Transcript Response

Lecture 1: Chapters 1, 2
Introduction, Sampling
Variable
Types and Roles
Summarizing Variables
4 Processes of Statistics
Data Production; Sampling
©2011 Brooks/Cole, Cengage
Learning
Elementary Statistics: Looking at the Big Picture
1
Example: Identifying Types of Variables

Background: Consider these headlines…





Dark chocolate might reduce blood pressure
Half of moms unaware of children having sex
Vampire bat saliva researched for stroke
Question: What type of variable(s) does each article
involve?
Response:



Dark chocolate or not is categorical;
blood pressure is quantitative.
Being aware or not of children having sex is categorical.
Bat saliva or not is categorical;
stroke recovery is probably categorical.
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
Practice: 1.2 p.11
L1.2
Example: Categorical Variable Giving Rise to
Quantitative Variable

Background: Individual teenagers were surveyed about drug
use.

Question: What type of variable(s) does this involve?
Response:
 marijuana or not is categorical
 harder drugs or not is categorical

©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
Practice: 1.6a p.12
L1.4
Example: Categorical Variable Giving Rise to
Quantitative Variable

Background: Percentages of teenagers using marijuana or
hard drugs are recorded for a sample of countries.

Question: What type of variable(s) does this involve?
Response:
 percentage using marijuana is quantitative
 percentage using harder drugs is quantitative

©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
Practice: 1.6b p.12
L1.6
Example: Categorical Variable Giving Rise to
Quantitative Variable

Background: Percentages of teenagers using marijuana or
hard drugs are recorded for a sample of countries.

Question: What type of variable(s) does this involve?
Response: (another perspective)
 type of drug (marijuana or harder drugs) is categorical.
 % using the drugs is quantitative.

©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
L1.8
Example: Quantitative Variable Giving Rise to
Categorical Variable



Background: Researchers studied effects of dental X-rays
during pregnancy.
 First approach: X-rays or not; baby’s weight
 Second approach: X-rays or not; classify baby’s wt. as at
least 6 lbs. (considered normal) or below 6 lbs.
Question: What type of variable(s) does each approach
involve?
Response:
 X-rays or not is categorical; baby’s weight is quantitative
 X-rays or not is categorical;
baby’s wt. at least 6 lbs. or below 6 lbs. is categorical
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
Practice: 1.8 p.12
L1.10
Summarizing Data

Categorical data:




Count: number of individuals in a category
Proportion: count in category divided by total
number of individuals considered
Percentage: proportion as decimal  100%
Quantitative data: mean is sum of values
divided by total number of values
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
L1.12
C or Q?

STATE EXAM





School 1 – 72% passed School 2 – 81% passed
School 3 – 64% passed School 4 – 58% passed
Is this C or Q?
Quantitative – Average the %
Can Quantitative data be summarized as C?
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
L1.13
Roles of Variables
When studying relationships between two
variables, we often think of one as
explanatory and the other as response.
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
L1.14
Example: Identifying Types and Roles



Background: Consider these headlines-- Men twice as likely as women to be hit by lightning
 Do Oscar winners live longer than less successful peers?
Questions: What types of variables are involved?
For relationships, what roles do the variables play?
Responses:
 Gender is categorical and explanatory;
Hit by lightning or not is categorical and response.
 Winning an Oscar or not is
categorical and explanatory;
Life span is quantitative and response.
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
L1.15
Practice: 1.17 p.13
Example: More Identifying Types and Roles



Background: Consider these headlines-- 35% of returning troops seek mental health aid
 Smaller, hungrier mice
 County’s average weekly wages at $811, better than U.S.
average
Questions: What types of variables are involved?
For relationships, what roles do the variables play?
Responses:
 Seeking mental health aid or not is categorical.
 Size is quantitative and explanatory.
Appetite is quantitative and response.
 Wages are quantitative.
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
L1.17
CAUSATION

Association DOES NOT imply
CAUSATION.
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
L1.19
Definitions





Sample
Population
Random
Probability
Statistical Inference
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
L1.20
Four-Stage Process - Key words




Data Production – How you collect
Displaying and Summarizing –
Organize and show data
Probability - Chance
Statistical Inference - Conclusion
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
L1.21
Data Production


Use a good sampling design to get an
unbiased sample so we can ultimately
generalize from sample to population (Part 4)
Create a good study design so what we learn
is unbiased summary of what’s true about the
variables in our sample (Part 2)
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
L1.22
Definition
Bias: tendency of an estimate to deviate in one
direction from a true value
Some sources of bias:
 selection bias: due to unrepresentative sample,
rather than to flawed study design
 sampling frame doesn’t match population
 self-selected (volunteer) sample
 haphazard sample
 convenience sample
 non-response

©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
L1.24
Example: Bias in Sampling

1.
2.
3.


1.
2.
3.
Background: Professor seeks opinions of 6 from 80 class
members about textbook…
Have students raise hand if they’d like to give an opinion
Sample the next 6 students coming to office hours
our “random”
Pick 6 names “off the top of his head” [Like
number selection.]
Questions: Is each sampling method biased? If so, how?
Responses:
Biased---Volunteer sample, favors people with strong
positive or negative opinions.
Biased---Convenience sample, includes too many students
who find the book difficult to understand.
Biased---Haphazard sample, may be unrepresentative due to
subconscious tendencies to pick certain types of student.
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
Practice: 2.6 p.26
L1.25
Example: More Bias in Sampling

1.
2.


1.
2.
Background: Professor seeks opinions of 6 from 80 class
members about textbook…
Assign each student in classroom a number (1, 2, 3, …),
then use software to select 6 at random…
Take a random sample from the roster of students enrolled;
mail them anonymous questionnaire…
Questions: Is each sampling method biased? If so, how?
Responses:
Biased---Sampling frame doesn’t match population
(students attending are different from all students enrolled).
Biased---Non-response may lead to a non-representative
sample: only students who feel strongly may take the
trouble to complete the questionnaire.
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
L1.27
Definitions



Probability sampling plan incorporates
randomness in the selection process so rules
of probability apply.
Simple random sample is taken at random
and without replacement.
Stratified random sample takes separate
random samples from groups of similar
individuals (strata) within the population.
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
L1.29
Definitions



Cluster sample selects small groups
(clusters) at random from within the
population (all units in each cluster included).
Multistage sample stratifies in stages,
randomly sampling from groups that are
successively more specific.
Systematic sampling plan uses methodical
but non-random approach (select individuals
at regularly spaced intervals on a list).
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
L1.30
SAMPLE TYPES

Which type of sampling plan is used?




A random sample of classes is taken from all
classes meeting at the university and they
interview every student in the selected classes.
Cluster Sample
Separate students by majors and choose a random
sample of students in each major.
Stratified Sample
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
L1.31
SAMPLE TYPES

Which type of sampling plan is used?




Separate students in schools (art, math, science,
english, etc.). Select random majors in each
school. Select random classes in each major.
Use every student in each of those classes.
Multi-stage Sample
Assign every student a number. Use a random
number generator to select students.
Simple Random Sample
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
L1.32
Sample Size

P. 22: Example 2.3





What is wrong with 1, 2, 3? Why?
1) too small and they are biased (they wouldn’t be
eating there if they don’t like it there.)
2) Biased (same)
3) too small
P. 27: 2.5, 2.13
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
L1.33
Lecture Summary (Introduction, Sampling)

Variables



Summaries






Categorical or quantitative
Explanatory or response
Categorical: count, proportion, percentage
Quantitative: mean
4 Processes: Data Production, Displaying and
Summarizing, Probability, Inference
Data Production: need unbiased sampling and
unbiased study design
Types of Bias
Types of Samples
©2011 Brooks/Cole,
Cengage Learning
Elementary Statistics: Looking at the Big Picture
L1.34