Transcript Getting Started Chapter 1

Getting Started Chapter 1
Observation that the firefly
population is declining
1.1 What is Statistics?
• Statistics – study of how to collect , organize, analyze,
and interpret numerical information from data.
• Individuals – people or objects in the study
• Variable – characteristic of individual to be measured
or observed
– Quantitative – has a value or numerical measurement for
which operations such as addition or averaging makes
sense
– Qualitative (or categorical) – places an individual in a
category or group (Gender, left vs right handed, senior vs
junior) Normally listed as percentages or proportions
1.1 What is Statistics?
• Population Data – data from every individual
of interest (census)
• Sample Data – data from only some of the
individuals of interest
• Ex p. 6
•
•
1.1 What is Statistics?
Levels of measurement
Nominal Level
–
–
•
consists of names, labels, or categories
cannot be put in order from smallest to largest
Ordinal
– Data that can be arranged in order
– Differences between data values cannot be determined or are meaningless
– Ex. Rankings in class or good, better, best
•
Interval
– data that can be arranged in order and differences between data values are meaningful
– Ex. Temperatures, dates
•
Ratio –
– data can be arranged in order; both differences and ratios of data values are meaningful. Data
has true zero
– Ex Length, age, salary
•
Helpful hint: to determine which level an example belongs to, start at the most
stringent, ratio
Ex p8 Homework p 10 1-9,
1.2 Random Samples
• Simple Random Sample (SRS)
– Sample size n from population
– Every sample of size n has an equal chance of
being selected
– Every member of the population has an equal
chance of being included in the sample
1.2 Random Samples
• Random Number Table
1. Number all members of population sequentially
2. Use a table, calculator, or computer to select
random numbers
3. Create sample by selecting members from
population with corresponding numbers
Random number Table
1.2 Random Samples
Methods for finding random sample
1. Table 1 in appendix (right after p 526)
depends on number of digits in total population
e.g. a) select 2 out of 10 items (use digits 0-9)
b) pick 5 out of 40 (use digits 01 to 40) 2
digits at a time
c)pick 25 out of 800 (use 3 digits 001 to 800)
2. Put names, numbers in a hat; pick out n names
3. Use randint or calculator
1.2 Random Samples
•
Sampling techniques
–
Simulation – numerical facsimile or representation of a realworld phenomenon
•
•
•
–
Heads or tails (0-4 H, 5-9 T) use table
Rolling a die (1-6 represent die value; ignore 0,7,8,9)
Computer driven (events following nuclear bomb) in class p17, 6
Stratified Sampling
1.
2.
Break population into strata – groups that show a common
characteristic (male/female or Junior/senior)
Take SRS from each strata
n usually based on proportionate size of strata
Advantage –can be better than SRS assuming strata all behave similarly
(assured of setting representative sample of all groups)
Can analyze within strata
1.2 Random Samples
• Sampling Techniques
– Systematic Sampling
• Arrange population in some natural sequential order (people
waiting in line)
• Start at random in front of line and select ever “nth” subject
– Cluster sampling
• Divide some area into sections
• Take SRS of sections to be analyzed
• Sample everyone in section
Advantage cheaper with some randomness
– Convenience sampling
• Sample from population members that are readily available
• First 20 people seen; your friends
• Homework p17 2,4,6,8,9,10,11
1.3 Introduction to Experimental Design
• Planning a Statistical Study
1. Identify individuals or objects of interest
2. Specify variables as sell as protocols for taking
measurements or making observations
3. Determine if you will use entire population or a
representative sample
If using a sample, decide on a viable sampling method
4. Address issues of ethics, confidentiality, privacy, getting
truthful responses etc in your data collection plan
5. Collect data
6. Use appropriate statistical methods to describe data and
to make conclusions (infer)
1.3 Introduction to Experimental Design
• Types of studies
– Census – measurements or observations from entire population are
used
– Sample – only part of the population is used
– Simulation – numerical facsimile of real world phenomena
• Real study will be dangerous (result of catastrophe)
• Cheaper to get rough idea of effect
– Observational Study – observations and measurements of individuals
are conducted in a way that does not change response or variable
being measured (poll, driving time to work)
– Experiment – impose a treatment or individuals in order to observe a
possible change in the response or variable being measured (e.g.
medical studies; effect of studying techniques or grades)
1.3 Introduction to Experimental Design
• Experiments – properly designed experiments require:
1. Control – A control group is needed to evaluate the relative
effect of the treatment. It helps to account for the influence
of other known or unknown variables that might be a
underlying cause of a change in response or experimental
group. These hidden variables are called lurking or
confounding variables. (ice cream sales vs. drowning)
• Placebo effect – some control groups are given a placebo
(fake or dummy pill that looks like treatment but is inactive).
Subject receives no treatment but believes they are and in
fact responds favorably.
2. Randomization – normally use volunteer to prevent bias,
individuals aree assigned at random to both control and
treatment groups. - helps to even out any differences in the
individuals
1.3 Introduction to Experimental Design
• After Control and Randomization…
3. Replication – use many patients in both groups to
reduce the possibility that differences in “pain
relief” for the 2 groups occurred by chance alone.
Other terms:
Double blind study – experiment where neither the
individuals in the study nor the observers (doctors)
know which treatment subjects are receiving.
This helps control for subtle biases that a doctor might
pass on to a patient.
Bias – Systematically favors certain outcomes
1.3 Introduction to Experimental Design
Diagramming an experiment:
Randomized two treatment experiment
Premise: doctors think magnets may reduce pain in
polio patients
Active Magnet
100 polio
Patients
50
randomly
assigned
50
evaluate pain
level
Placebo – inactive magnet
1.3 Introduction to Experimental Design
• Matched pairs Design
– Compare 2 treatments
– Subjects are matched in way to reduce variation
1. Allow subjects to receive 2 treatments one after another
Randomly assign which treatment is given first
Randomly
Assign
Workers
20
Treatment 1
70 °
20
Treatment 1
Treatment 2
90 °
70 °
Evaluate
productivity
Treatment 2
90 °
compare
productivity
Good example: weight loss programs weigh subject before and after.
1.3 Introduction to Experimental Design
• Block Designs
– Block Group of subjects that are known to be similar in
some way and are expected to affect response of variables
– Random assignment to treatments done within each block
– Typically separate men/women in medical treatments
Ex: 50 men and 80 women for blood pressure medicine
25
BP treatment
Compare
Men
25
Placebo
results
Subject
50
Randomized
40
80
Women
40
BP treatment
Placebo
Compare
results
1.3 Introduction to Experimental Design
Bias –systematically favors certain outcomes:
• Voluntary Response Sample: people choose themselves by responding
voluntarily Ex. Normally people with strong opinions (radio talk shows)
• Convenience Sampling: contacts individuals easiest to reach (surveys at
malls)
• Nonresponse: people refuse to answer questions
• Undercoverage: misses certain segments of population (phone surveys
miss people without phones)
• Response Bias: Respondent lies: behavior of interviewer could affect
respondent
• Poorly worded questions (or order of questions): can lead respondent to
certain responses
• Generalizing results beyond population surveyed
– Test on rats; will work on people
– Survey students of FRHS on presidential election to know next president