Statistical Sciences 2244A/B Chapter Notes - Chapter 7: Confounding, Dependent And Independent Variables, Statistic
22 May 2018
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Stats 2244
Samples and observational studies
Chapter 7
CHAPTER 7.1
Observation versus experiment
- There are 2 approaches to collecting data
1. Observation
o Subject of inquiry is disturbed as little as possible by the act of gathering information
o Observes individuals and measures variables of interest but does not attempt to
influence the responses
o Purpose: describe and compare existing groups or situations
o Ex: use this approach for things like heights of humans or behavior or animals in the
wild
o Poor way to study the effect of an intervention
o May reveal associations bw variables that are worth exploring further but rarely
provide evidence that one variable causes the effect on another
2. Experiment
o Actively impose some treatment or condition in order to observe the response
o Purpose: study whether the treatment causes a change in the response
o Use this when our goal is cause and effect
▪ To see a response to a change, we must actually impose the change
- Cofounding variables: 2 variables (explanatory variables or lurking variables) are cofounded
when their effects on a response variable cannot be distinguished from eachother
o Explanatory variable: a variable that may explain or influence changes in another
variable (aka independent variable)
o Lurking variable: variable that is not among the explanatory or response variables in a
study and yet may influence the interpretation of relationships among these variables
o Response variable: a variable that measures an outcome of a study (aka dependent
variable)
- Ex: they did a study and saw that women who took estrogen after menopause reduced their risk
of heart attacks →but women who elect to take hormones may be better informed and see
doctors more often and may do many other things to maintain their health
o So the effects of actually taking hormones are confounded with (mixed up with) the
characteristics of women who choose to take hormones
o explanatory variable = estrogen use after menopause
o lurking variable = how well they maintain their health
o response variable = risk of heart attack
- observational studies of the effect of one variable on another often fail to demonstrate causality
bc the explanatory variable is confounding with the lurking variables
CHAPTER 7.2
Sampling
- Population: entire group of individuals (not necessarily people) about which we want
information
- Sample: part of the population from which we actually collect info – use this info to draw
conclusions about the entire population
o Samples are representative of only the population from which they are taken
▪ Ex: if a clinical trial for a new drug is only done on men (the sample) then this
ensures drug effectiveness and safety for men alone
find more resources at oneclass.com
find more resources at oneclass.com
- Sampling design: describes exactly how to choose a sample from the population
- Steps in a proper sample design:
o 1) say exactly what population we want to describe
o 2) say exactly what we want to measure (give exact definitions of our variables)
- not all statistical studies use samples that are drawn directly from the entire population of
interest
o ex: studies of animal behavior cant realistically capture animals from their entire
wildlife habitat
o consequences of this: conclusions from the experiment cant always be extended to the
whole intended population
VIDEO:
- ex: if we are are interested in the average weight of all the fish in a lake
- population→collection of all the fish in the lake
- parameter()→average weight of all fish in the lake
- we get a sample of fish and use them to approximate the complete population
- the sample of fish must be caught in such a way that they are representative of the population!!!
o Ex: we wouldn’t want to just catch all the big ones
- Use the avg of the sample to approximate the avg of the population
- Suppose we catch a sample size of N=100 fish
- If we stack them in order from smallest to largest
- Based on our sample data, a reasonable approx. of (population avg weight)
- If we use the avg weight of all the fish in our sample would be the sample average or the sample
mean
- The value/quantity that we get from sample data is called a sample statistic
- The sample and the stats we do for that sample constitute the data available to us about the
population and parameters were interested in
- Then we apply statistical principles to extract meaningful information from the data
- So coming up with the average weight of all the fish in our sample is easy but we have no reason
to believe that the avg of our sample will be exactly equal to the population avg
- SO we have to translate sample information to the population level
- So lets say that the avg weigh of our population was 215ounces (avg weight of all the fish in the
sea) but our sample average aws 219ounces
- SO during experiments we see the sample average but we want to make statements about (avg
weight of population)
- SOOO in statistics, we get sample statistics from sample data and use them to approximate the
population parameters
- Goal in statistics: use sample data and sample statistics to construct an interval for a population
parameter, for which we can quantify our level of confidence (this is called a confidence interval)
OR to make a fformal decision about the value of a population parameter, using a hypothesis test –
with some stated level of confidence
CHAPTER 7.3
Sampling Designs
- Purpose of a sample: give us information about a larger population
- Statistical inference→ process of drawing conclusions about a population on the basis of sample
data (we infer info about the population from what we know about the sample)
Poor Sampling Designs
- Convenience sample
o Easiest but not the best sampling design
o Type of poor sampling design
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Population: entire group of individuals (not necessarily people) about which we want. Sampling design: describes exactly how to choose a sample from the population. Steps in a proper sample design: 1) say exactly what population we want to describe, 2) say exactly what we want to measure (give exact definitions of our variables) Video: ex: if we are are interested in the average weight of all the fish in a lake. Population collection of all the fish in the lake. Parameter( ) average weight of all fish in the lake. Suppose we catch a sample size of n=100 fish. If we stack them in order from smallest to largest. Use the avg of the sample to approximate the avg of the population. Based on our sample data, a reasonable approx. of (population avg weight) If we use the avg weight of all the fish in our sample would be the sample average or the sample mean.
