chapter 1 introduction to statistics. 1.1 an overview of statistics

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Chapter 1 Introduction to Statistics

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Page 1: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

Chapter 1Introduction to

Statistics

Page 2: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

1.1An Overview of

Statistics

Page 3: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

Definitions:O Data – consists of information

coming form observations, counts, measurements, or responsesO Population – the complete

collection of individuals to be studiedO Sample – part of a population

O Statistics – the science of collecting, organizing, analyzing, and interpreting data in order to make decisions

Page 4: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

EX: Identify the population and the sample

O In a recent survey, 614 small business owners in the U.S. were asked whether they thought their companies Facebook presence was valuable.

O The U.S. Department of Energy conducts weekly surveys of approximately 800 gas stations to determine the average price per gallon of regular gas.

Page 5: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

Definitions:O Parameter – a numerical

description of a population O Statistic – a numerical description

of a sample

Page 6: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

EX: Determine whether the numerical value is a parameter or a statistic.

O A recent survey of approximately 400,000 employers reported that the average starting salary for marketing majors is $53,000.

O The freshman class at a university has an average SAT math score of 514.

O In a random check of 400 retail stores, the FDA found that 34% of the stores were not storing fish at the proper temperature.

Page 7: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

Branches of StatisticsO Descriptive Statistics – the branch

of stats that involves the organization, summarization, and display of data.

O Inferential Statistics – the branch of stats that involve using a sample to draw conclusions about a population

Page 8: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

EX: O A large sample of men, aged 48, was

studied for 18 years. For unmarried men, approximately 70% were alive at age 65. For married men, 90% were alive at age 65.

O A) Which part of the study represents descriptive statistics?

O

B) What conclusions might be drawn from the study using inferential statistics?

Page 9: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

1.2Data

Classification

Page 10: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

Types of DataO Qualitative Data – consists of

attributes, labels, or nonnumerical entriesO EX: Names of Basketball Players

O Quantitative Data – consists of numerical measurements or countsO EX: Heights of Basketball Players

Page 11: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

EX:

Page 12: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

EX: Determine whether the data is qualitative or quantitative.

O Jersey numbers of soccer playersO Mile times of runnersO Hair color of your classmates

Page 13: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

Levels of MeasurementO Nominal – Qualitative data only

O No math computations can be done with data

O EX: names of collegesO Ordinal – Qualitative or quantitative

dataO Data can be ordered but differences

are meaninglessO EX: Top 10 Colleges in the U.S.

Page 14: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

O Interval – Quantitative data onlyO Data can be ordered, differences are

meaningful, but there is no natural zero starting point (where none of the quantity is present)

O EX: YearsO Ratio – Quantitative data only

O Data can be ordered, differences are meaningful, there is a natural zero starting point, and ratios are meaningful

O EX: Money in your wallet

Page 15: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics
Page 16: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

EX: Determine the level of measurement.

O The final standings for the Pacific Division of the NBA

O A collection of phone numbersO The hourly body temperatures of a

preemie in the NICUO The heart rates (in beats per minute)

of a preemie in the NICU

Page 17: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

1.3Data Collection and Experimental Design

Page 18: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

Statistical StudiesO Goal: To collect data and then use

the data to make a decision about the whole population.

O Note: Any decision that is made using the results is only as good as the process used to obtain the dataO If the process is flawed…the results

will be questionable

Page 19: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

Types of StudiesO Observational – a researcher does

not influence the responsesO Just observations are madeO No changes are made to existing

conditions

Page 20: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

Types of StudiesO Experiment – a researcher

deliberately applies a treatment before observing the responsesO Treatment Group – part of the

population that receives the treatmentO Control Group – part of the population

that does not receive the treatmentO Experimental Units – all subjects in

both groupsO Placebo – a fake treatment, that is

made to look like the real treatment, often given to the control group

Page 21: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

EX: Determine whether the study is an observational study or an experiment.

O Researchers study the effect of vitamin D supplementation among patients with antibody deficiency or frequent respiratory tract infections. To perform the study, 70 patients receive 4000 IU of vitamin D daily for a year. Another group of 70 patients receive a placebo daily for one year.

Page 22: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

O Researchers conduct a study to find the U.S. public approval rating of the U.S. president. To perform the study, researchers call 1500 U.S. residents and ask them whether they approve or disapprove of the job being done by the president.

Page 23: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

Data CollectionO Simulation – the use of a

mathematical or physical model to reproduce the conditions of a situation or process.O EX: Car crashes

O Survey – an investigation of one or more characteristics of a populationO EX: Asking people questionsO Make sure questions are worded in a

way that does not lead to biased results

Page 24: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

Experimental DesignO To produce meaningful and unbiased

results, experiments should be carefully designed and executed.

O Elements of a well-designed experiment:O 1) ControlO 2) RandomizationO 3) Replication

Page 25: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

1) ControlO Influential factors must be

controlled:O Confounding variable – occurs when

an experimenter cannot tell the difference between different factors on the variableO EX:

Page 26: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

O Placebo effect – when a subject reacts favorably to a placebo when in fact the subject was given a fake treatment

O Techniques to minimize the placebo effect:O Blinding – the subjects do not know

whether they are receiving a treatment or placebo

O Double- Blinding – neither the experimenter nor the subjects know

Page 27: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

2) Randomization O A process of randomly assigning

subjects to different treatment groupsO Completely randomized design – treatment

groups chosen by random selectionO Blocks – groups of subjects with similar

characteristicsO Randomized block design – subjects with

similar characteristics separated into blocks. Subjects form each block are then randomly chosen.

Page 28: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

O Randomized block design example:

Page 29: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

O Matched-pairs design – subjects are paired up according to similarity (age, location, physical characteristics…)O One person in the pair receives the

treatment and the other receives the placebo

O EX:

Page 30: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

3) Replication O The repetition of an experiment

under the same or similar conditions.O Sample size – the number of subjects

in a studyO EX:

Page 31: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

EX: O A company wants to test the

effectiveness of a new gum developed to help people quit smoking. Identify a potential problem with the given experimental design and suggest a way to improve it:O A company identifies ten adults who are

heavy smokers. Five are given the new gum and the other five are given a placebo. After two months, the subjects are evaluated and it is found that the five subjects using the new gum have quit smoking.

Page 32: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

O The company identifies 1,000 adults who are heavy smokers. The subjects are divided into blocks according to gender. Females are given the new gum and males are given the placebo. After two months, a significant number of the female subjects have quit smoking.

Page 33: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

O The company identifies 240 adults who are heavy smokers. The subjects are randomly assigned to be in a treatment group or in a control group. Each subject is also given a DVD featuring the dangers of smoking. After 4 months, most of the subjects in the treatment group have quit smoking.

Page 34: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

Sampling TechniquesO Census – a count or measure of the

entire populationO Sampling – a count or measure of

part of the populationO Must be representative of the entire

populationO If it is not representative of the

population, a sampling error has occurred.

Page 35: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

Sampling TechniquesO Random sample – every member of

the population has an equal chance of being selected

O Simple random sample – every possible sample of the same size has the same chance of being selected

O To collect a SRS:O Assign a number to each member of

the populationO Then use a calculator or computer

program to generate random numbers

Page 36: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

EX:O There are 731 students enrolled in a

stats course at your school. You wish to form a sample of 8 students to answer some survey questions. Select the students who will belong in the SRS using your calculator.

Page 37: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

Other sampling techniques:

O Stratified sample – population is divided in to two or more subsets, called strata, that share similar characteristics. A sample is then randomly selected from each strata.

O EX:

Page 38: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

O Cluster sample – population is divided into groups, called clusters, and all members in one or more clusters are selected

O EX:

Page 39: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

O Systematic sample – each member of the population is assigned a number. Members are ordered and selected at regular intervals

O EX: every 3th person

Page 40: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

O Convenience sample – consists of members of the population that are easy to getO Often biased so not recommendedO EX: asking your friends around you

Page 41: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

EX:O You are doing a study to determine

the opinions of students at your school regarding stem cell research. Identify the sampling technique used. Discuss any bias (if any).O You divide the student population with

respect to majors and randomly select and question some students in each major.

Page 42: Chapter 1 Introduction to Statistics. 1.1 An Overview of Statistics

O You assign each student a number and generate random numbers. You then question each student whose number is randomly selected.

O You select students who are in your biology class.

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O You select a class at random and question each student in the class.

O You assign each student a number and, after choosing a starting number, question every 25th student.