What is an Hypothesis? There are scientific procedures that must be followed

to determine whether or not a hypothesis is incorrect.

To determine whether or not a hypothesis is incorrect,researchers describes a set of conditions under which

the hypothesis would be rejected. To test hypotheses,

we use empirical comparison. For example, using

empirical data, we can compare the income of

people having less education to the incomes of

people having more education. In general, we use

empirical comparison to test the hypotheses. We will

learn more about the set of procedures fordetermining whether or not the hypothesis is incorrect.

56 Writing Hypothesis

Writing Hypothesis After we have determine the two variables whose relationship we are

trying to examine, we can start our hypothesis by linking one category of

the independent variable with another category of the dependent variable

and make a statement about their relationship in terms of more likely or

less likely type of relationship. We can use the following format:

In comparing [put the name of the units of analysis here], those who

are/those having [put the name of one of the category of the independentvariable here] are more likely to [put the name of one of the category of

the dependent variable being considered here] than those who are/those

having [put the name of a different category of the independent variable

with the lowest percentage here].

For example, in the attitude towards gun permit, we can make a statement such as:

In comparing individuals, those who are women will be more likely to favor

handgun permits than those who are men.


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57 Writing Hypothesis

Writing Hypothesis After we have determine the two variables whose relationship we are

trying to examine, we can start our hypothesis by linking one category of

the independent variable with another category of the dependent variable

and make a statement about their relationship in terms of more likely orless likely type of relationship. We can use the following format:

In comparing [put the name of the units of analysis here], those who

are/those having [put the name of one of the category of the independent

variable here] are more likely to [put the name of one of the category of

the dependent variable being considered here] than those who are/those

having [put the name of a different category of the independent variable

with the lowest percentage here].

For example, in the attitude towards gun permit, we can make a statement such as:

In comparing individuals, those who are women will be more likely to favor

handgun permits than those who are men.


Examples A Gallup Youth Poll was conducted at a certain

university to determine topics that students most want

to discuss with parents. The findings show that 55%

would like more to discuss about family financial

situation, 35% would like to talk about school, and

10% would like to talk about religion. The survey was

based on a sampling of 500 students.

Question 1: What is the population of interest in this

study?

Answer: The population of interest is all students

attending that particular university.


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to discuss with parents. The findings show that 55%would like more to discuss about family financial




Question 2: What is the variable of interest being

study?

Answer: The variable of interest is the topics thatstudents most want to discuss with parents.









Question 3: What are the values of this variable ofinterest?

Answer: The values of this variable are: discuss about

family financial situation, talk about school, and talk

about religion.


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to discuss with parents. The findings show that 55%would like more to discuss about family financial




Question 4: What is the size of the sample used?

Answer: The sample size is 500 students.









Question 6: What was a descriptive statistics used inthis study?

Answer: Of the 500 students, 55% would like more to discuss

about family financial situation, 35% would like to talk about

school, and 10% would like to talk about religion.


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Examples A Gallup Youth Poll was conducted at a certain university to

determine topics that students most want to discuss with

parents. The findings show that 55% would like more to discuss


school, and 10% would like to talk about religion. The survey

was based on a sampling of 500 students.

Question 7: What statistical inference could be made

from this study?

Answer: 55% of all students in that university would

like more to discuss about family financial situation.

That is, majority of all students would like more to

discuss about family financial situation. Very fewstudents would like to talk about religion.


Examples A Gallup Youth Poll was conducted at a certain university to

determine topics that students most want to discuss with

parents. The findings show that 55% would like more to discuss


school, and 10% would like to talk about religion. The survey

was based on a sampling of 500 students.

Question 8: What statistical inference could be made

from this study?

Answer: 55% of all students in that university wouldlike more to discuss about family financial situation.

That is, majority of all students would like more to

discuss about family financial situation. Very few

students would like to talk about religion.


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Examples A Gallup Youth Poll was conducted at a certain university to determine topics that students most

want to discuss with parents. The findings show that 55% would like more to discuss aboutfamily financial situation, 35% would like to talk about school, and 10% would like to talk

about religion. The survey was based on a sampling of 500 students.

Question 9: State a possible hypothesis. (Hint: use yourcreativity to come out with explanations why majority of all students

would like more to discuss about family financial situation but very few

students would like to talk about religion.)

Answer: In comparing individuals, students who are

more concern about their own financial aid eligibility


situation and students who are less concern about their

own financial aid eligibility would like to talk about

religion.


Examples A Gallup Youth Poll was conducted at a certain university to determine topics that students most

want to discuss with parents. The findings show that 55% would like more to discuss aboutfamily financial situation, 35% would like to talk about school, and 10% would like to talk

about religion. The survey was based on a sampling of 500 students.

Question 11: For your hypothesis, what is the

independent and dependent variable?

Answer: Independent variabledegree of concern of

students own financial aid eligibility. Dependent

variabletopics that teenagers most want to discuss

with parents.

Question 12: For your hypothesis, list possible

control variables.

Answer: family income.


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Control Variables In conducting a research, the independent variable may not be

the only variable that might have effects on the dependent

variable. Similarly, there may be other variables that could

influence the relationship among the variables. If such variables

are not controlled, they can confuse the interpretation of the

research results.

The variables which are not part of the variables under

investigation but could potentially influence or affect the

relationship among the variables if not controlled are called

controlled variables. Controlled must be held constant, or must

be prevented from varying, otherwise, they can confuse the

interpretation of the research results. Control variables are

important because they limit the focus of the research only tospecific subgroups

68 Control Variables

Control Variables Suppose in a study, we are interested in understanding why some people

perform much better academically than others. A researcher may propose

that class attendance plays a causal role. This may lead to a statement that

students who attend class more are more likely to perform better

academically, on the average, than students who attend class less. In this

case, the variable we want to explain (the dependent variable) is academic

performance, and the variable that represents the causal factor in the

explanation (the independent variable) is class attendance.

However, there might be additional explanations that can affect academic

performance other than class attendance. For instance, amount of hours of

study, age of student, class participation, social responsibilities, etc. mightalso have influence on academic performance. As a result, the researcher

can limit the study to a certain age group, or a particular amount of class

participation.


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EOP Statistics CHAPTER 1