chapter 1: introduction to statistics section 1.1: an overview of statistics

CHAPTER 1:

INTRODUCTIO

N TO

STATISTIC

S

S E C T I ON 1

. 1: A

N OV E R V I E

W OF S

T A T I ST I C

S

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

Data – information coming from observations, counts, measurements, or responses

Where have you seen statistics being used before?

DATA SETS: POPULATIONS VS. SAMPLESA population is the collection of all

outcomes, responses, measurements, or counts that are of interest

A sample is a subset of a population

In a recent survey, 1708 adults in the US were asked if they think global warming is a problem that requires immediate government action. 939 of the adults said yes.

Identify the population and the sample.

The US Department of Energy conducts weekly surveys of approximately 800 gasoline stations to determine the average price per gallon of regular gasoline. On Feb. 12, 2007, the average price was $2.24 per gallon.

Identify the population and the sample.

Parameter – a numerical description of a POPULATION characteristic

Statistic – a numerical description of a SAMPLE characteristic

**P’s stay together, and S’s stay together**Population = parameter**Sample = statistic

DISTINGUISH BETWEEN A PARAMETER AND STATISTIC1. A recent survey of a sample of MBAs reported

that the average salary for an MBA is more than $82,000.

2. Starting salaries for the 667 MBA graduates from the University of Chicago Graduate School of Business increased 8.5% from the previous year.

3. In a random check of a sample of retail stores, the Food and Drug Administration found that 34% of the stores were not storing fish at the proper temperature.

4. In 2006, major league baseball teams spent a total of $2,326,706,685 on players’ salaries.

BRANCHES OF STATISTICSDescriptive Statistics – the

branch of statistics that involves the organization, summarization, and display of data.

Inferential Statistics – the branch of statistics that involves using a sample to draw conclusions about a population.

SECTION 1.1 ASSIGNMENTPg. 8 - 11 #1 - #36 ALL

SECTION 1.2

D A TA CL A S S I F

I CA T I O

N

DATA CLASSIFICATIONData can be just about ANYTHING pertinent to the question

at hand:Data about Students at BJSHS:

TYPES OF DATAQualitative Data – consists of attributes,

labels, or nonnumerical entries (movie ratings, favorite color, teams, etc…)

Quantitative Data – consists of numerical measurements or counts (amounts, times, etc…)

NOTE: NUMBERS DO NOT MEAN QUANTITATIVE

LEVELS OF MEASUREMENT1.Nominal – qualitative only2.Ordinal – qualitative or

quantitative3.Interval – quantitative only4.Ratio – quantitative only

LEVELS OF MEASUREMENT

1. Nominal – categorized by names, labels or qualities

Yes/No QuestionsJersey NumbersNamesHair Color

2. Ordinal – able to be ranked or ordered, difference mean nothing particular

S/M/L/XL shirts1st, 2nd, 3rd,…Movie Ratings

3. Interval – when 0 does NOT mean “nothing”; can’t find ratios

TemperatureYears (NOT TIME BETWEEN THINGS)

4. Ratio – when 0 means “none” or “nothing”; true count, ratio between two data points can be formed

Population# of pages in a bookLengthPrice/Money

SECTION 1.2 ASSIGNMENTCase Study on Page 17 (SUBMIT) [Groups of 3 or

less]

INDIVIDUAL:Pg. 15 – 16 #1 - #24 ALL(Level of Measurement means: nominal, ordinal,

interval or ratio)

EXPERIMENTAL D

ESIGN

S E C T I ON 1

. 3

DESIGNING A STATISTICAL STUDY1.Identify the variables2.Develop a plan for collecting data3.Collect the data4.Describe the data (using

DESCRIPTIVE statistics)5.Interpret the data (using

INFERENTIAL statistics)6.Identify any possible errors.

DATA COLLECTION

1.Do an Observational Study

2.Perform an Experiment3.Use a Simulation4.Use a Survey

DATA COLLECTION1.Observational Study

- Researcher observes and measure characteristics of interest, but does

NOT change existing conditions.

DATA COLLECTION2. Perform an Experiment

- a TREATMENT is applied to part of a population and responses are observed- Control Group – part of population where NO treatment is applied- Subjects are given a PLACEBO – harmless, unmedicated treatment that is made to look like the real treatment

- Effects of treatment can be compared to control group- Subjects of a study also knows as EXPERIMENTAL UNITS

DATA COLLECTIONINSIGHT

IN AN OBSERVATION STUDY, A RESEARCHER DOES NOT INFLUENCE THE RESPONSES, IN AN EXPERIMENT, A RESEARCHER DELIBERATELY APPLIES A TREATMENT BEFORE OBSERVING THE RESPONSES.

DATA COLLECTION3. Use a Simulation- Use of a mathematical or physical

model to reproduce the conditions of a situation or process- Allows you to study situations

that are impractical, or dangerous- Saves companies time and money

DATA COLLECTION4. Use a Survey- An investigation of one or more

characteristics of a population- Customer Service Surveys- QUESTIONS MUST BE WORDED SO

THEY DO NOT LEAD TO BIASED RESULTS

Which method of data collection would you use to collect data for each study?

1.A study of the effect of exercise on relieving depression?

2.A study of the success of graduates of a large university finding a job within on e year of graduation.

EXPERIMENTAL DESIGN

3 KEY ELEMENTS OF A WELL-DESIGNED EXPERIMENT

1.CONTROL2.RANDOMIZATION3.REPLICATION

EXPERIMENTAL DESIGN: CONTROLConfounding variable – occurs when an

experimenter cannot tell the difference between the effects of different factors on a variable

Example:- Coffee Shop owner redecorates to

attract more costumers- At the same time, a shopping mall

nearby has a grand opening- VARIABLES ARE CONFOUNDED

EXPERIMENTAL DESIGN: CONTROLPLACEBO EFFECT – when a subject reacts

favorably to a placebo when in fact, he or she has been given no medicated treatment at all

To avoid this, we use BLINDING

EXPERIMENTAL DESIGN: CONTROLBLINDING – WHEN THE SUBJECT

DOES NOT KNOW WHETHER HE OR SHE IS RECEIVING A TREATMENT OR A PLACEBO

DOUBLE BLINDING – NEITHER THE SUBJECT NOR THE THE EXPERIMENTER KNOWS IF THE SUBJECT IS RECEIVING A TREATMENT OR PLACEBO (PREFERRED)

EXPERIMENTAL DESIGN: RANDOMIZATION

Randomization – process of randomly assigning subjects to different treatment groups

1.Completely Randomized Design

2.Randomized Block Design3.Matched Pairs Design

EXPERIMENTAL DESIGN: RANDOMIZATION2. Randomized Block Design- Divide subjects with similar

characteristics into blocks, and randomly assign subjects to treatments within each block

All Subjects

30 – 39 year olds

Control

Treatment

40 – 49 year olds

Control

Treatment

EXPERIMENTAL DESIGN: RANDOMIZATION

3. Matched-Pairs Design- Subjects are paired according to a

similarity- Subjects may be paired based on

age, residency, etc.- One receives one treatment, and

the other receives another treatment

EXPERIMENTAL DESIGN: REPLICATIONReplication – repetition of an

experiment using a large group of subjects

- More subjects, more value added to the result of your experiment

- We’re always looking for a large sample size

SAMPLING TECHNIQUES1.Census – count or measure of ENTIRE population2.Sampling – count or measure of PART of a

population- Random Sample- Simple Random Sample- Stratified Sample- Cluster Sample- Systematic Sample

- Sampling Error – difference between the results of a sample and those of the population

SAMPLING TECHNIQUESSampling Error – difference between the

results of a sample and those of the population

Biased Sample – one that is NOT representative of the population from which it is drawn.

Example: A sample of 18 – 22 year old college students would NOT be representative of the entire 18 – 22 year old population in the country.

SAMPLING TECHNIQUESRandom Sample – every member of the

population has an equal chance of being selected

Simple Random Sample – every possible sample of the same size has the same chance of being selected

USE OF RANDOM NUMBER GENERATORS!

SAMPLING TECHNIQUESWHEN IT IS IMPORTANT FOR THE SAMPLE TO HAVE

MEMBER FROM EACH SEGMENT OF THE POPULATION

Stratified Sample – members of population are divided into two or more subsets (strata), then sample is randomly selected from each strata

**Ensures that each segment of the population is represented

SAMPLING TECHNIQUESWHEN THE POPULATION FALLS INTO NATURALLY

OCCURRING SUBGROUPS

CLUSTER SAMPLE – Divide the population into groups (clusters), and select ALL of the members in one or more (but NOT ALL) of the clusters.

**Must be important that all clusters have similar characteristics

SAMPLING TECHNIQUES: INSIGHTFor STRATIFIED SAMPLING, each of the

strata contains members with a certain characteristic.

For CLUSTERS, each consist of geographic groupings, and should consist of members with ALL characteristics.

- Stratified – Some of members of each group are used

- Cluster – All of members of one or more groups are used

SAMPLING TECHNIQUES- Systematic Sample – a sample in which

each member of the population is assigned a number, those members are then ordered and then sample members are selected at regular intervals starting with the starting number.

# # # # # # # # #

SAMPLING TECHNIQUES

Convenience Sample – sample consists only of available members of population (not recommended)

ASSIGNMENT

Pg. 25 #1 - #14, #17 - #26 (identify sampling technique)

Pg. 27 #29- #30

HOMEWORK SELECTED ANSWERSSection 1.1

5. False

6. True

7. True

8. False

9. False

10. True

11. Pop

12. Sam

13. Sam

14. Pop

15. Sam

16. Pop

21. Pop: all adults in US

Sam: 1000 surveyed

22. Pop: all infants in Italy

Sam: 33043 infants in study

23. Pop: all households in US

Sam: 1906 households surveyed

24. Pop: all computer users

Sam: 496 students surveyed

29. Statistic

30.Statistic

31.Parameter

32. Parameter

33. Statistic

34. Parameter

35. Statistic

36. Parameter

Section 1.21. N and O2. O, I and R3. False4. False5. False6. False7. Qualitative8. Quantitative9. Quantitative10. Qualitative11. Qualitative12. Quantitative13. Qualitative, O14. Qualitative, N15. Qualitative16. Quantitative, R17. Qualitative, O18. Quantitative, R19. O20. R21. N22. R23. I, N, R, O24. I,N,I,R

Section 1.35. True6. False7. False8. False9. Fasle10. True11. P an E12. Survey13. Simulation14. Census17. SRS18. Stratified19. Convenience20. Cluster21. SRS22. Systematic23. Stratified24. Convenience25. Systematic26. SRS29. Census30. Survey