Exam 1 study guide PDF

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Study guide from exam 1- also helpful for the final exam!!...

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Exam 1 Study Guide Test 1: Chapter 1-6 Chapter 1: The Benefits and Risks of Using Statistics ● Statistics: a collection of procedures and principles for gaining and analyzing information in order to help people make decisions when faced with uncertainty ○ Why is it important?: it will allow you to critically evaluate results of studies, detect misleading statistics and recognize biased samples. ● Uses of Statistics: ○ Finding differences and relationships and determining whether or not they are real ○ Collecting and summarizing information ● To Conduct a Statistical Study Properly One Must: ○ 1. Get a representative sample ○ 2. Get a large enough sample ○ 3. Decide whether the study should be an observational study or a randomized experiment ● 1. Get A Representative Sample: ○ Sample: those actually studied ○ Population: larger group from which sample was chosen ○ GOAL: researchers want to extend results beyond just the sample ● 2. Get A Large Enough Sample: ○ The more variable the individuals are within each group → larger sample needed to detect a difference ○ Sample size needed depends on: Magnitude of the difference or relationship & natural variability among the measurements ■ Little natural variability→ small sample is adequate ■ Lots of natural variability → large sample needed ● 3. Observational Study or Randomized Experiment: ○ Observational Study: merely observe things about our sample ■ Cannot determine conclusions ○ Randomized Experiment: Randomly assign participants to one of various treatment groups ■ Can determine conclusions ■ Random Assignment: randomly assigning individuals to receive different treatments→ the groups should be similar on everything except the treatment they are given ■ If a study is conducted using a representative sample or a large enough group → results from the sample can be applied to the population as well ● Improper Statistics

○ Sample not representative of population ○ Using wrong units: should report the results per person or per unit, not the group as a whole ○ Making a causal connection from an observation study ● Remember!! ○ Results of a study are never enough! ○ You need to know how data was collected & who was asked Chapter 2: Reading the News ● Data: a collection of numbers or other pieces of information to which meaning has been attached ○ News rarely presents actual data→ don’t always believe what you read ● 7 Critical Components!!- these should be included in news reports of statistical studies ○ 1. The source of the research and of the funding ■ If funded by an organization that would likely have a strong preference for a particular outcome → not a sound study ○ 2. The researchers who had contact with the participants ■ Participants often give answers to please others ■ It’s best if the person collecting the data doesn’t know the desired outcome ○ 3. The individuals or objects studied and how they were selected ■ Results extend only to individuals similar to those in the study ■ How participants were enlisted- volunteers ■ Volunteer Response: volunteers are likely to be biased because only those who feel strongly about the issues are likely to respond→ cannot be extended to any larger group

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● VOLUNTEER RESPONSE & SAMPLE: CAN ONLY BE APPLIED TO THOSE IN THE STUDY 4. The exact nature of the measurements made or questions asked ■ Some things are difficult to measure- need exact definitions being used ■ wording/ ordering of questions influences answers 5. The setting in which the measurements were taken ■ When and where measurements were taken & how respondents were contacted (ie: landlines would exclude those without or if survey taken on a website rather than in a lab, respondents might feel more anonymous) ■ A study can be biased by timing 6. Differences in the groups being compared, in addition to the factor of interest ■ If 2 or more groups are being compared on a factor of interest, it’s important to consider other ways in which the groups may differ that might influence the comparison 7. The extent or size of any claimed effects or differences

■ Without knowing the size of the effect or difference, it is hard to assess if the results are of practical importance ■ It’s important to know the details of how a study was conducted so you can decide if the results apply to you ■ If the study does apply to you, it’s important to know how large the difference found was ● How Research Results are Originated & How They Make it into the News ○ Origins of news stories ■ Academic conferences ■ Published articles in scholarly journals ■ Government and private agency research reports ■ University media office ○ Meaning attached to data and results depends on how well info was obtained & summarized Chapter 3: Measurements, Mistakes, and Misunderstandings ● Problems with Measuring- simple measures don’t exist ○ It’s important to understand how the information was collected & what was measured or asked ○ It is difficult to precisely define and measure some things & measurements differ depending on the situation ● Wording! Simple changes of words can make a big difference in the outcome of a survey! ● Pitfalls when asking questions: ○ Deliberate Bias: Questions can be deliberately worded to support a certain cause ■ Do you AGREE that→ usually people just say yes unless strongly against ○

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■ Indicating a desired answer Unintentional Bias: Questions are worded such that the meaning is misinterpreted by many ■ Do you use drugs?- what kind ■ What is the most important date in your life?- calendar date or like wedding day ■ The same word can have MULTIPLE meanings Desire to Please: Most respondents have a desire to please the person who is asking the question ■ People tend to understate responses about undesirable social habits ■ People that smoke cigarettes doesn’t match cigarette sales Asking the Uninformed: People do not like to admit they don’t know what you’re talking about Unnecessary Complexity: Questions may be easy to misinterpret- not simple enough ■ Too confusing questions: double negatives

■ Asking more than one question at once ○ Ordering of Questions: The order in which questions are presented can change the results ■ One question can require respondents to think about something they may not have otherwise considered, which can change the results ■ Survey respondents assume that questions on the survey are related to each other, so they will interpret later questions in context ○ Confidentiality vs. Anonymity: People answer differently based on the degree to which they are anonymous ■ Confidentiality: researcher knows the identity of respondent ■ Anonymity: researcher doesn’t know the identity of respondents ■ → surveys on private matters like sexual behavior and income are hard to conduct accurately ■ It is easier to try to ensure confidentiality than true anonymity ● Questioning Formats: ○ Open Question: respondents are allowed to answer in their own words ■ Advantages: respondents are free to say whatever they want ■ Disadvantages: ● Responses are difficult to summarize ● Logical responses may not readily come to mind ● The wording of the question might unintentionally exclude answers that they would have chosen if the had a list ○ Closed Question: respondents are given a LIST of alternatives from which to choose their answer ■ Advantages: Easier to administer & analyze & you don’t have to come up with the answer on your own ■ Disadvantages: ● Limited options b/c respondents will rarely fill in “other” ● Recency Effect: Respondents tend to choose the options given later in the list, especially over the phone ○ COMPROMISE of Both Studies: ■ Pilot Study: a small group of people are asked the question in open form & their responses are used to create the choices for the closed form ● Defining what is being measured- Degree of Precision?? ○ Language: A precise definition should always go along with what is being measured ○ Some concepts are hard to define: Intelligence, Stress ■ There is no fixed definition of either ■ So, it's important the reader is informed about HOW the researchers measured the response variable

○ Measuring Attitudes & Emotions: How to measure happiness or self-esteem ■ Common Method: respondents read statements & determine extent to which they agree with statements ○ Need to figure out how to measure a variable consistently- for everyone ● Definitions! ○ Categorical/ Qualitative Variables: Those we can place into a category, but they may not have any logical ordering (male or female) ■ Ordinal: Categorical variables whose categories have a natural ordering (strongly agree to strongly disagree, level of education) ■ Nominal: Categorical Variables whose categories do not have a natural ordering ○ Measurement/ Quantitative Variables: Those for which we can record a numerical value & then order respondents according to those values (IQ, age, height, # of cigarettes smoked per day) ■ Interval: Quantitative variables in which we can talk about differences, but not ratios (temperature- it’s not twice as hot, it’s 20 degrees warmer) ■ Ratio: Quantitative variables that have a meaningful zero (Pulse rate- it doubled after exercise) ● Measurement Variables Cont’d ○ Discrete Variables: You can actually count the possible responses (NUMBER OF)- it couldn’t be 2 ½, 3.8, etc.- number of car accidents ○ Continuous Variables: Can be anything within a given range (AMOUNT OF)age- falls on a continuum ● Validity, Reliability, & Bias ○ Valid Measurement: Valid- Actually measures what it claims to measure (ie: IQ test is not a valid measurement of happiness)- KEY: need to know exactly what was measured/ definition of the measurement ○ Reliable Measurement: Consistent -A measurement that will give you or anyone else approx. the same result time after time, when taken on the same object or individual (physical measurement measured with a precise measuring instrument is the most reliable)- KEY: watch for degree of precision being reported (measuring a pool w a ruler)- not necessarily valid ○ Biased Measurement: A measurement that is systematically off the mark in the same direction (time on a clock that’s fast or a scale that always weighed you 5 lbs lighter) ○ → if valid has to be reliable!! ○ → can be reliable & biad, but NOT valid ○ → can be valid & reliable, but no biased ● Variability across Measurements: ○ Variability: used when we talk about 2 or more measurements in relation to each

other- measurements are likely to differ from one time to the next or from one individual to the next b/c of unpredictable errors, discrepancies, or natural differences ○ Measurement Error: amount by which each measurement differs from the true value ○ Natural Variability: results from changes across time in the individual or system being measured (blood pressure can differ one month to the next)- why many measurements differ across individuals ● The Importance of Natural Variability: ○ 3 Reasons Variability Occurs: ■ 1. Measurement Error: measurements are imprecise ■ 2. Natural variability across several individuals at any given timeeveryone is different ■ 3. Natural variability in a characteristic of the same individual across timeyour pulse rate changes throughout the day ○ Heart of Modern Statistics: ■ Goal in stats: make variability as small as possible ■ Comparing natural variability to the variability created by different treatments in studies ■ If there were NO variability within groups, it would be easy to detect differences b/w the 2 groups ■ The more variability there is within each group- the more difficult it is to detect a difference b/w groups Chapter 4: How to Get A Good Sample ● Common Research Strategies ○ Sample Surveys: a subgroup of a large population (a sample) is questioned on a set of topics ■ The results from the sample are used as if they were representative of the larger population, which they will be if the sample was chosen correctly ○ Experiment: measures the effect of manipulating the environment in some waytreatment added ○ Randomized Experiments: The manipulation/ treatment is assigned to participants on a random basis ■ Explanatory Variable: the independent variable- what was changedtreatment or no treatment- feature being manipulated ■ Response Variable: Dependent variable- the outcome/ result of the manipulation ■ Randomized experiments allow us to DETERMINE CAUSE & EFFECT ■ Participants are randomly assigned to receive the treatment or be in the control group ■ Purpose of random assignment- to make the 2 group as equal as possible

except for the explanatory variable ○ Observational Study: manipulation occurs naturally rather than being imposed by the experimenter ■ Cannot determine cause & effect (causal relationship) ■ Case-Control Study: Used in medical research- an attempt to include an appropriate control group ○ Meta-Analysis: A quantitative review of a collection of studies all done on a similar topic ■ Study authors just compile & analyze the results of other prior studies ■ May result in the emergence of patterns or effects that weren’t available from the individual studies ○ Case Study: an in-depth examination of one or a small number of individuals ■ Researcher observes & interviews that individual & others who know about the topic of interest ■ Don’t assume you can extend the findings of a case study to anything other than what was studied ● Definitions! ○ Unit: a single individual or object to be measured ○ Population: the entire collection of units about which we would like information or the entire collection of measurements we would have if we could measure the whole population ○ Sample: the collection of units we actually measure or the collection of measurements we actually obtain. Can be used to infer something about a population ○ Sampling Frame: A list of units from which the sample is chosen. Ideally, it includes the whole population ■ The list of names when randomly selecting people for something using a random digits table ■ TO USE IT: # EACH PERSON ACROSS THE ROWS, THEN COUNT EVERY 2 DIGIT # TO ARRIVE AT THE DESIRED # OF SUBJECTS ○ Sample Survey: In a sample survey, measurements are taken on a subset, or sample, of units from the population ○ Census: A survey in which the entire population is measured ● Advantages of Sample Surveys over a Census: ○ Accuracy of a Sample Survey: ■ Most sample surveys are used to estimate the proportion or percentage of people who have a certain trait or opinion ■ Margin of Error: The measure of accuracy ■ Add & subtract the margin of error to the sample value & the resulting interval almost surely covers the true population value- most of the time, the population proportion will be within one

■ As sample size increases, margin of error decreases ○ When a Census Isn’t Possible- blood lab tests ○ Speed ■ It’s much faster to collect a sample than a census if the population is large ○ Accuracy: ■ It is easier to accurately get information from a smaller group of people then to accurately get information from a census ● Simple Random Sampling- SURVEYS ○ Probability Sampling Plans: Methods that make sure everyone in the population has a specified change of making it into the sample ■ Methods of this nature have the ability of a relatively small sample to accurately reflect the opinions of a huge population ○ Simple Random Sample: Every conceivable group of people of the required size has the same change of being the selected sample→ small samples can accurately reflect the population- the BEST WAY to make sure you get a representative sample ■ You need: a list of the units in the population & a source of random numbers (table of random digits) ■ Ie: have to have a list of everyone numbered in your class, use table of random digits to pick 25 students, then interview the people on your list whose numbers were selected ■ Ie: organizations need a numbers list of all adults in the country ● Other Sampling Methods:- SURVEYS ○ Stratified Random Sampling: collected by 1st dividing the population of units into strata (groups) & then taking a simple random sample from each ■ Strata: natural groups the population of units sometimes falls into (taking separate samples from each region of the country) ■ Ie: choosing a sentence randomly on each page & counting the # of words ■ Population is divided into groups: randomly select from every group ○ Cluster Sampling: The population units are divided into clusters, but rather than sampling within each group, we select a random sample of clusters & measure only those cluster ■ Ie: randomly select 3 chapters, but count the number of words in every sentence from those chapters ■ Population is divided into groups: randomly select a few groups to measure, but measure everyone in those groups ○ Systematic Sampling: Divide the list into as many consecutive segments as you need, randomly choose a starting point in the first segment, then sample at that same point in each segment ■ Choosing the every 50th name on the list

■ Ie: Starting from page 1, count the number of words in every 5th sentence ■ However, can lead to bias ○ Random Digit Dialing: Results in a sample that approximates a simple random sample of all adults in the US who have telephones ■ Randomly sampling telephone numbers and calling them ○ Multistage Sampling: Using a combination of methods. ■ Ie: Stratifying by region of country, then by urban or rural, then choose a random sample of communities within those strata, then divide those into clusters and sample some of them ● Difficulties & Disasters in Sampling SURVEYS ○ Difficulties: ■ 1. Using the wrong sampling frame ● Sometimes a sampling frame either will include unwanted units or exclude desired units ■ 2. Not reaching the individuals selected ■ 3. Having a low response rate ○ Disasters: ■ 1. Getting a volunteer or self-selected sample ● Relying on a volunteer SAMPLE is a waste of time- can’t generalize it at all ● Volunteer Sample: study can be generalized to ONLY THE PEOPLE IN THE STUDY ■ 2. Using a convenience or haphazard sample ● Sampling people conveniently available- not representative of any larger population Chapter 5: Experiments and Observational Studies ● Definitions! ○ Treatment: One or a combination of the categories of the explanatory variable assigned by the experimenter- the manipulation applied by the experimenter ○ Randomized Experiment: We create differences in the explanatory variable and then examine the results- each experimental unit is randomly assigned to a treatment ○ Observational Study: We observe differences in the explanatory variable and then notice whether these are related to differences in the response variable ○ When to use an observational study over an experiment: ■ 1. It is unethical or impossible to assign people to receive a specific treatment ■ 2. Certain explanatory variable, such as handedness, are inherent traits and cannot be randomly assigned ○ Confounding Variables: Is related to the explanatory variable & affects the response variable

■ DISADVANTAGE: Bigger problems in observational studies than experiments ■ IE: measuring the effect of a mother who smoked during pregnancy on the IQ of the child ● Confounding variables: women who smoke might have poor nutrition, or lower levels of education, ro lower income ● IF a randomized design: there are NO confounding variables as the randomization of treatment balances out possible confounded ○ Effect Modifier: the subgroup variable- modifies the effect of the explanatory variable on the outcome- the effect on the response can’t be separated ■ Ie: When a relationship exists b/w an explanatory and response variable, but the magnitude of the relationships differs for subgroups ○ Interaction: an interaction b/w 2 explanatory variables occurs when the relationship of one of them to the response depends on the other one ○ Experimental Units: The smallest basic objects to which we can assign different treatments in a randomized experiment ○ Observational Units: The objects or people measured in any study ○ Participants/ Subjects: commonly used when the observational units are peoplemost of the time, participants in studies are volunteers ● Designing a Good EXPERIMENT: ○ Randomization: Random selection t...