chapter 1: introduction to statistics section 1.1: an overview of statistics
DESCRIPTION
DATA SETS: POPULATIONS VS. SAMPLES A population is the collection of all outcomes, responses, measurements, or counts that are of interest A sample is a subset of a populationTRANSCRIPT
![Page 1: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/1.jpg)
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
![Page 2: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/2.jpg)
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?
![Page 3: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/3.jpg)
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
![Page 4: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/4.jpg)
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.
![Page 5: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/5.jpg)
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.
![Page 6: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/6.jpg)
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
![Page 7: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/7.jpg)
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.
![Page 8: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/8.jpg)
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.
![Page 9: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/9.jpg)
SECTION 1.1 ASSIGNMENTPg. 8 - 11 #1 - #36 ALL
![Page 10: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/10.jpg)
SECTION 1.2
D A TA CL A S S I F
I CA T I O
N
![Page 11: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/11.jpg)
DATA CLASSIFICATIONData can be just about ANYTHING pertinent to the question
at hand:Data about Students at BJSHS:
![Page 12: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/12.jpg)
![Page 13: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/13.jpg)
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
![Page 14: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/14.jpg)
LEVELS OF MEASUREMENT1.Nominal – qualitative only2.Ordinal – qualitative or
quantitative3.Interval – quantitative only4.Ratio – quantitative only
![Page 15: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/15.jpg)
![Page 16: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/16.jpg)
LEVELS OF MEASUREMENT
1. Nominal – categorized by names, labels or qualities
Yes/No QuestionsJersey NumbersNamesHair Color
![Page 17: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/17.jpg)
2. Ordinal – able to be ranked or ordered, difference mean nothing particular
S/M/L/XL shirts1st, 2nd, 3rd,…Movie Ratings
![Page 18: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/18.jpg)
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
![Page 19: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/19.jpg)
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)
![Page 20: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/20.jpg)
EXPERIMENTAL D
ESIGN
S E C T I ON 1
. 3
![Page 21: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/21.jpg)
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.
![Page 22: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/22.jpg)
DATA COLLECTION
1.Do an Observational Study
2.Perform an Experiment3.Use a Simulation4.Use a Survey
![Page 23: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/23.jpg)
DATA COLLECTION1.Observational Study
- Researcher observes and measure characteristics of interest, but does
NOT change existing conditions.
![Page 24: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/24.jpg)
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
![Page 25: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/25.jpg)
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.
![Page 26: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/26.jpg)
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
![Page 27: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/27.jpg)
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
![Page 28: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/28.jpg)
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.
![Page 29: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/29.jpg)
EXPERIMENTAL DESIGN
3 KEY ELEMENTS OF A WELL-DESIGNED EXPERIMENT
1.CONTROL2.RANDOMIZATION3.REPLICATION
![Page 30: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/30.jpg)
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
![Page 31: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/31.jpg)
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
![Page 32: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/32.jpg)
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)
![Page 33: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/33.jpg)
EXPERIMENTAL DESIGN: RANDOMIZATION
Randomization – process of randomly assigning subjects to different treatment groups
1.Completely Randomized Design
2.Randomized Block Design3.Matched Pairs Design
![Page 34: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/34.jpg)
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
![Page 35: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/35.jpg)
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
![Page 36: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/36.jpg)
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
![Page 37: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/37.jpg)
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
![Page 38: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/38.jpg)
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.
![Page 39: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/39.jpg)
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!
![Page 40: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/40.jpg)
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
![Page 41: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/41.jpg)
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
![Page 42: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/42.jpg)
![Page 43: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/43.jpg)
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
![Page 44: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/44.jpg)
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.
# # # # # # # # #
![Page 45: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/45.jpg)
SAMPLING TECHNIQUES
Convenience Sample – sample consists only of available members of population (not recommended)
![Page 46: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/46.jpg)
ASSIGNMENT
Pg. 25 #1 - #14, #17 - #26 (identify sampling technique)
Pg. 27 #29- #30
![Page 47: CHAPTER 1: INTRODUCTION TO STATISTICS SECTION 1.1: AN OVERVIEW OF STATISTICS](https://reader031.vdocument.in/reader031/viewer/2022012914/5a4d1b1c7f8b9ab059993a60/html5/thumbnails/47.jpg)
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