Unit 1: Introduction to data Lecture 1: Data collection, observational studies, and experiments. Statistics 101. Gary Larson Duke University

Transcription

1 Unit 1: Introduction to data Lecture 1: Data collection, observational studies, and experiments Statistics 101 Gary Larson Duke University June 29, 2015

2 Sta 101 Welcome to Stat 101! 1 Welcome to Stat 101! Introduction to Inference Populations and Samples Sampling from a population Sampling bias Observational studies and experiments Cereal breakfast Observations and variables Principles of experimental design Recap 2 Syllabus & policies Logistics Details Support Policies Tips 3 To do

3 Today s agenda Relevant reading from OpenIntro Stat (2nd ed.): Sections 1.2, 1.3, 1.4, 1.5. Other: Intro to inference Populations, and sampling from them Sampling bias Observational studies & experimental studies Types of data Principles of experimental design Course overview (see course website ) Outside survey Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

4 Introduction to Inference So...what is statistics? Statistics is the art and science of learning from data. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

5 Introduction to Inference So...what is statistics? Statistics is the art and science of learning from data. Data are a set of measurements taken on a set of individual units Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

6 Introduction to Inference So...what is statistics? Statistics is the art and science of learning from data. Data are a set of measurements taken on a set of individual units Steps for statistical inference / scientific inquiry 1 Identify a hypothesis or research question Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

7 Introduction to Inference So...what is statistics? Statistics is the art and science of learning from data. Data are a set of measurements taken on a set of individual units Steps for statistical inference / scientific inquiry 1 Identify a hypothesis or research question 2 Collect relevant data Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

8 Introduction to Inference So...what is statistics? Statistics is the art and science of learning from data. Data are a set of measurements taken on a set of individual units Steps for statistical inference / scientific inquiry 1 Identify a hypothesis or research question 2 Collect relevant data 3 Analyze the data Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

9 Introduction to Inference So...what is statistics? Statistics is the art and science of learning from data. Data are a set of measurements taken on a set of individual units Steps for statistical inference / scientific inquiry 1 Identify a hypothesis or research question 2 Collect relevant data 3 Analyze the data 4 Form a conclusion Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

10 Introduction to Inference So...what is statistics? Statistics is the art and science of learning from data. Data are a set of measurements taken on a set of individual units Steps for statistical inference / scientific inquiry 1 Identify a hypothesis or research question 2 Collect relevant data 3 Analyze the data 4 Form a conclusion 5 Communicate the results 6 Present your data Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

11 Introduction to Inference Step 1: Identify a Hypothesis or Research Question A well-formed hypothesis will clearly identify a population and associated parameters of interest. Population: group of individuals or subjects exhibiting some characteristic. We would like to make inferences about this population. Parameters: True values of characteristics in the population we want to study. We make inferences about the population by using data to learn about the parameter(s). Let s make these definitions more concrete via examples... Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

12 Introduction to Inference Step 1: Identify a Hypothesis or Research Question A well-formed hypothesis will clearly identify a population and associated parameters of interest. Population: group of individuals or subjects exhibiting some characteristic. We would like to make inferences about this population. Parameters: True values of characteristics in the population we want to study. We make inferences about the population by using data to learn about the parameter(s). Let s make these definitions more concrete via examples... How many names given to newborn babies in 2012 in the United States begin with the letter j? Population? Parameter? Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

13 Introduction to Inference Step 2: Collect the data Each year the Social Security Administration collects and releases data on the how many babies are given a certain name. They released these data for years 1880 to 2013 for each gender. We often store and present such data in data sets, comprised of variables measured on individual cases (a.k.a. records). Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

14 Introduction to Inference Data Sets data set or data matrix variable type price weight 1 small midsize observation midsize Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

15 Introduction to Inference Baby Names Data Set Besides looking at the frequency of first initials, what else could we learn from this data set? Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

16 Introduction to Inference Visualize the Data: Rank Table Top Baby Names in 2012 Rank Male Female 1 Jacob Sophia 2 Mason Emma 3 Ethan Isabella 4 Noah Olivia 5 William Ava 6 Liam Emily 7 Michael Abigail 8 Jayden Mia 9 Alexander Madison 10 Aiden Elizabeth oact/ babynames Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

17 Introduction to Inference Visualize the Data: Rank Table Top Baby Names in 2013 Rank Male Female 1 Noah Sophia 2 Liam Emma 3 Jacob Olivia 4 Mason Isabella 5 William Ava 6 Ethan Mia 7 Michael Emily 8 Alexander Abigail 9 Jayden Madison 10 Daniel Elizabeth oact/ babynames Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

18 Introduction to Inference Visualize the Data: Time Dependencies How has the popularity of a name changed over time? voyager#prefix=&sw=both& exact=false Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

19 Introduction to Inference Visualize the data: time dependencies Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

20 Introduction to Inference What about the first initials? 1 Obtain data from SS website: name, gender, frequency. d <- read.csv("yob2012.txt") Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

21 Introduction to Inference What about the first initials? 1 Obtain data from SS website: name, gender, frequency. d <- read.csv("yob2012.txt") 2 Use an R function (substring) to extract the initial of the name. d$initial = substring(d[,1],1,1) Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

22 Introduction to Inference What about the first initials? 1 Obtain data from SS website: name, gender, frequency. d <- read.csv("yob2012.txt") 2 Use an R function (substring) to extract the initial of the name. d$initial = substring(d[,1],1,1) 3 Make a barplot of the initials, by gender if desired. barplot(table(d$initial)) barplot(table(d$initial[d$gender == "M"])) barplot(table(d$initial[d$gender == "F"])) Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

23 Introduction to Inference Initials All names in A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

24 Introduction to Inference Initials All names in 201 (M) A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Initials All names in 2012 (F) A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

25 Introduction to Inference Step 4: Form a conclusion In 2012, newborn babies in the US were given 3,000 unique names that began with the letter j based on the data from the Social Security database The list of babies from the Social Security data set is a sample, a group of individuals taken from the entire population. The number of individuals in the sample is usually denoted with the letter n. A statistic is any function of the data collected in the sample (e.g., mean, median, etc). So, the count of the babies in the Social Security data set for 2012 who have first initial j is a statistic. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

26 Populations and Samples Data Collection Be aware that there exist bad samples. There are three kinds of lies: lies, damned lies, and statistics. If poor sampling techniques are utilized, then the observed statistics will not be applicable to the true population of interest. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

27 Populations and Samples Data Collection Be aware that there exist bad samples. There are three kinds of lies: lies, damned lies, and statistics. If poor sampling techniques are utilized, then the observed statistics will not be applicable to the true population of interest. Example: data collection: Raise your hand if you have been on an airplane in the past two years. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

28 Populations and Samples Data Collection Be aware that there exist bad samples. There are three kinds of lies: lies, damned lies, and statistics. If poor sampling techniques are utilized, then the observed statistics will not be applicable to the true population of interest. Example: data collection: Raise your hand if you have been on an airplane in the past two years. What does this tell us about how many year olds have ridden an airplane in the past two years? Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

29 Sampling from a population Census Wouldn t it be better to just include everyone and sample the entire population, i.e. conduct a census? Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

30 Sampling from a population Census Wouldn t it be better to just include everyone and sample the entire population, i.e. conduct a census? Some individuals are hard to locate or hard to measure. And these difficult-to-find people may have certain characteristics that distinguish them from the rest of the population. Even if you could take a census, a population is always changing, so it s never possible to get a perfect measure. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

31 Sampling from a population Census Wouldn t it be better to just include everyone and sample the entire population, i.e. conduct a census? Some individuals are hard to locate or hard to measure. And these difficult-to-find people may have certain characteristics that distinguish them from the rest of the population. Even if you could take a census, a population is always changing, so it s never possible to get a perfect measure. templates/ story/ story.php?storyid= Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

32 Sampling from a population Exploratory analysis to inference Sampling is natural. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

33 Sampling from a population Exploratory analysis to inference Sampling is natural. Think about sampling something you are cooking - you taste (examine) a small part of what you re cooking to get an idea about the dish as a whole. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

34 Sampling from a population Exploratory analysis to inference Sampling is natural. Think about sampling something you are cooking - you taste (examine) a small part of what you re cooking to get an idea about the dish as a whole. When you taste a spoonful of chili and decide the single spoonful you tasted isn t spicy enough, that s exploratory analysis. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

35 Sampling from a population Exploratory analysis to inference Sampling is natural. Think about sampling something you are cooking - you taste (examine) a small part of what you re cooking to get an idea about the dish as a whole. When you taste a spoonful of chili and decide the single spoonful you tasted isn t spicy enough, that s exploratory analysis. If you generalize and conclude that your entire chili is not spicy enough either, that s an inference. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

36 Sampling from a population Exploratory analysis to inference Sampling is natural. Think about sampling something you are cooking - you taste (examine) a small part of what you re cooking to get an idea about the dish as a whole. When you taste a spoonful of chili and decide the single spoonful you tasted isn t spicy enough, that s exploratory analysis. If you generalize and conclude that your entire chili is not spicy enough either, that s an inference. For your inference to be valid, the sample (the spoonful you tasted) needs to be representative of the population (entire pot). If all the spices are sitting at the bottom of the pot, what you tasted is probably not representative of the whole pot. If all the spices are well-mixed before you taste, your spoonful will more likely be representative of the whole pot. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

37 Sampling bias Landon vs. FDR A historical example of a biased sample yielding misleading results: In 1936, Landon was the Republican presidential candidate opposing the re-election of FDR. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

38 Sampling bias The Literary Digest poll The sample: The Literary Digest polled about 10 million Americans, and got responses from about 2.4 million. The inference: Landon would likely be the overwhelming winner and FDR would get only 43% of the votes. The reality: Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

39 Sampling bias The Literary Digest poll The sample: The Literary Digest polled about 10 million Americans, and got responses from about 2.4 million. The inference: Landon would likely be the overwhelming winner and FDR would get only 43% of the votes. The reality: FDR won, with 62% of the votes. The magazine was completely discredited because of the poll, and was soon discontinued. How could they have been so wrong? Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

40 Sampling bias The Literary Digest Poll - what went wrong The magazine had surveyed its own readers, registered automobile owners, and registered telephone users. These groups had incomes well above the national average of the day (remember, this is Great Depression era) which resulted in lists of voters far more likely to support Republicans than a truly typical voter of the time, i.e. the sample was not representative of the American population at the time, so it was impossible to accurately generalize the results from the sample to the population. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

41 Sampling bias Large samples are preferable, but... The Literary Digest election poll was based on a sample size of 2.4 million, which is huge, but since the sample was biased, the sample did not yield an accurate prediction. Back to the chili analogy: If the chili is not well stirred, it doesn t matter how large a spoon you have, it will still not taste right (the sample won t be representative of the population). If the chili is well stirred, a small spoon will suffice to test the chili. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

42 Sampling bias A few sources of bias Non-response: If only a (non-random) fraction of the randomly sampled people choose to respond to a survey, the sample may no longer be representative of the population. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

43 Sampling bias A few sources of bias Non-response: If only a (non-random) fraction of the randomly sampled people choose to respond to a survey, the sample may no longer be representative of the population. Voluntary response: Occurs when the sample consists of people who volunteer to respond because they have strong opinions on the issue, and hence is not representative of the population. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

44 Sampling bias A few sources of bias Non-response: If only a (non-random) fraction of the randomly sampled people choose to respond to a survey, the sample may no longer be representative of the population. Voluntary response: Occurs when the sample consists of people who volunteer to respond because they have strong opinions on the issue, and hence is not representative of the population. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

45 Sampling bias A few sources of bias Non-response: If only a (non-random) fraction of the randomly sampled people choose to respond to a survey, the sample may no longer be representative of the population. Voluntary response: Occurs when the sample consists of people who volunteer to respond because they have strong opinions on the issue, and hence is not representative of the population. edition.com, Aug 29, 2013 Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

46 Sampling bias A few sources of bias Non-response: If only a (non-random) fraction of the randomly sampled people choose to respond to a survey, the sample may no longer be representative of the population. Voluntary response: Occurs when the sample consists of people who volunteer to respond because they have strong opinions on the issue, and hence is not representative of the population. edition.com, Aug 29, 2013 Convenience sample: Individuals who are easily accessible are more likely to be included in the sample. What type of bias do reviews on Amazon.com have? What about reviews on RateMyProfessor.com? Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

47 Sampling bias Participation question A school district is considering whether it will no longer allow high school students to park at school after two recent accidents where students were severely injured. As a first step, they survey parents by mail, asking them whether or not the parents would object to this policy change. Of 6,000 surveys that go out, 1,200 are returned. Of these 1,200 surveys that were completed, 960 agreed with the policy change and 240 disagreed. Which of the following statements are true? I. Some of the mailings may have never reached the parents. II. The school district has strong support from parents to move forward with the policy approval. III. It is possible that majority of the parents of high school students disagree with the policy change. IV. The survey results are unlikely to be biased because all parents were mailed a survey. (a) Only I (b) I and II (c) I and III (d) III and IV (e) Only IV Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

48 Sampling bias Participation question A school district is considering whether it will no longer allow high school students to park at school after two recent accidents where students were severely injured. As a first step, they survey parents by mail, asking them whether or not the parents would object to this policy change. Of 6,000 surveys that go out, 1,200 are returned. Of these 1,200 surveys that were completed, 960 agreed with the policy change and 240 disagreed. Which of the following statements are true? I. Some of the mailings may have never reached the parents. II. The school district has strong support from parents to move forward with the policy approval. III. It is possible that majority of the parents of high school students disagree with the policy change. IV. The survey results are unlikely to be biased because all parents were mailed a survey. (a) Only I (b) I and II (c) I and III (d) III and IV (e) Only IV Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

49 Sampling bias A picture s worth a lot, but... A lot of the time we only have part of the story. BabyCenter: Our data comes from nearly half a million parents who shared their baby s name with us in top-baby-names The Netflix effect Orange is the New Black: Galina, Piper, Nicky, Alex, Gloria House of Cards : Garrett, Claire, Robin, Wright 2 A blizzard of Frozen names (Elsa, Hans, Kristin) Are we comfortable making decisions about these name trends based on this data? Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

50 Sampling bias A picture s worth a lot, but... A lot of the time we only have part of the story. BabyCenter: Our data comes from nearly half a million parents who shared their baby s name with us in top-baby-names The Netflix effect Orange is the New Black: Galina, Piper, Nicky, Alex, Gloria House of Cards : Garrett, Claire, Robin, Wright 2 A blizzard of Frozen names (Elsa, Hans, Kristin) Are we comfortable making decisions about these name trends based on this data? The name Elsa soared 29 percent on our list of names for baby girls. Is this sample statistic enough for us to conclude that the population parameter of the percent of newborn girls in the United States who are named Elsa has increased from 2013 to 2014? top-baby-names-2014 Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

51 Observational studies and experiments Correlation vs. causation 1 Is there an increase in the popularity of the number of baby girls named Elsa from 2013 to 2014? 2 Has the popularity in Frozen caused an increase in the number of baby girls that were named Elsa? Causal Effect 3 Is the popularity in Frozen related to the increase in the number of baby girls that were named Elsa? Correlation, or relationship We collect our data differently depending on the type of relationship (causal or correlation) that we are interested in. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

52 Observational studies and experiments Observational vs. experimental studies An experimental study (a.k.a. experiment ) is a controlled study in which the researchers impose treatments upon the subjects. Subjects are assigned to control and treatment groups using random assignment. Experiments are the preferred method of data collection we can conclude that the treatments caused the response of the study (i.e. results can be attributed as causal) Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

53 Observational studies and experiments Blocking We would like to design an experiment to investigate if energy gels makes you run faster: Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

54 Observational studies and experiments Blocking We would like to design an experiment to investigate if energy gels makes you run faster: Treatment: energy gel Control: no energy gel Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

55 Observational studies and experiments Blocking We would like to design an experiment to investigate if energy gels makes you run faster: Treatment: energy gel Control: no energy gel It is suspected that energy gels might affect pro and amateur athletes differently, therefore we block for pro status: Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

56 Observational studies and experiments Blocking We would like to design an experiment to investigate if energy gels makes you run faster: Treatment: energy gel Control: no energy gel It is suspected that energy gels might affect pro and amateur athletes differently, therefore we block for pro status: Divide the sample to pro and amateur Randomly assign pro athletes to treatment and control groups Randomly assign amateur athletes to treatment and control groups Pro/amateur status is equally represented in the resulting treatment and control groups Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

57 Observational studies and experiments Blocking We would like to design an experiment to investigate if energy gels makes you run faster: Treatment: energy gel Control: no energy gel It is suspected that energy gels might affect pro and amateur athletes differently, therefore we block for pro status: Divide the sample to pro and amateur Randomly assign pro athletes to treatment and control groups Randomly assign amateur athletes to treatment and control groups Pro/amateur status is equally represented in the resulting treatment and control groups Why is this important? Can you think of other variables to block for? Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

58 Observational studies and experiments Observational vs. experimental studies An experimental study (a.k.a. experiment ) is a controlled study in which the researchers impose treatments upon the subjects. Subjects are assigned to control and treatment groups using random assignment. Experiments are the preferred method of data collection we can conclude that the treatments caused the response of the study (i.e. results can be attributed as causal) Experiments are not always feasible or ethical (e.g. effect of second-hand smoke on newborns) Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

59 Observational studies and experiments Observational vs. experimental studies An experimental study (a.k.a. experiment ) is a controlled study in which the researchers impose treatments upon the subjects. Subjects are assigned to control and treatment groups using random assignment. Experiments are the preferred method of data collection we can conclude that the treatments caused the response of the study (i.e. results can be attributed as causal) Experiments are not always feasible or ethical (e.g. effect of second-hand smoke on newborns) An observational study is a study in which the researchers did not assign the subjects to treatments. Observational studies retain the notion of treatment and control groups. Observational studies still require the researcher to clearly define a research question. This requires identification of the response variable that they will measure on each subject in the study. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

60 Cereal breakfast Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

61 Cereal breakfast What type of study is this, observational study or an experiment? Girls who regularly ate breakfast, particularly one that includes cereal, were slimmer than those who skipped the morning meal, according to a study that tracked nearly 2,400 girls for 10 years. [...] As part of the survey, the girls were asked once a year what they had eaten during the previous three days. What is the conclusion of the study? Who sponsored the study? Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

62 Cereal breakfast What type of study is this, observational study or an experiment? Girls who regularly ate breakfast, particularly one that includes cereal, were slimmer than those who skipped the morning meal, according to a study that tracked nearly 2,400 girls for 10 years. [...] As part of the survey, the girls were asked once a year what they had eaten during the previous three days. This is an observational study since the researchers merely observed the behavior of the girls (subjects) as opposed to imposing treatments on them. What is the conclusion of the study? Who sponsored the study? Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

63 Cereal breakfast What type of study is this, observational study or an experiment? Girls who regularly ate breakfast, particularly one that includes cereal, were slimmer than those who skipped the morning meal, according to a study that tracked nearly 2,400 girls for 10 years. [...] As part of the survey, the girls were asked once a year what they had eaten during the previous three days. This is an observational study since the researchers merely observed the behavior of the girls (subjects) as opposed to imposing treatments on them. What is the conclusion of the study? There is an association between girls eating breakfast and being slimmer. Who sponsored the study? Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

64 Cereal breakfast What type of study is this, observational study or an experiment? Girls who regularly ate breakfast, particularly one that includes cereal, were slimmer than those who skipped the morning meal, according to a study that tracked nearly 2,400 girls for 10 years. [...] As part of the survey, the girls were asked once a year what they had eaten during the previous three days. This is an observational study since the researchers merely observed the behavior of the girls (subjects) as opposed to imposing treatments on them. What is the conclusion of the study? There is an association between girls eating breakfast and being slimmer. Who sponsored the study? General Mills. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

65 Cereal breakfast 3 possible explanations: Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

66 Cereal breakfast 3 possible explanations: 1 Eating breakfast causes girls to be thinner. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

67 Cereal breakfast 3 possible explanations: 1 Eating breakfast causes girls to be thinner. 2 Being thin causes girls to eat breakfast. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

68 Cereal breakfast 3 possible explanations: 1 Eating breakfast causes girls to be thinner. 2 Being thin causes girls to eat breakfast. 3 A third variable is responsible for both. What could it be? Any extraneous variables that affect both the explanatory and the response variable and that make it seem like there is a relationship between the two are called confounding variables. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

69 Cereal breakfast Observational studies and experiments (Recap) Observational study: Researchers collect data in a way that does not directly interfere with how the data arise, i.e. they merely observe, and can only establish an association between the explanatory and response variables. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

70 Cereal breakfast Observational studies and experiments (Recap) Observational study: Researchers collect data in a way that does not directly interfere with how the data arise, i.e. they merely observe, and can only establish an association between the explanatory and response variables. Experiment: Researchers randomly assign subjects to various treatments in order to establish causal connections between the explanatory and response variables. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

71 Cereal breakfast Observational studies and experiments (Recap) Observational study: Researchers collect data in a way that does not directly interfere with how the data arise, i.e. they merely observe, and can only establish an association between the explanatory and response variables. Experiment: Researchers randomly assign subjects to various treatments in order to establish causal connections between the explanatory and response variables. If you re going to walk away with one thing from this class: correlation does not imply causation. xkcd.com/ 552/ Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

72 Cereal breakfast Random assignment vs. random sampling ideal experiment Random sampling No random sampling Random assignment Causal conclusion, generalized to the whole population. Causal conclusion, only for the sample. No random assignment No causal conclusion, correlation statement generalized to the whole population. No causal conclusion, correlation statement only for the sample. most observational studies Generalizability No generalizability most experiments Causation Correlation bad observational studies Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

73 Observations and variables Types of variables all variables numerical categorical continuous discrete regular categorical ordinal measured counted unordered categories ordered categories Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

74 Observations and variables Types of variables (cont.) type: small, midsize or large. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

75 Observations and variables Types of variables (cont.) type: small, midsize or large. (categorical, ordinal) Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

76 Observations and variables Types of variables (cont.) type: small, midsize or large. (categorical, ordinal) price: average price in $1000 s Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

77 Observations and variables Types of variables (cont.) type: small, midsize or large. (categorical, ordinal) price: average price in $1000 s (numerical, continuous) Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

78 Observations and variables Types of variables (cont.) type: small, midsize or large. (categorical, ordinal) price: average price in $1000 s (numerical, continuous) mpgcity: city mileage per gallon Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

79 Observations and variables Types of variables (cont.) type: small, midsize or large. (categorical, ordinal) price: average price in $1000 s (numerical, continuous) mpgcity: city mileage per gallon (numerical, continuous) Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

80 Observations and variables Types of variables (cont.) type: small, midsize or large. (categorical, ordinal) price: average price in $1000 s (numerical, continuous) mpgcity: city mileage per gallon (numerical, continuous) drivetrain: front, rear, 4WD Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

81 Observations and variables Types of variables (cont.) type: small, midsize or large. (categorical, ordinal) price: average price in $1000 s (numerical, continuous) mpgcity: city mileage per gallon (numerical, continuous) drivetrain: front, rear, 4WD (categorical) Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

82 Observations and variables Types of variables (cont.) type: small, midsize or large. (categorical, ordinal) price: average price in $1000 s (numerical, continuous) mpgcity: city mileage per gallon (numerical, continuous) drivetrain: front, rear, 4WD (categorical) passengers: passenger capacity Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

83 Observations and variables Types of variables (cont.) type: small, midsize or large. (categorical, ordinal) price: average price in $1000 s (numerical, continuous) mpgcity: city mileage per gallon (numerical, continuous) drivetrain: front, rear, 4WD (categorical) passengers: passenger capacity (numerical, discrete) Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

84 Observations and variables Types of variables (cont.) type: small, midsize or large. (categorical, ordinal) price: average price in $1000 s (numerical, continuous) mpgcity: city mileage per gallon (numerical, continuous) drivetrain: front, rear, 4WD (categorical) passengers: passenger capacity (numerical, discrete) weight: car weight in pounds Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

85 Observations and variables Types of variables (cont.) type: small, midsize or large. (categorical, ordinal) price: average price in $1000 s (numerical, continuous) mpgcity: city mileage per gallon (numerical, continuous) drivetrain: front, rear, 4WD (categorical) passengers: passenger capacity (numerical, discrete) weight: car weight in pounds (numerical, continuous) Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

86 Principles of experimental design Participation question A study is designed to test the effect of light level and noise level on exam performance of students. The researcher also believes that light and noise levels might have different effects on males and females, so wants to make sure both genders are represented equally under different conditions. Which of the below is correct? (a) There are 3 explanatory variables (light, noise, gender) and 1 response variable (exam performance) (b) There are 2 explanatory variables (light and noise), 1 blocking variable (gender), and 1 response variable (exam performance) (c) There is 1 explanatory variable (gender) and 3 response variables (light, noise, exam performance) (d) There are 2 blocking variables (light and noise), 1 explanatory variable (gender), and 1 response variable (exam performance) Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

87 Principles of experimental design Participation question A study is designed to test the effect of light level and noise level on exam performance of students. The researcher also believes that light and noise levels might have different effects on males and females, so wants to make sure both genders are represented equally under different conditions. Which of the below is correct? (a) There are 3 explanatory variables (light, noise, gender) and 1 response variable (exam performance) (b) There are 2 explanatory variables (light and noise), 1 blocking variable (gender), and 1 response variable (exam performance) (c) There is 1 explanatory variable (gender) and 3 response variables (light, noise, exam performance) (d) There are 2 blocking variables (light and noise), 1 explanatory variable (gender), and 1 response variable (exam performance) Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

88 Principles of experimental design Difference between blocking and explanatory variables Factors are conditions we can impose on the experimental units. Blocking variables are characteristics that the experimental units come with, that we would like to control for. Blocking is like stratifying, except: Blocking used in experimental settings when randomly assigning the sample to treatment / control. Stratifying used when sampling. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

89 Principles of experimental design Principles of experimental design Reading: Open Intro Chapter 1.5: Experiments 1 Control: Compare treatment of interest to a control group. 2 Randomize: Randomly assign subjects to treatments. 3 Replicate: Within a study, replicate by collecting a sufficiently large sample. Or replicate the entire study. 4 Block: If there are variables that are known or suspected to affect the response variable, first group subjects into blocks based on these variables, and then within each block, randomize cases to treatment/control groups. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

90 Principles of experimental design More experimental design terminology... Placebo: fake treatment, often used as the control group for medical studies Placebo effect: experimental units showing improvement simply because they believe they are receiving a special treatment Blinding: when experimental units do not know whether they are in the control or treatment group Double-blind: when both the experimental units and the researchers do not know who is in the control and who is in the treatment group Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

91 Recap Participation question What is the main difference between observational studies and experiments? (a) Experiments take place in a lab while observational studies do not need to. (b) In an observational study we only look at what happened in the past. (c) Most experiments use random assignment while observational studies do not. (d) Observational studies are completely useless since no causal inference can be made based on their findings. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

92 Recap Participation question What is the main difference between observational studies and experiments? (a) Experiments take place in a lab while observational studies do not need to. (b) In an observational study we only look at what happened in the past. (c) Most experiments use random assignment while observational studies do not. (d) Observational studies are completely useless since no causal inference can be made based on their findings. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

93 Recap More... Want more baby name analysis? Freakonomics podcast: How Much Does Your Name Matter? freakonomics.com/ 2013/ 04/ 08/ how-much-does-your-name-matter-a-new-freakonomics-radio-podcast/ Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

94 Sta 101 Syllabus & policies 1 Welcome to Stat 101! Introduction to Inference Populations and Samples Sampling from a population Sampling bias Observational studies and experiments Cereal breakfast Observations and variables Principles of experimental design Recap 2 Syllabus & policies Logistics Details Support Policies Tips 3 To do

95 Syllabus & policies Logistics General Info Instructor: Lecture: Lab: Gary Larson Weekdays 11:00 AM - 12:15 PM Link 088 (Classroom 4) Tu, Th 1:30 PM - 3 PM Link 072 (Classroom 6) Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

96 Syllabus & policies Logistics Office Hours These are subject to change. Check the website for the most current. Mon 12:45-2:00 PM Tue 3:15-4:30 PM Wed 2:15-3:30 PM Thu 3:15-4:30 PM Fri 12:45-2:00 PM If asking about a problem set or lab, you must have tried it out before coming to Office Hours! Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

97 Syllabus & policies Logistics Required materials Textbook Calculator OpenIntro Statistics Diez, Barr, Çetinkaya-Rundel ISBN: Available at link above (free) or in print from Amazon (for about $10) (Optional) You might need a four function calculator that can do square roots for this class. No limitation on the type of calculator you can use. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

98 Syllabus & policies Logistics Webpage stat.duke.edu/ gjl7/ courses/ summer15/ sta / Also accessible via: Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

99 Syllabus & policies Details Course structure Seven learning units. Set of learning objectives and required and suggested readings, videos, etc. for each unit. Prior to beginning the unit, complete the readings and familiarize yourselves with the learning objectives. Class time: split between lecture, discussion/application. Computing labs. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

100 Syllabus & policies Details Class Slides will be posted on the course webpage (under schedule) on the day of the course. Discussion of concepts as well as hands on activities and exercises to complement them. Attend class to keep up with the pace and not fall behind + to contribute to application activities completed in teams. You are responsible for all the material covered in all components of the course, not just the class. Please ask questions in class, office-hours or by if you are struggling (or just curious), do not wait until just before an exam - it will be too late! Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

101 Syllabus & policies Details Participation questions: attendance and participation Objective: Make you an active participant and help me pace the class. On new material being discussed in class that day. Credit for participation, regardless of whether you have the correct answer. Up to two unexcused late arrivals or absences will not affect your participation grade. While I might sometimes call on you during the class discussion, it is your responsibility to be an active participant without being called on. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

102 Syllabus & policies Details Problem sets and labs Problem sets: Objective: Help you develop a more in-depth understanding of the material and help you prepare for exams. Individual: collaborate but don t copy! submit in class, show all work. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

103 Syllabus & policies Details Problem sets and labs Problem sets: Objective: Help you develop a more in-depth understanding of the material and help you prepare for exams. Individual: collaborate but don t copy! submit in class, show all work. Labs: Objective: Give you hands on experience with data analysis using statistical software. In partners turn in lab report on Sakai by the following day at 5 PM. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

104 Syllabus & policies Details Problem sets and labs Problem sets: Objective: Help you develop a more in-depth understanding of the material and help you prepare for exams. Individual: collaborate but don t copy! submit in class, show all work. Labs: Objective: Give you hands on experience with data analysis using statistical software. In partners turn in lab report on Sakai by the following day at 5 PM. Lowest score dropped for both. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

105 Syllabus & policies Details Exams Midterm: TENTATIVE Monday, July 20, in class Final: Saturday, August 8th (9:00 AM - 12:00 PM) (Cumulative) Exam dates cannot be changed. No make-up exams will be given. If you cannot take the exams on these dates you should drop this class. You must bring a calculator to the exams (no cell phones, etc.) and you are also allowed to bring one sheet of notes ( cheat sheet ). This sheet must be no larger than and must be prepared by you (no photocopies). You may use both sides of the sheet. Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57

106 Syllabus & policies Details Grading In Class Participation/Activities: 5% Quizzes: 5% Problem sets: 20% Labs: 15% Midterm: 25% Final: 30% Sta 101 (G. Larson Duke University) U1 - L1: Data coll., obs. studies, experiments June 29, / 57