EXAM 1 Stats
range of values is:
(from sample statistic-margin of error) to (sample statistic +margin of error) usually defined as a 95% level of confidence
Statistical Investigation Questions:
1. Formulate investigative questions: 2. Collect/ Consider Data: data can be collected first hand of the data that has been collected points to consider: what types of variables are in the data, what are the possible outcomes for the variables, how was the data collected, what limitations exist in the data 3. Analyze the data 4. Interpret the results:
elon dining wants to determine how satisfied all elon students are with the dining options on campus. they decide to survey the first 100 students that visit mcewan dining hall on a monday morning
100 people people do not represent elon students and the population as a whole -not representative does not include people who never eat breakfast or those that do not live on campus
Self intrest bias
creating a study that favor's one's own position, for instance sending out a survey to set of republican voters to ask if they are voting for a republican senator -many advertisements contain data that claim to show that the product being advertised is superior to its competitors ex. 3 in 4 dentists recoment wigman's toothpaste (if a buisness invests intrest in a company sometimes use a bias sample) people who have an intrest in the outcome of a study have an incentive to use biased methods
continuous
data can take on any value in a given interval. For instance, weight is continuous because it can be reported at varying levels of precision. ex. For instance, if someone records their weight, they could stand on one scale and it says 150 lbs. Another scale may be 150.3 lbs, and an even more exact scale could say 150.33 lbs. Since weight can be reported as any value in an interval it is continuous.
quanitative
data consists of values representing counts or measurements ex. a height, a weight, length, speed, distance, percentage
retrospective
data has already been collected, simply observing what happened at some time in the past Ex. A contractor wants to determine what type of heating leads to higher bills, gas or electric. He asks 20 of his customers, 10 with gas and 10 with heat, to report how much they spent in utility bills over the past year.
why might it be difficult for the engineer to draw a simple random sample of blocks? describe a convenience sample he could draw.
difficult because heavy and difficult to move so you take the one on top, or on the edge because blocks on the bottom become weaker depending on how long they sit there.
response bias
exists when the answers on a survey do not reflect the true feelings of the respondent. responses can include: interviewer error: this is error that occurs in how the interviewer asks questions. interviewers should be well trained, so they are able to elicit truthful responses and make interviewees feel comfortable misrepresented answer: some survey questions results in responses that misrepresent facts or have responses that respondents simply do not know (data not reliable) wording of questions: the way a question is worded can lead to response bias. questions must be asked in a balanced form. do you oppose the reduction of estate taxes? should be written do you favor or oppose the reduction of estate taxes
cluster sampling
first divide the population into groups or clusters and select some of these clusters at random. then obtain the sample by choosing all the members within each of the selected clusters. ex. an irs researcher investigates false reporting of tip income by waiters and waitresses by surveying all waiters and waitresses at 20 randomly selected restaurants ex. divide the pop into groups baltimore, new jersey group. then select all the members within the clusters. choosing some of the cluster by random
prospective
following a group of subjects for an extended period of time ex. Beginning in 1948, 5209 men and women from the town of Framingham, Massachusetts were given physical exams and lifestyle interviews, to discover different factors that increase the risk of heart disease.
systematic sampling
generate a random number then every kth object in the poplation ex. at an automobile factory, every 5th car is chosen to undergo a detailed check of the steering system so every 5th 10th 15th and so on
ex problem: Do you believe in ufo's: a june 2019 poll found 49% of americans believing there are "people somewhat like ourselves" living on other planets. a much larger percentage, 75% said that "life of some form" exists elsewhere in the universe identity the following: goal of the study, population, sample, parameter, statistic
goal of the study: to determine what percentage of americans believe if life exists on other planets population: americans sample: whoever answered the poll the 10,594 faculty and staff members interviewed parameter: 49% and 75% statistic: 28% feel passed over for a promotion or opportunity
bias
if it design or conduct tends to favor certain results
left skewed
if its values are more spread out on the left side
right skewed
if its values are more spread out on the right ride
double blind
if neither the participants nor any experimenters know who belongs to the treatment group and who belongs to the control group ( the experimenter or researcher also does not know)
single blind
if the participants do not know whether they are members of the treatment group or members of the control group, but the experimenters do know (the participants do not know but the researchers do)
population
in a statistical investigation, the population is the complete set of people or things being studied
variables of intrest
in a statistical study are the items or quantities that the study seeks to measure ex. goal of the study/ how could I measure
margin of error
in a statistical study is used to describe the range of values
control group
in an experiment is the group of subjects who do not receive the treatment being tested (serve as baseline)
treatment group
in an experiment is the group of subjects who recieve the treatment being tested (ex. clinical drug trial is the group of people recieving this drug tried out)
quanitative can be
interval or ratio and discrete and continuous
representative sample
is a sample in which the relavent characteristics of the sample members are generally the same as the characteristics of the (population) *in order to make claims (or parameters) about the population of intrest based on the sample, it is inherent that the sample is as representative of the population as it can be
convinience sample
is a sample that is not drawn by a well defined random method. in some cases it is difficult or impossible to draw a sample in a truly random way ex. a construction engineer has just recieved a shipment of 1000 concrete blocks, each weighing approximately 50 pounds. the blocks have been deliveered in a large pile. the engineer wants to investigate the crushing strength of the blocks by measuring the strength of a sample of 10 blocks
explanatory variable
is a variable that may explain or cause the effect
response variable
is a variable that responds to the changes in the explanatory variable (what has happened outcomes that are studying)
matched pairs
is an experimental design in which the subjects are paired up. The pairs are selected so that they are related in some way (i.e., the same person before and after a treatment, twins, husband and wife, same geographical location, and so on). There are only two levels of treatment in a matched-pairs design.
completely randomized design
is one in which each subject is randomly assigned to a treatment.
preventing bias
is one of the greatest challenges in statistical research
simple random sample
is one where every sample of size n is equally likely to be chosen using random number generators, so that an individual in a population has the same probability of being chosen as any other. ex. there are 300 employees in a company. the human resources department wants to draw a SRS of 20 employees to fill out a survey about their jobs. They make a list of all 300 employees and number them 1-300. They then use a random number generator to randomly choose 20 numbers znd send the survey to those 20 employees
ordinal
level of measurement applies to qualitative data that can be arranged in some order. usually, computatations with this data is not done. ex. class rank at elon first year, second year, third year, fourth year,
ratio
level of measurement applies to quanitative data in which both intervals and ratios are meaningful. multiplication and division can be preformed. A value of zero means the absense of the quanity.
interval
level of measurement applies to quanitative data in which intervals are meaningful, but ratios are not. Addition and subtraction can be preformed. Zero does not mean the absense of the quantity. ex. temperature 0 degrees does not mean there is a sense of temperature
nominal
level of measurement is characherized by data that consists of names, labels, or categories only. these data are qualitative and cannot be ranked or ordered ex. haircolor
confidence interval
likely to contain the population parameters
sampling bias
means that the technique is used to obtain the sample's individuals tends to favor one part of the population over another sampling bias also results due to undercoverage which occurs when the proportion of one segment of the population is lower in a sample than it is in the population (should be representative of population of interest) It is often difficult to gain an entire list of a population ex. random telephone surveys often exclude homes that do not have phones or homes that are cell phone only homes. it also excludes homeless people
cross sectional
measurements taken at one point in time Ex. A doctor randomly chooses 500 of her patients to take a urine test to detect their levels of bisphenol A, a chemical found in the linings of food and beverage containers. She found that those with higher levels of the chemical were more likely to have diabetes.
campus recreation and wellness wants to determine how often faculty on campus use the fitness center. over the course of a week, they count how often faculty members visit the center, and average the number of visits per faculty member.
more representative because it is having and creating an average. potentially not representative. this is counting those faculty members that use the fitness center not all faculty. there are plenty of faculty members who do not use it at all, so they would not be included in this count. perhaps a small survey to all faculty would be better.
In a survey conducted by representatives of the nuclear power industry, people were asked the question: "Do you favor the construction of nucelaer power plants in order to reduce our dependence on foreign oil?" A group opposed to the use of nuclear power conducted a survey with the question: "Do you favor the construction of nuclear power plants that can kill thousands of people in an accident?" Do you think that the percentage of people favoring the construction of nuclear power plants would be about the same in both surveys? Would either of the two surveys produce reliable results? Explain
no because the way the questions are worded can leave people to think differently using the social acceptility bias
observational study
no influence on the subjects simply observing what happens. researchers observe or measure characteristics of the subjects, but do not attempt to influence or modify these characteristics.
uniform distribution
no mode
qualitative can be
nominal or ordinal
A bank sent out surveys to a SRS of 500 customers asking whether they would like the bank to extend its hours. 80% of those surveyed said they would like the bank to extend its hours. Of the 500 surveys sent out, 20 were returned.
non response
Nonresponse bias
not everyone who is in the sample answered ex. a survery not answered by everyone who was sent the survey -exists when individuals selected to be in the sample who do not respond to the survery have different opinions from those who do
statistics
numbers describing characteristics of the sample found by summarizing raw data
experimenter effect
occurs when a researcher or experimenter somehow influences subjects through such factors as facial expression, tone of voice, or attitude
single peaked distribution
one mode
qualitative
or categorical data consists of values that can be placed into non numerical categories ex. haircolor, year at elon, freshman, zipcode, identity, a location
subject
people, animals or other living things, or objects chosed for the sample if the subjects are people, then they may be called the participants in the study
When creating graphs to display data, the type of variable must be determined. Not every type of graph is appropriate for every variable type. • Considerations: • Quantitative or Qualitative
qualitative the number of categories if quanitative, discrete or continous data as well as the range of data
Graphs for quanitative data
quanitative data can be presented using the folowing charts 1.histograms 2. bargraphs 3. scatterplots 4. line graphs note: scatterplots are not always appropriate for discrete data
placebo effect
refers to the situation in which patients improve simply because they believe they are receiving a useful treatment
A sign in a restaurant claims that 95% of their customers believe them to have the best food in the world.
self intrest
To estimate the prevalence of illegal drug use in a certain high school, the principal interviewed a SRS of 100 students and asked them about their drug use. Five percent of the students acknowledged using illegal drugs.
social acceptability
confounding variables
some variable not accounted for in a study that has an influence on the outcomes. is a variable that is related to both the treatment and the outcome. when a confounding variable is present, it is difficult to determine whether differences in the outcome are due to the treatment or the confounding variable ex. taking tests online provide better results than on paper.
experiment
study where the variables are manipulated in some way by the researcher ex. clinical drug trial, testing new drug, to see its impact on people)
will a new drug help prevent heart attacks?
subject: people ev: what type of drug rv: response to this new drug to see if it will help pervent heart attacks if they get them
Voluntary response bias
survey is one in which people are invited to participate in order to express their opinions often people with strong opinions are likely to participate. thus the opinions may not reflect those of the entire population ex. reviewing restaraunts (with their strong opinions)
example: a braun research poll asked 1,000 office workers how they wake up in time for work; 60% of them said they used an alarm clock.
the margin of error was 3 percentage points. 57%,63% is the confidence interval or range of values for this study
Observational Study vs Experiment
• In an observational study, if an association exists between an explanatory variable and response variable, the researcher cannot claim causality, i.e. that the explanatory variable caused the response to happen. • To demonstrate how changes in the explanatory variable cause changes in the response variable, the researcher needs to conduct an experiment.
Cautions about Graphics
• Not all graphics we see display accurate information.
Graphs for Qualitative Data
• Qualitative (or categorical) data usually has a count associated with it. For instance, the number of home states represented at Elon. • The following graphs are appropriate for categorical data: 1. bar graphs 2. pareto graphs (a special bar graph where the bars are ordered from smallest to largest, or vise versa) 3. pie/ circle graphs or charts
axis scaling
• The scale we choose for the vertical axis can also distort the data. The two graphs above are showing the same data.
parameter
are specific numbers describing characteristics of the population
treatments
are the procedures applied to each subject in a study. there are always two or more treatments. the purpose is to determine weather the choice of treatment affects the outcome.
Statistical Problem Solving Example
A friend wanted to determine the number of hours they sleep on average. They wear a fitbit watch every day that records the amount of time they sleep. they found that during the week of July 31-Aug 6 they slept the following amount of time. 3 hours 30 minutes, 6 hr 41 min, 8hr 30 min, 9hr 24 min, 8hr 8 min, 5 hr 41 min Calculated the mean and found that they sleep on average 7 hours a night, since the recommended amount of sleep for adults is between 7-9 hours of sleep a night, their sleep pattern is fine problem solve statistical problems: formulate statistical questions: is my friend getting enough sleep at night? collect/consider data: he used his fitbit watch and wrote down how many hours and minutes he slept every night for 7 days. Limitations could be the battery could die, forget to wear it, it could malfunction. analyze the data: I compared the data against the recommended sleep for adults Interpret the results: because the reccomended sleep for adults is 7-9 hours, my friends sleep pattern is normal How might you have engaged in the cycle differently? Can you pose any more questions? Should my friend have collected more data etc? why is your sleep pattern so different between days, and why did you only get 3.5 hours of sleep on the first day. More data would have been useful because the data is so different we need more data.
discrete
For instance, if a student reports how many days they missed in a class in a given semester, this number can only be reported as a whole number. A student can report they have missed 2 days, but reporting that they have missed 2.47 days does not make sense.
Goals scored in a season by a soccer player Volume of water lost each day through a leaky faucet Length (in minutes) of a country song Number of Sequoia trees in a randomly selected acre of Yosemite National Park Temperature on a randomly selected day in Memphis, TN Points scored in an NCAA basketball game
Goals scored in a season by a soccer player -discrete why because you cannot score half of a goal Volume of water lost each day through a leaky faucet- continous why because it is continously changing and will keep going even if you turn on a fauset Length (in minutes) of a country song- continuous not whole minutes Number of Sequoia trees in a randomly selected acre of Yosemite National Park discrete: cannot have half of a tree Temperature on a randomly selected day in Memphis, TN continuous why because it will fluctuate and will not be one temperature Points scored in an NCAA basketball game discrete why because you cannot score half of a point
Heights of 1,000 randomly selected adult women Hours spent watching football on TV in January for 1,000 randomly selected adult Americans Weekly sales throughout the year at a retail clothing store for children The number of people with particular last digits (0 through 9) in their Social Security Numbers
Heights of 1,000 randomly selected adult women- one mode, single peak Hours spent watching football on TV in January for 1,000 randomly selected adult Americans- bimodal people that do or do not watch it could also be one mode Weekly sales throughout the year at a retail clothing store for children- trimodal, likely to have several modes The number of people with particular last digits (0 through 9) in their Social Security Numbers- uniform should have no mode, uniformly distributed
Histograms vs. bar charts
• Histograms and bar charts are often confused with one another since they both use bars. • Bar charts can be used for categorical or quantitative data, but histograms are only to be used with quantitative data. -histograms have gaps bar charts do not
• Problem A farmer wishes to determine the optimal level of a new fertilizer on his soybean crop. Design an experiment that will assist him. Identify the problem to be solved. Determine the factors that affect the response variable. Determine the number of subjects. Determine the level of the factors (control and placebo, or various levels of a medicine) Conduct the experiment Test the claim, make an inference from the results to the general population
Identify the problem to be solved identify optimal level of fertilizer for growing soy beans Determine the factors that affect the response variable. crop yield: fertilizer, precipitation Determine the number of subjects. control are fertilizer: things like precipitation, sunlight, type of soil, plant Determine the level of the factors (control and placebo, or various levels of a medicine) treatment A: soybean plants receive no fertilizer treatment B: 20 soybean plants receive 2 teaspoons of fertilizer every 2 weeks treatment C: 20 soybeans plants receive 4 teaspoons of fertilizer every 2 weeks Conduct the experiment number of plants 1-60 use random number generator to choose 20 numbers for treatment A the next 20 for treatment B, and the next 20 for C at the end of crop season we begin to determine the crop Test the claim, make an inference from the results to the general population At the end of the experiment, we will compare the crop yield, if the treatment C does better, we may encourage the farmer to try that treatment for all of his plants during his next planting.
The Steps to Designing an Experiment
Identify the problem to be solved. Determine the factors that affect the response variable. Determine the number of subjects. Determine the level of the factors (control and placebo, or various levels of a medicine) Conduct the experiment Test the claim, make an inference from the results to the general population
classify if these are quanitative or qualitative Nation of origin Number of siblings Grams of carbohydrates in a doughnut Number on a football player's jersey Number of unpopped kernels in a bag of popcorn Assessed value of a house Phone number Student ID number
Nation of origin- qualitative (data) Number of siblings-quanitative (representing data) Grams of carbohydrates in a doughnut-quanitative measurement Number on a football player's jersey- qualitative (number describing) Number of unpopped kernels in a bag of popcorn -quantitative (measurement) Assessed value of a house- quanitiative (number holds a value) Phone number-qualitative (identifies and describes you) Student ID number- qualitative (identifies and describes you)
Nation of origin Movie ratings of one star through five stars. Volume of water used by a household in a day Year of birth of college students Highest degree conferred (high school, bachelor's, and so on) Eye color
Nation of origin- qualitative, and nominal Movie ratings of one star through five stars. quanitative and interval and ratio: compare the ratings or ordinal and qualitative Volume of water used by a household in a day: quanitative and ratio and interval Year of birth of college students: quanitative and ordinal Highest degree conferred (high school, bachelor's, and so on) qualitative and ordinal Eye color: qualitative and nominal Assessed value of a house: quanitative and interval and ratio Time of day measured in military time. interval/ratio or ordinal
Social Acceptibility Bias
People are reluctant to admit to behavior that may reflect negatively on them. This can affect the results of surveys. For instance, it might seem reasonable to ask " did you vote in the last presidential election" many people will say yes even if they didnt because of the social stigma that may come with not voting could be rephrased to "as in the 2016 presidential election between hilary clinton and donald trump, did things come up that kept you from voting, or did you happen to vote? people are more likely to answer truthfully
Pictographs
Pictographs are graphs embellished with additional artwork. This may make them more visually appealing, but it can also distract or mislead. Consider the pictograph that follows. What are some problems with this graph? the picture makes it hard to read, also like overlapping, size of character, no contrast in colors, and do not know the exact average makes females in India look smaller What's another way we could display this data? bar graph would be a better representation
to counteract non response bias
callbacks can be conducted for those that do not respond (people get surveys but choose not to respond) -rewards, such as cash payments, also can be a way to incentivize answering surveys, questionaires, interviews. (offer a reward 10 dollar starbucks gift card etc)
For each distribution would you expect the distribution to be symmetric, left-skewed or right-skewed? The reaction times of 500 randomly selected drivers, measured under standard conditions. The heights of 500 male students, half of whom are adults while the other half are 8 years old. The weights of cars in a fleet consisting of 500 compact cars and 50 delivery trucks. The ages of people who visit Disneyworld. The ages of 1,000 randomly selected dementia patients.
The reaction times of 500 randomly selected drivers, measured under standard conditions. - one mode symmetrical: random selected drivers new drivers and old driving people The heights of 500 male students, half of whom are adults while the other half are 8 years old. - bimodal and symmetric 8 year old boys and adult men would be further up The weights of cars in a fleet consisting of 500 compact cars and 50 delivery trucks. 2 modes symmetric The ages of people who visit Disneyworld. right skewed one mode, most of young people who go there The ages of 1,000 randomly selected dementia patients. left skewed, one mode: majority dementia patients are older
lesson 1:b
components of a statistical investigation, definitions
cohort study
a group of subjects (the cohort) is studied to determine whether various factors of interest are associated with an outcome
A big sample does not make up for bias
a sample is useful only if it is drawn by a method that is likely to represent the population well if a biased method is used to draw a sample, drawing a bigger sample that still used that method doesn't help
sample vs random sample
a simple random sample is often the most representative sample, but not always. likewise, a convenience sample is often not very representative, but it can be the representativeness of the sample is really determined after the sample is chosen the term random sample is often used to describe a sample when the sample hasn't been chosen at random at all.
placebo
a treatment that should have no effect, such as a sugar pill in a drug trial (on participants =no major impact)
stratified sampling
the population is divided into groups, called (strata) aka teers , where the members of each stratum are similar in some way. then a (subset) is chosen from each strata to make up the new sample ex. seperate group from baltimore and a group from jersey that a subset is chosen like a girl from baltimore and a girl from jersey ex. elon dining wants to determing the satisfaction rating of all elon students on campus. they obtain a list of students seperated by year in school. (first year, sophmores, juniors, seniors) they then select 100 random students from each year in school and send the survey to those 400 students
goal of the study:
the questions not just a yes or no question but are investigating some phenomenon, and is the complete set of people or things being studied
shapes of distributions
the shape distributin is often described with three characteristics: 1. a number of modes 2. symmetry or skewes 3. variation
sample
the subset of the population from which data are actually obtained
trimodal distribution
three modes (peaks)
bi modal distribution
two modes a peak in the graph, distinct peak
case control study
two samples of interest (one with variable of interest, other without) ex. a sample could have a specific disease the other could not • Example: S.S. Nielsen and colleagues conducted a case-control study to determine whether exposure to pesticides is related to brain cancer in children. • They sampled 201 children under the age of 10 who had been diagnosed with brain cancer and 285 who had not.
To determine his constituents' feelings about an election reform, a politician sends a survey to people who have subscribed to his newsletter. More than 1000 responses are received.
voluntary response
• All good graphs should be labeled properly to honestly and accurately portray the data included within. Every graph should have:
• A ___title__________ explaining what is being shown • A ____labeled__________ vertical axis with appropriately spaced tick marks • A __labeled_____________ horizontal axis with appropriate tick marks • A key or____legend___________ if necessary to understand the graph.
box plots
• A box plot is a type of graph that displays the 5-number summary of a data set and shows the skew of data. • Box plots can only be used to display ___quanitative___________ data. 1. min 2. Q1 lower quartile 3. Q2 median 4. Q3 upper quartile 5. Max inter quartile range is the difference between Q1 and Q3
symmetry
• A distribution is ____symmetric__________ if its left half is a mirror image of its right half.
dot plots
• A dot plot is a graphical display of data using _______dots_________. • Dot plots can display quantitative and qualitative data on the ______horizontal__________ axis. • For instance, the dot plot below shows the number of minutes it takes people to eat breakfast. How many people take 9 minutes to eat breakfast?
A Matched-Pairs Design
• An educational psychologist wants to determine whether listening to music has an effect on a student's ability to learn. Design an experiment to help the psychologist answer the question. • We will use a matched-pairs design by matching students according to IQ and gender (just in case gender plays a role in learning with music). • We match students according to IQ and gender. For example, we match two females with IQs in the 110 to 115 range. For each pair of students we flip a coin to determine which student is assigned a quiet room to study and the other in a room with music playing. • Each student will be given a statistics book and told to study section 1.1. They will then be given a short quiz in the same testing center. We then compare the differences in the scores of each matched pair. Any differences in scores will be attributed to the treatment.
Does regularly taking aspirin help protect people against heart attacks? The Physicians' Health Study I was a medical experiment that helped answer this question. The subjects in this experiment were 21,996 male physicians. Half of these subjects took an aspirin tablet every other day and the remaining subjects took a dummy pill that looked and tasted like the aspirin but had no active ingredient. After several years, 239 of the control group but only 139 of the aspirin group had suffered heart attacks. This difference is large enough to provide convincing evidence that taking aspirin does reduce heart attacks. • Describe the population of interest for this study. Describe the sample. • Who are the subjects? • What are the response and explanatory variables? • Is this an observational study or an experiment? • Describe any blinding in the study. Describe the treatment group and control group. • Describe any confounding variables that may be present in this study.
• Describe the population of interest for this study. Describe the sample. the population of intrest is the people at risk for heart attack specifically men • Who are the subjects? the people specifically 21,996 male physicians participated in this study • What are the response and explanatory variables? explanatory variable is the asprin tablet/ taking it response: if someone had a heart attack • Is this an observational study or an experiment? is an experiment because it is a group of people with treatment groups and control as well, by the researcher • Describe any blinding in the study. Describe the treatment group and control group. no blinding is described treatment the ones that took the asprin, control: the group that took the dummy pill • Describe any confounding variables that may be present in this study. all physicians have additional knowledge -diet exercise over time would impact you from having a heart attack -all male
Lipitor is a cholesterol-lowering drug. In a Diabetes study, the effect of Lipitor on cardiovascular disease was assessed in 2838 subjects, ages 40 to 75, with type 2 diabetes, without prior history of cardiovascular disease. In this placebo-controlled, double-blind experiment, subjects were followed for 4 years. The response variable was the occurrence of any major cardiovascular event. • Lipitor significantly reduced the rate of major cardiovascular events (83 events in the Lipitor group versus 127 events in the placebo group). There were 61 deaths in the Lipitor groups versus 82 deaths in the placebo group. The Characteristics of an Experiment • What does it mean for the experiment to be placebo-controlled? • What does it mean for the experiment to be double-blind? • What is the population for which this study applies? What is the sample? • What are the treatments? • What is the response variable?
• What does it mean for the experiment to be placebo-controlled? control group is given a placebo instead of the drug see if the drug works • What does it mean for the experiment to be double-blind? is when people in study and people administering neither knows who is getting the actual treatment could minimize • What is the population for which this study applies? What is the sample? 2838 subjects with ages 40 to 75 with type 2 diabetes have prior knowledge of cardiovascular disease • What are the treatments? receiving the lipitor or a placebo daily of 10 mg • What is the response variable? any major cardiovascular event: such as a stroke or not