Lessons 11-17
Lesson 12- Discuss differences between following ?;s, each of which could be basis for statistical study. What % of Internet dates lead to marriage? What % of marriages begin w/Internet dates?
- ?'s have different populations.
Lesson 13- Describe importance of labeling on graph, &briefly discuss kinds of labels that should be included on graphs.
- Graph should have title or caption (or both) that explains what is shown &, if applicable, lists source of data. Without this label, might not be clear what graph is supposed to illustrate. - If multiple data sets displayed on single graph, there should be legend/key to identify individual data sets. Otherwise, comparisons among data sets not possible & confusion among data sets could occur. - Categories should be clearly indicated along horizontal axis, & there should be label that describes variable that categories represent. Without either, not possible to know what data graph is supposed to show. - #'s along vertical axis should clearly indicate scale, & there should be label that describes variable shown on vertical axis. Without either, would be no way of interpreting data shown in graph.
Lesson 13- What two types of graphs are most common when the categories are qualitative data?
- In bar graph, categories are clearly indicated along horizontal axis. Over each category is rectangle whose height indicates frequency or relative frequency of category. #'s along vertical axis clearly indicate the scale. - In pie chart, each category corresponds to wedge of circle. The size of each wedge is proportional to relative frequency of category it represents.
Lesson 12- Y/N: A research group that tracks tuition rates at colleges & universities compares the tuition at a small college today & 10 years ago & claims that tuition has increased 150% during that period.
- No, since it is not clear whether inflation was taken into account.
Lesson 13- What is distinction between qualitative data & quantitative data?
- Qualitative data describe categories, while quantitative data represent counts or measures. Brand names of shoes in consumer survey & eye colors are examples of qualitative data. Heights of students & quiz scores are examples of quantitative data.
Lesson 12- T/F: My experiment proved beyond a doubt that vitamin C can reduce severity of colds, bc I controlled experiment carefully for every possible confounding variable.
- Statement does not make sense bc inot always easy to discover confounding variables.
Lesson 13- Y/N: Your pie chart must be wrong, bc when I added the percentages on wedges, they totaled 124%.
- T: Statement makes sense bc pie charts are used primarily for relative frequencies, so total pie must always represent total relative frequency of 100%.
Lesson 13- Determine whether following variable is qualitative or quantitative & explain why. The annual salaries of NBA basketball players
- Variable is quantitative bc salaries are numerical categories.
Lesson 12- T/F: The local Chamber of Commerce claims that the average number of employees among all businesses in town is 12.5.
- No, there is not reason. The Chamber of Commerce would have no reason to distort its data.
Lesson 11- A researcher wants to determine the average. Describe how the researcher should apply the five basic steps in a statistical study. (Assume that all the people in the poll answered truthfully.) *The average number of workplaces per city that have a water cooler*
1. First basic step. - The population is all cities. The researcher wants to estimate the avg # of workplaces per city that have a water cooler. 2. Second basic step. - The researcher should gather data about water coolers from the largest sample of workplaces about whom the researcher can gather data. 3. Third basic step. - Sample statistic of interest is the avg # of workplaces per city that have a water cooler. 4. Fourth basic step. - Researcher should use the sample statistic as an estimate for the population value of the avg # of workplaces that have a water cooler & then uses the methods of statistics to determine how good that estimate is. 5. Fifth basic step. - Researcher should use the methods of statistics to determine the quality of the estimate of the population parameter & draw conclusions based on this estimate accordingly.
Lesson 11- A researcher wants to determine the average given below. Describe how the researcher should apply the five basic steps in a statistical study. (Assume that all the people in the poll answered truthfully.) The average time to failure of batteries in a particular model of stopwatch.
1. First basic step. - The population is all stopwatches of this model. 2. Second basic step. - Researcher should gather raw data about battery life from the largest sample of stopwatches about which he/she can gather data. 3. Third basic step. - Sample statistic of interest is the avg time for stopwatches in the sample to have their batteries wear down. 4. Fourth basic step. - Researcher should use the sample statistic as an estimate for the population value of the avg life of batteries & then use the methods of statistics to determine how good that estimate is. 5. Fifth basic step. - Researcher should use the methods of statistics to determine the quality of the estimate of the population parameter & draw conclusions based on this estimate accordingly.
Lesson 11- Study done at Center for Disease at certain university tracked 18,771 asymptomatic patients w/ certain disease who started therapy at different points in progression of infection. It was discovered asymptomatic patients who postponed antiretroviral treatment until disease more advanced faced higher risk of dying than those who initiated drug treatment earlier.
1. Identify population & population parameter(s) of interest. - Population is all asymptomatic patients w/ disease who have undergone treatment. Population parameters are survival rates & times which treatment began. 2. Describe sample & sample statistic. - Sample is 18,771 asymptomatic patients w/disease. Sample statistics are survival rates & times which treatment began for those in sample. 3. Identify type of study. - Observational study.
Lesson 11- In order to gauge public opinion about how to handle Iran's growing nuclear program, a research group surveyed 996 Americans by telephone and asked them to rate the threat Iran's nuclear program poses to the world on a scale of 1 to 10. Describe the population, sample, population parameters, and sample statistics.
1. Identify the population. - All Americans. 2. Identify the sample. - The 996 Americans surveyed by telephone. 3. Identify the population parameter. - The mean threat rating of all Americans on Iran's nuclear program 4. Identify the sample statistic. - The mean threat rating on Iran's nuclear program of the 996 Americans surveyed by telephone.
Lesson 11- Each year, a group surveys 50,000 households to study internet usage. In one area of the study, the group is interested in finding out how many hours a day the household spends streaming video from the internet. Describe the five basic steps in a statistical study.
1. State the goal of your study. In this case, it is to discover how many hours per day a household spends streaming internet video. 2.Choose a representative sample from the population. In this case, it would be choosing a sample of 50,000 households. 3. Collect raw data from the sample and summarize these data by finding sample statistics of interest. In this case, it would be asking the households how many hours they spend streaming internet video and turning this data into an average. 4. Use the sample statistics to infer the population parameters. In this case, based on the data gathered, the group estimates the average time per day that a household spends streaming internet video. 5. Draw conclusions to determine what you learned and whether you achieved your goal. In this case, we discovered the average time per day that a household spends streaming internet video.
Lesson 11- What is a placebo? Describe the placebo effect and how it can make experiments difficult to interpret. How can making an experiment single-blind or double-blind help?
1. What is a placebo? -A placebo lacks the active ingredients of a treatment being tested in a study but is identical in appearance to the treatment. 2. Describe the placebo effect and how it can make experiments difficult to interpret. -A situation in which a patient improves simply because they believe they are receiving a useful treatment. It can sometimes be difficult or impossible to distinguish between effects that arise from the actual treatment and those that arise from psychological factors. 3. How can making an experiment single-blind or double-blind help? -If experiment is blinded, then any effect arising from psychological factors should affect all groups equally.
Lesson 11- What is bias? How can it affect a statistical study? Give examples of bias.
1. What is bias? How can it affect a statistical study? -Bias refers to any problem in the design or conduct of a statistical study that tends to favor certain results. 2. Give examples of bias. -Non-representative sample -Researcher with a personal stake in the outcome distorts the true meaning of data. -Experiment that is not blinded.
Lesson 11- Why is it so important that a statistical study use a representative sample? Briefly describe four common sampling methods.
1. Why is it so important that a statistical study use a representative sample? -If the sample fairly represents the population as a whole, then it is reasonable to make inferences from the sample to the population. 2. Four (4) common sampling methods. -Simple random sampling; Systematic sampling; Convenience sampling; Stratified sampling
Lesson 12- Consider statistical study where researchers are looking to discover what breed of dog sleeps most. Briefly describe each of the eight guidelines for evaluating statistical studies. Describe how each would apply to a statistical study in which researchers are looking to discover what breed of dog sleeps the most.
1.) First guideline for evaluating statistical study. - Get a big picture view of study. In example study, goal is to discover sleeping habits in a population of dogs with an observational study. 2.) Second guideline. - Consider the source. In example study, veterinarians have no preference on which breed gets most sleep. 3.) Third guideline. - Look for bias in sample. In example study, all breeds were given appropriate sleeping quarters. 4.) Fourth guideline. - Look for problems in defining/measuring variables of interest. In example study, sleep is strictly measured according to set guidelines. 5.) Fifth guideline. - Beware of confounding variables. In example study, researchers gave dogs the same amount of activity before letting them sleep. 6.) Sixth guideline. - Consider setting & wording in surveys. In example study, researchers phrased sleep data in clear wording. 7.) Seventh guideline. - Check results are presented fairly. In example study, data supports breed that the researchers claim sleeps the most. 8.) Eighth guideline. - Stand back & consider conclusions. In example study, researchers achieved goal of finding which breed of dog sleeps most.
Lesson 12- What are confounding variables, & what problems can they cause?
1.) What are confounding variables? - Items/quantities not intended to be part of study. 2.) What problems can confounding variables cause? - Can cause incorrect conclusions to be drawn from the study. - Can cause study to favor certain results unexpectedly.
Lesson 13- Use 4-point bins (96 to 99, 92 to 95, etc.) to make frequency table for set of exam scores shown. Include columns for relative frequency & cumulative frequency. 86 90 81 86 77 83 82 87 84 84 89 93 93 84 85 98 81 79 92 95
Complete frequency table below. Scores: Frequency: Relative Frequency: Cumulative Frequency: 96-99 1 5% 1 92-95 4 20% 5 88-91 2 10% 7 84-87 7 35% 14 80-83 4 20% 18 76-79 20 100% 20 Total: 20 100% 20
Lesson 13- A professor records the following final grades in one course. Construct a frequency table for the grades. A A A A A B B B B B B C C C C C C C D D D D F
Complete the table. Grade Frequency: Relative Frequency: Cumulative Frequency: A: 5 20.8% 5 B: 6 25% 11 C: 7 29.2% 18 D: 4 16.7% 22 F: 2 8.3% 24 Total: 24 1=100% 24
Lesson 12- T/F: TV survey got more than 1 million phone-in responses, it is clearly more valid than survey by professional pollsters, based on interview w/only a few hundred people.
F. Statement does not make sense. Eight guidelines for evaluating statistical study need to be reviewed before one study can be called more valid than another.
Lesson 12- Headline "Drugs shown in 98% of movies" accompanied news story that described "government study" claiming drug use, drinking, or smoking was depicted in 98% of top movie rentals. Discuss whether headline accurately represents story.
Headline refers to drugs whereas story refers to "drug use, drinking, or smoking." Headline very misleading bc term "drugs" is generally considered to consist of drugs other than cigarettes/alcohol. Also, all movies consist of more than just the top movie rentals.
Lesson 12- Y/N: A TV talk show host asks the TV audience, "Do you support new national mileage standards for automobiles?" & asks people to vote by telephone at a toll-free number.
Is there reason to question the results? - Yes, there is reason. Call-in polls tend to be biased. - Yes, there is reason. The TV audience might not be representative of the population. - Yes, there is reason. The wording of the question might produce inaccurate/dishonest responses.
Lesson 11- Y/N In my statistical study, I used a sample that was larger than the population.
No, the statement does not make sense. A sample is a subset of the population and cannot be larger than the population.
Lesson 11- Determine whether study is observational study or experiment. If study is experiment, identify control & treatment groups, & discuss whether single- or double-blinding is necessary. If study is observational, state whether case-control study, & if so, identify cases & controls. Study at university separated 118 volunteers into groups, based on psychological tests designed to determine how often they lied & cheated. Those w/ tendency to lie had different brain structures than those who did not lie.
Observational study; case control; cases are the volunteers that had a tendency to lie, & the controls are the volunteers that did not lie.
Make a bar graph of populations of 5 most populous states (from census data) in certain country, w/bars in descending order.
State: Population: A 39.8 million B 25.3 million C 21.8 million D 19.8 million E 12.7 million **bar graph is going highest to lowest**
Lesson 11- Determine whether study is observational or experiment. If study is experiment, identify control & treatment groups, & discuss whether single- or double-blinding is necessary. If study is observational, state whether a retrospective study, & if so, identify cases and controls. Using survey of 1533 ppl in country, researchers determined that 83% of ppl in country believe country is more politically divided than in past & those divisions will persist.
Study is observational. 1. If study is experiment, identify control & treatment groups. - Study not an experiment. 2. If study is experiment, discuss whether single- or double-blinding necessary. - Study not experiment. 3. If study is observational, state whether it's retrospective study. - Study is observational, but not retrospective study. 4. If study is retrospective study, identify cases & controls. - Study not retrospective.
Lesson 11- Following statistical study gives sample statistic & margin of error. Find confidence interval & answer additional ?'s. Poll conducted day before state election for senator. There are two candidates running for office. Poll results show 55% of voters favor Republican candidate, w/margin of error of 4 percentage points. Should republican expect to win? Why/why not?
The confidence interval is 51%-59%. Republican likely to win bc both endpoints of confidence interval greater than 50%.
Lesson 11- Following statistical study gives sample statistic & margin of error. Find confidence interval & answer additional ?'s. In survey of 1002 ppl, 701 (or 70%) voted particular presidential election. The margin of error for survey was 3 percentage points. However, actual voting records show only 59% of eligible voters actually did vote. Does this imply ppl lied when they responded in survey?
The confidence interval is 67%-73%. Does this imply ppl lied when they responded in survey? - Confidence interval doesn't include the 59% value. If survey conducted properly, then unlikely its results would be different from actual results, implying either respondents intentionally lied to appear favorable to pollsters or their memories were inaccurate.
Lesson 12- What do we mean by variables of interest in a study?
The items or quantities that the study seeks to measure.
Lesson 12- An article noted that chocolate is rich in flavonoids. Article reports, "regular consumption of foods rich in flavonoids may reduce risk of coronary heart disease." Study received funding from candy company & chocolate manufacturers association. Identify & explain at least one source of bias in the study described. Then suggest how the bias might have been avoided.
The researchers may have been more inclined to provide favorable results bc funding was provided by party w/definite interest. The bias could have been avoided if researchers were not paid by candy company & chocolate manufacturers.
Lesson 11- U want to determine avg (mean) # of robocalls received/day by adults in New Zealand. Sample 1: A set of 521 New Zealanders w/ phone numbers randomly selected from a list of all phone numbers in New Zealand Sample 2: The first 521 ppl to visit a particular Auckland grocery store one day. Sample 3: The 521 adults in New Zealand who respond to a survey published in a newspaper. Sample 4: A set of 521 New Zealanders randomly selected from list of all licensed car owners in New Zealand Which sample is most likely to be a representative sample? For each other sample explain why that sample is not likely to be a representative sample.
The sample most likely to be a representative sample is sample 1. 1. Why is sample 1 most likely to be representative sample? - List is a random sample not likely biased. 2. Why is sample 2 not likely to be representative sample? - Likely biased bc it's limited to geographic region of Auckland. 3. Why is sample 3 not likely to be representative sample? - Is convenience sample limited to readers of the newspaper & therefore, likely to be biased. 4. Why is sample 4 not likely to be representative sample? - Biased bc it includes only car owners & doesn't include those who cannot afford a car.
Lesson 12- Identify potential sources of bias in following study. An exit poll designed to predict the winner of a local election uses interviews with every Republican who votes between 7:00 and 7:30 a.m.
What sources of bias, if any, might this study have? - Selection bias only.
Lesson 11- To determine mood, Carolyn divides her day into three parts: morning, afternoon, & evening. Then measures mood at 2 random times during the day.
What type of sampling used? -Stratified sampling.
Lesson 12- According to newspaper, 26% of Americans rate potatoes their favorite vegetable, making it the most popular vegetable.
Which is crucial info that u would want to know before acting on the study? - Were respondents given choice of potatoes, or did they suggest it without a prompt. - How ? was asked. - How respondents were chosen.
Lesson 12- Much like sound-bytes of news stories, statistical studies are often reduced to one- or two- sentence stat-bytes. For following stat-byte, discuss what crucial info missing & what more u would want to know before acting on the study. Newspaper reports that over 60% of adults avoid dentist because of fear.
Which of the following is crucial info that u would want to know before acting on study? - How respondents were chosen. - The size of the sample. - The ?'s respondents were asked.