Docsity
Log inSign up
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources
Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study
Go to the blog

Nature of Statistics - Introduction to Statistics - Lecture notes, Study notes of Statistics

Institute of Mathematics and ApplicationsStatistics

Nature of Statistics, Populations, Samples of populations, Two Branches of Statistics, Variables and Data, Descriptive Statistics, Inferential Statistics, Qualitative and Quantitative Variables are learning points available in this lecture notes.

Typology: Study notes

2011/2012

Uploaded on 11/14/2012

dharm
dharm 🇮🇳

4.3

(24)

59 documents

1 / 8

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
1
Section 1
The Nature of Statistics
Introduction
Statistics is the science of conducting studies to collect, organize, summarize, analyze,
and draw conclusions from data.
• Basically two parts: Getting & Using data
We conduct these studies on populations or samples of populations.
A population consists of all subjects (human or otherwise) that are being studied.
A sample is a group of subjects from a population.
Why Sample?
Because Populations can get really Big!
For better or worse we are already very familiar with statistics:
“4 out of 5 dentists prefer Crest”
It is our goal to learn how to use statistics in a disciplined and appropriate manner AND
to be aware of those statistics that are misleading and improperly used.
Basic Terminology and The Two Branches of Statistics:
“Every day in the United States about 120 golfers claim they made a whole in one”
Variables & Data
We study samples and populations.
• The property we study is called a variable.
A variable is a characteristic or attribute that can assume different values.
Variables whose values are determined by chance are called random variables.
• When we observe or measure a variable we get data
Data are the values a variable assumes. A data set is a collection of data values
also called datum.
2 Branches of Statistics
Docsity.com
pf3
pf4
pf5
pf8

Partial preview of the text

Download Nature of Statistics - Introduction to Statistics - Lecture notes and more Study notes Statistics in PDF only on Docsity!

Section 1 The Nature of Statistics Introduction Statistics is the science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data.

  • Basically two parts: Getting & Using data We conduct these studies on populations or samples of populations. A population consists of all subjects (human or otherwise) that are being studied. A sample is a group of subjects from a population. Why Sample? Because Populations can get really Big! For better or worse we are already very familiar with statistics: “4 out of 5 dentists prefer Crest” It is our goal to learn how to use statistics in a disciplined and appropriate manner AND to be aware of those statistics that are misleading and improperly used. Basic Terminology and The Two Branches of Statistics: “Every day in the United States about 120 golfers claim they made a whole in one” Variables & Data We study samples and populations.
  • The property we study is called a variable. A variable is a characteristic or attribute that can assume different values. Variables whose values are determined by chance are called random variables.
  • When we observe or measure a variable we get data Data are the values a variable assumes. A data set is a collection of data values also called datum. 2 Branches of Statistics

Descriptive Inferential Describes a situation Uses probability Consists of the collection, organization, summarization, and presentation of data. Generalizations from samples to populations, often using estimations or predictions backed up by hypothesis testing. Focuses on the relationship between variables. The U.S. Census Collect relevant data Organize and summarize data into meaningful observations using graphs, pie charts, etc. Smoking Causes Cancer Not proven but strong correlations by hypothesis testing with test groups. Descriptive or Inferential?

  1. “The average lifespan of Labrador retrievers is 7.4 years”

answer: _________________________

  1. “In the year 2010, 28 million Canadians will be on the dole”

answer: _________________________

  1. “Expenditures for the music industry were 5.66 Billion in 1996”

answer: _________________________

  1. “Eye exercises alleviate the need for laser surgery”

answer: _________________________

Variables and Types of Data: Qualitative and Quantitative Variables Variables can be classified as either qualitative or quantitative.

  • Qualitative variables have distinct categories. Variable Categories Gender male, female Eye color blue, brown, green, hazel... Nationality American, English, German... *Note sometimes this is open to interpretation. Do eye colors really have distinct categories or is that just a socially accepted practice of distinguishing between people?

Measurement Scales Sometimes classifying data into qualitative and quantitative is not enough.

  • Are grades in school (A, B, C, D, F) quantitative or qualitative? Qualitative variables like grades are not numerical but we can rank them.
  • Is there a difference between the measure of temperature and height? These are quantitative and absolute zero is the difference – temperature is just a relative measurement, height is absolute. Measurement Scales provide further classification Measurement Scales Nominal-level Ordinal-level Interval-level Ratio-level Non-overlapping exhaustive categories No absolute zero No ranking Categories, but without precise differences No absolute zero Can be ranked Precise differences between units No absolute zero Can be ranked Precise differences between units Absolute zero Can be ranked Zip code Gender Political party Grades Judging (first place, second..) Rating scale (good, excellent, poor) Temperature SAT scores IQ Height Time Age Which Category? Time required for a plumber to clear a pipe: _____________________________ Marital Status of English department faculty: ______________________ Number of stars given to movies in the local paper: ______________________ The temperature outside: ______________________ Data Collection and Sampling Techniques. “Only one third of crimes committed are reported to the police”

Collection Methods/The Survey Data is collected in many ways such as studying records and direct observation but the most common method is the survey. **1) Personal Interview Survey Pros: In depth responses to questions Cons: Need to train interviewers = costly

  1. Telephone surveys Pros: Less costly than interviews People may be more candid Cons: Some people don’t have phones Some won’t answer their phone Unlisted numbers & cell phones Interviewer tone of voice / influence
  2. Mailed questionnaires Pros: Wider geographic regions due to low cost Respondents can remain anonymous Cons: Low number of responses Inappropriate answers to questions Requires reading skills** Sampling Sampling saves time and money. It also can allow a researcher to pursue a particular variable more efficiently. If samples are collected arbitrarily they can bias a study. Sampling Type Description Examples Random Using chance methods or random numbers to select subjects.

**- Cards in a bowl

  • Computer/calculator
  • Dice, coins Systematic** Number the population and select systematically. - Select the first subject randomly, then every n th thereafter. Stratified Divide by characteristic purposely by a particular variable or characteristic - Opinions of freshmen vs. sophomores Cluster Geographic Areas - School Districts, apartment complex, New York City

In experimental statistics the variable being manipulated (independent) is called the explanatory variable , and the variable being studied (dependent) is the outcome variable.

  • A confounding variable is one that influences the dependent (outcome) variable but cannot be separated from the independent (explanatory) variable.
  • To study the affect of changing a particular variable there must be at least two study groups: o A treatment group (or multiple ones) in which the variable is manipulated. o A control group that is not manipulated. Because of the Hawthorne effect it is often useful to trick the group into thinking they are being treated in the same way by administering a placebo. This will vary depending on the experiment type. A Dangerous Science/ Examples of Mis-use “There are three types of lies – lies, damn lies, and statistics” Remember, statistics is the “getting” and the “using” of data. “Getting” Data (Misuse)
    • Suspect samples Ex: “4 out of 5 doctors recommend brand A” Ex: A phone survey of people’s homes during the day Ex: A survey of volunteers for a paid medical study Very small samples are inaccurate estimations. How we select our subjects is of paramount importance
    • Faulty survey questions Survey question 1: Would you like the mayor to build a new performance theater to bolster the arts and attract acts to our city? Survey question 2: Would you like the mayor to increase taxes, raise the price of parking tickets and meters, and reduce road and pothole repair in order to build a new theater in our city? Clearly the phrasing of a question can bias the survey.

“Using” Data (Misuse)

  • The ambiguous term “average” When studies quote the term average it can have many meanings. We will learn mean , median , mode , and midrange in particular.
  • Changing the subject/ wording emphasis “ The CEO of WidgetCorp allowed losses of $1,000,000.00 last year alone” “Last year the CEO of WidgetCorp recorded losses of less than 1% of total revenues” As any good spin-doctor knows the truth is in the wording. Do these say anything about the responsibility of the CEO for the losses? Figures don’t lie, but liars figure.
  • Detached statistics “Jump brand tennis shoes last 30% longer.” “Advil works four times faster.”
  • Implied Connections “Jump tennis shoes may make you jump higher” “Studies suggest Advil works four times faster than generic brands” The Moral: Be wary but not jaded. It is our goal in this class to introduce ourselves to the science of statistics.