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Policy Inquiry – Lecture 1 Common Sense and the Elementary Forms of Statistical Reason.

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1 Policy Inquiry – Lecture 1 Common Sense and the Elementary Forms of Statistical Reason

2 We rely on crude statistical thinking at all times We count things all the time We count things all the time Only difference between how we talk and how statisticians talk is in how carefully we count Only difference between how we talk and how statisticians talk is in how carefully we count 76% of VT students favor faculty evaluations 76% of VT students favor faculty evaluations Most of the students favor faculty evaluations Most of the students favor faculty evaluations The students at VT favor faculty evaluations The students at VT favor faculty evaluations

3 Common Sense While people regularly dismiss statistical arguments, they regularly submit to common sense While people regularly dismiss statistical arguments, they regularly submit to common sense If we trust common sense, we should trust statistics more If we trust common sense, we should trust statistics more Why? Well, how do we create common sense – what methods do we use, and are they different from statistics? Why? Well, how do we create common sense – what methods do we use, and are they different from statistics?

4 We depend on typicality The most important method seems to be to arrange things in terms of how typical we think they are The most important method seems to be to arrange things in terms of how typical we think they are We do this automatically, without thinking about it We do this automatically, without thinking about it We readily talk about average ability, normal intelligence, typical appearance, business as usual We readily talk about average ability, normal intelligence, typical appearance, business as usual

5 Task Draw a typical building Draw a typical building Share Share Could we program this? Could we program this?

6 Typification Typification is a necessary component of human communication Typification is a necessary component of human communication It is a form of logic – or a logical form It is a form of logic – or a logical form It appears in both ordinary discourse and statistical work It appears in both ordinary discourse and statistical work

7 Assessing Typicality The way we do it in statistics is basically the same as how we do it every day The way we do it in statistics is basically the same as how we do it every day Actually, in everyday discourse, we often get much fancier Actually, in everyday discourse, we often get much fancier Most prevalent method – look around and figure out what is predominant Most prevalent method – look around and figure out what is predominant New MPA class mostly male or female? New MPA class mostly male or female? Describe the typical senator Describe the typical senator What do statisticians call this kind of typicality? What do statisticians call this kind of typicality?

8 Typicality cont. We be black and they white. They got things and we aint. They do things and we cant. Its just like living in jail. We be black and they white. They got things and we aint. They do things and we cant. Its just like living in jail. Richard Wright, Native Son What is Richard Wright telling us? List the typicalities What is Richard Wright telling us? List the typicalities The point is that through literature Wright is making a statistical argument The point is that through literature Wright is making a statistical argument hes using a logical form – the idea of typicality hes using a logical form – the idea of typicality Does this passage still apply today? How can we tell? Are things different? How much different? Does this passage still apply today? How can we tell? Are things different? How much different?

9 Task Everybody standup and line up by height at the back of the room Everybody standup and line up by height at the back of the room least-tall on left, least-short on right least-tall on left, least-short on right Whos in the middle? Whos in the middle? What kind of typicality is this? What kind of typicality is this? Where do we see this type of average used the most? Why? Where do we see this type of average used the most? Why?

10 Task Measure your heads Measure your heads Measure you hands Measure you hands Add all together and divide by number of people in the room Add all together and divide by number of people in the room What type of average is this? What type of average is this? When do we do this kind of averaging? Why? When do we do this kind of averaging? Why? Keep you measurements! Keep you measurements!

11 Typical Statistical Averages Mode Mode What is there the most of? What is there the most of? Median Median Whats in the middle? Whats in the middle? Mean Mean If you put everything together and then equally distributed it, how much would everybody get? If you put everything together and then equally distributed it, how much would everybody get? Other less typical (for us!) Other less typical (for us!) http://en.wikipedia.org/wiki/Average http://en.wikipedia.org/wiki/Average

12 Task Write down description of a typical one-person band Write down description of a typical one-person band The type of musician that performs on street corners and can play multiple instruments at the same time The type of musician that performs on street corners and can play multiple instruments at the same time Where did you get this idea? Where did you get this idea? If it were a short Ethiopian woman playing the viola and clarinet at the same time, would that alter your thinking of the typical one-person band? If it were a short Ethiopian woman playing the viola and clarinet at the same time, would that alter your thinking of the typical one-person band? What do we call a conceptual average that is hard to break? What do we call a conceptual average that is hard to break?

13 Why Typify? So, why do we typify? So, why do we typify? Consider you are about to meet someone for the first time and you know little about this person Consider you are about to meet someone for the first time and you know little about this person If you are wise, you will assume s/he is more or less a typical person – WHY? If you are wise, you will assume s/he is more or less a typical person – WHY? Answer: it minimizes total sum of errors Answer: it minimizes total sum of errors What would happen if we decided that every new person we met was a jerk? How much re- evaluation would be necessary? What would happen if we decided that every new person we met was a jerk? How much re- evaluation would be necessary?

14 Folk Terms for Central Tendency Average, commonplace, consistent, humdrum, conventional, normal, ordinary, standard, stereotypical, popular, prevailing, regular, stock, typical, unexceptional, uniform, usual Average, commonplace, consistent, humdrum, conventional, normal, ordinary, standard, stereotypical, popular, prevailing, regular, stock, typical, unexceptional, uniform, usual Any time you see one of these words used in spoken or written communication, a statistical argument is being made Any time you see one of these words used in spoken or written communication, a statistical argument is being made

15 Folk vs. Statistical While people often believe that folk ways of assessing things are easier than statistical ways, it is most often the opposite. While people often believe that folk ways of assessing things are easier than statistical ways, it is most often the opposite. Consider Richard Wrights statement again and the complexities involved in what he is saying Consider Richard Wrights statement again and the complexities involved in what he is saying

16 The Atypical If we are interested in typicalities, we are automatically interested in differences If we are interested in typicalities, we are automatically interested in differences We cannot compare without thinking about differences We cannot compare without thinking about differences Even small differences can precipitate fights, depression, arrogance, humility, etc. Even small differences can precipitate fights, depression, arrogance, humility, etc. In the 80s and 90s, a lot of consideration in organizations about the differences between Americans and the Japanese In the 80s and 90s, a lot of consideration in organizations about the differences between Americans and the Japanese

17 Atypical cont. People are neurotically obsessed with differences People are neurotically obsessed with differences People act on differences all the time People act on differences all the time Actual or just believed Actual or just believed How many of you are trying to eat less? How many of you are trying to eat less? Why? Why? If one neighborhood gets better trash service than another, does it matter? Why? If one neighborhood gets better trash service than another, does it matter? Why? Concern with the atypical defines much of public administration Concern with the atypical defines much of public administration

18 Folk terms for Atypical Alien, antithesis, contrast, deviant, difference, discrepancy, disparity, dissimilar, distinct, divergent, diversity, heterogeneity, incomparable, individuality, mismatched, modified, originality, peculiar, special, unequal, unlike, variance, variation, unusual, strange, etc… Alien, antithesis, contrast, deviant, difference, discrepancy, disparity, dissimilar, distinct, divergent, diversity, heterogeneity, incomparable, individuality, mismatched, modified, originality, peculiar, special, unequal, unlike, variance, variation, unusual, strange, etc…

19 Difference for each average Mode Mode Why do we care about what characteristics the typical senator has? Why do we care about what characteristics the typical senator has? Why do we care how many men vs. women are in graduate school? Why do we care how many men vs. women are in graduate school? Median Median Why do we care about median income? Why do we care about median income? (Arithmetic) Mean (Arithmetic) Mean Why would we care about your head size? Why would we care about your head size? What if IQ was involved? What if IQ was involved?

20 Task How atypical are you? How atypical are you? Calculate the difference of your head size from the arithmetic mean of the class Calculate the difference of your head size from the arithmetic mean of the class Who are the deviants? Who are the deviants? Where do we set the bars? Where do we set the bars?

21 All Research is Primarily about TWO things Averages Averages And differences from the average And differences from the average

22 Counting Students generally think that stats is highly numerical (true) Students generally think that stats is highly numerical (true) Students generally think that ordinary conversation is not usually numerical (false) Students generally think that ordinary conversation is not usually numerical (false) Only difference is how conscientious we are about our counting Only difference is how conscientious we are about our counting

23 Careful Counting We all count, and we count nearly all the time We all count, and we count nearly all the time The last bullet contains some counts The last bullet contains some counts Everyday conversation is loaded with hyperbole that results from not counting correctly (sometimes on purpose, sometimes not) Everyday conversation is loaded with hyperbole that results from not counting correctly (sometimes on purpose, sometimes not) I never do anything right I never do anything right If you count the number of times I do things wrong, it will equal the number of times I have done anything at all If you count the number of times I do things wrong, it will equal the number of times I have done anything at all Obviously a bad count, and can have serious emotional consequences for the person who believes it Obviously a bad count, and can have serious emotional consequences for the person who believes it

24 Hyperbole vs. Careful Counting in PA This will be one of the forms of statistical reasoning you will deal with the most This will be one of the forms of statistical reasoning you will deal with the most Just about (a count) every complaint that you will receive will include an implicit count Just about (a count) every complaint that you will receive will include an implicit count That count will usually (a count) not be a careful count That count will usually (a count) not be a careful count That bridge construction project is taking forever! Or, too long! That bridge construction project is taking forever! Or, too long! We are under-serving our disadvantaged citizens! We are under-serving our disadvantaged citizens! Our recreation resources are terrible compared to other towns. Our recreation resources are terrible compared to other towns. As a public administrator, you will have to deal with bad counting from both public AND your political bosses. As a public administrator, you will have to deal with bad counting from both public AND your political bosses.

25 Folk Modifiers for Counting Many Many Much Much Some Some Numerous Numerous A little A little Often Often A lot A lot A few A few Plenty Plenty Commonly Commonly Rarely Rarely

26 What do we count? Categorization The scientist (social or otherwise) is concerned with categorization more than anything else The scientist (social or otherwise) is concerned with categorization more than anything else It drives what gets counted and analyzed It drives what gets counted and analyzed Statement 1: The estimated average density of the known universe is equal to one hydrogen atom per ten cubic meters Statement 1: The estimated average density of the known universe is equal to one hydrogen atom per ten cubic meters Statement 2: The average classroom contains 20 students Statement 2: The average classroom contains 20 students

27 Categorization, cont. First statement has well defined categories First statement has well defined categories Hydrogen atom – has a well defined and excepted definition – dont need to wonder whether it is big/small, rich/poor, sick/healthy, old/young, male/female Hydrogen atom – has a well defined and excepted definition – dont need to wonder whether it is big/small, rich/poor, sick/healthy, old/young, male/female Second statement is not well defined Second statement is not well defined Category student offers no clue as to what it is referring to – older students, special ed, graduate, grade school? Category student offers no clue as to what it is referring to – older students, special ed, graduate, grade school? Category classroom is equally ambiguous – lecture hall at a college or elementary school classroom? Category classroom is equally ambiguous – lecture hall at a college or elementary school classroom?

28 Task Define explicitly college student vs. town resident for a census count of Blacksburg Define explicitly college student vs. town resident for a census count of Blacksburg Present and defend your categorization Present and defend your categorization

29 Probability What is probable is what is average What is probable is what is average POLICY is passed based on a belief of averages! POLICY is passed based on a belief of averages! Why should we try to minimize drug use in teens? Why should we try to minimize drug use in teens? Administrative decisions are made on a belief in averages! Administrative decisions are made on a belief in averages! Why would a locality send its police officers to training? Why would a locality send its police officers to training?

30 Task Lets draw a frequency distribution Lets draw a frequency distribution Across the bottom, lets divide head size into 5 categories (smallest to largest) Across the bottom, lets divide head size into 5 categories (smallest to largest) One by one, read off your head measurements One by one, read off your head measurements For each category, draw a box for each head that fits that category, stack them up as you get more than one for that category For each category, draw a box for each head that fits that category, stack them up as you get more than one for that category Calculate the probability of having a head size in the middle category Calculate the probability of having a head size in the middle category

31 Probability cont. Probability is a measure of how likely we think it is that something is going to happen. Probability is a measure of how likely we think it is that something is going to happen. We figure this out by comparing to the average We figure this out by comparing to the average How sure we are of our estimate depends on the variability of the data around the average How sure we are of our estimate depends on the variability of the data around the average What is we all had the same head size? What is we all had the same head size?

32 Relationships The human mind is not content with knowing averages and atypicalities The human mind is not content with knowing averages and atypicalities It also wants to find patterns or relationships – knowing these relationships makes life much easier It also wants to find patterns or relationships – knowing these relationships makes life much easier You buy your boyfriend/girlfriend a gift You buy your boyfriend/girlfriend a gift Why? What relationship do you believe exists Why? What relationship do you believe exists You entertain out of town friends by bringing them to an expensive restaurant youve never been to You entertain out of town friends by bringing them to an expensive restaurant youve never been to Why? What relationships do you believe exist? Why? What relationships do you believe exist? You help pass legislation that makes any medicine containing oxycodone be sold behind the counter (you have to ask the pharmacist for it) You help pass legislation that makes any medicine containing oxycodone be sold behind the counter (you have to ask the pharmacist for it) Why? Why?

33 Relationship Defined Where you find X, you find Y Where you find X, you find Y Where you dont find X, you dont find Y Where you dont find X, you dont find Y This is actually a positive relationship This is actually a positive relationship What would a negative relationship be? What would a negative relationship be? How about curvilinear How about curvilinear Y Not Present Y Present X Present -+ X Not Present +-

34 Relationship Linguistics Expressed in many forms Expressed in many forms If we cut taxes, people will spend more money If we cut taxes, people will spend more money If the road construction contractor finishes on time, hell get his bonus If the road construction contractor finishes on time, hell get his bonus Honor your mother and father. Honor your mother and father. Moral arguments usually have an implicit statistical argument Moral arguments usually have an implicit statistical argument Eat your spinach! Eat your spinach!

35 Task Read off your head measurement and hand-spread measurement for me to plot Read off your head measurement and hand-spread measurement for me to plot Do we see a correlation (a relationship)? Do we see a correlation (a relationship)? Do we see causation (a relationship where A actual makes B happen)? Do we see causation (a relationship where A actual makes B happen)?

36 Folk Terms for Relationships Affiliation, affinity, agreement, association, belonging to, comparable, connection, contingency, dependence, effect, grouping, interdependence, interrelationship, pattern, linkage, proportionate, etc. Affiliation, affinity, agreement, association, belonging to, comparable, connection, contingency, dependence, effect, grouping, interdependence, interrelationship, pattern, linkage, proportionate, etc.

37 Sampling To find relationships, statisticians infer from samples of whatever they are looking at To find relationships, statisticians infer from samples of whatever they are looking at Tends to give stats a bad name – why? Example? Tends to give stats a bad name – why? Example?

38 Sampling cont. Fact is, All human knowledge, in one way or another, is knowledge derived from a sampling of the world around us Fact is, All human knowledge, in one way or another, is knowledge derived from a sampling of the world around us It would be very difficult to function otherwise It would be very difficult to function otherwise Youre preparing fettuccini alfredo for a group of friends and you sample it to see if it is seasoned properly Youre preparing fettuccini alfredo for a group of friends and you sample it to see if it is seasoned properly Anyone against sampling would have to eat the entire dish to make sure Anyone against sampling would have to eat the entire dish to make sure Look out the side window. Is it raining? Look out the side window. Is it raining? Anyone against sampling would have to check a window on each side of the house to make that determination Anyone against sampling would have to check a window on each side of the house to make that determination

39 Folk Sampling Gone Bad Youre brought up in a middle-class, white, protestant home and you consider people like this as normal. Others are not normal, and, possibly bad (you saw some bad African Americans on COPs). Youre brought up in a middle-class, white, protestant home and you consider people like this as normal. Others are not normal, and, possibly bad (you saw some bad African Americans on COPs). You go to a garage and they mess up. You say you will never return (a generalization about the quality of all their work)! Turns out its the best garage in town and only makes one error for every 10,000. You go to a garage and they mess up. You say you will never return (a generalization about the quality of all their work)! Turns out its the best garage in town and only makes one error for every 10,000. What is wrong with these samples and generalizations? N! What is wrong with these samples and generalizations? N!

40 Control (Standardization) By a show of hands, how many of you have ever attempted to grow a mustache or beard? By a show of hands, how many of you have ever attempted to grow a mustache or beard? What percentage of the class is that? What percentage of the class is that? Divide the little number by the big number Divide the little number by the big number So, what is our conclusion about the popularity of facial hair among men at Virginia Tech? So, what is our conclusion about the popularity of facial hair among men at Virginia Tech? Is there a problem with this conclusion? What? Is there a problem with this conclusion? What?

41 Control cont. We use control and standardization to simplify complex matters so that we can make comparisons. We use control and standardization to simplify complex matters so that we can make comparisons. Would you compare two runners with one running on a 400yd track and the other a 400m track? Would you compare two runners with one running on a 400yd track and the other a 400m track? Anytime you hear Yes, but… or Have you considered… you are being asked a question about control and standardization Anytime you hear Yes, but… or Have you considered… you are being asked a question about control and standardization

42 Control, cont. Can you come up with the Yes, but… Can you come up with the Yes, but… They say if you eat less, you lose weight. Im eating less, but Im not losing weight. They say if you eat less, you lose weight. Im eating less, but Im not losing weight. If poor people would just get some ambition, they could have anything they want. America is a land of equal opportunity for all. If poor people would just get some ambition, they could have anything they want. America is a land of equal opportunity for all. If we get better gas mileage from our cars, we will be going a long way toward improving the environment. If we get better gas mileage from our cars, we will be going a long way toward improving the environment. I figure I have a good lawyer in my case because he said he won every trial he was in. I figure I have a good lawyer in my case because he said he won every trial he was in. Is X REALLY related to Y, or is there a third variable, Z, that might be influencing the results? Is X REALLY related to Y, or is there a third variable, Z, that might be influencing the results?

43 Folk Control Phrases Yes, but have you considered… Yes, but have you considered… You are leaving something out… You are leaving something out… If you take so and so into account… If you take so and so into account… Yes, but that could also be caused by… Yes, but that could also be caused by…

44 Model When you put together all your supposed relationships with all necessary controls, you get a model When you put together all your supposed relationships with all necessary controls, you get a model

45 There are two Types of Models What are they? What are they? 1.Physical – A smaller tangible thing you can mess with 2.Symbolic - Use words, pictures, lines, equations, or computer programs to represent elements and illustrate relationships

46 Folk Terms for Symbolic Models Exemplar, archetype, ideal, map, paradigm, portrayal, presentation, stereotype, etc… Exemplar, archetype, ideal, map, paradigm, portrayal, presentation, stereotype, etc…

47 Task Write down three questions that you would put on a questionnaire if you were tasked with surveying CPAP MPA student opinions about the orientation program for incoming students. Write down three questions that you would put on a questionnaire if you were tasked with surveying CPAP MPA student opinions about the orientation program for incoming students. Task time: 5 minutes Task time: 5 minutes

48 Basic Model Construction What am I trying to figure out – what concepts am I trying to measure? What am I trying to figure out – what concepts am I trying to measure? What do I need to count to help me figure it out? What do I need to count to help me figure it out? What variables could represent the concept? What variables could represent the concept? What relationship does this thing youre counting have with the concept youre trying figure out? What relationship does this thing youre counting have with the concept youre trying figure out? If class requirements are clear the student will be happier If class requirements are clear the student will be happier What controls might be needed? What controls might be needed?

49 Task Now, with the benefit of basic model building, split into three groups Now, with the benefit of basic model building, split into three groups Detail your model Detail your model What concepts are you trying to measure? What concepts are you trying to measure? What are the relationships between your variables and the concept (positive or negative)? What are the relationships between your variables and the concept (positive or negative)? Should any control variable be used? Should any control variable be used? Now, formulate, as a group, a question that could be asked to collect data for each variable Now, formulate, as a group, a question that could be asked to collect data for each variable Task time: 10 minutes Task time: 10 minutes Did your questions change? Why? Did your questions change? Why? One group will be called up to present their model and defend themselves to their colleagues. One group will be called up to present their model and defend themselves to their colleagues.

50 Forms of Statistical Logic Average Average Deviation Deviation Careful Counting Careful Counting Probability Probability Relationships Relationships Control Control Model Model Categorization Categorization

51 Assignment Write 1 paragraph describing, in your own words, each form of statistical logic Write 1 paragraph describing, in your own words, each form of statistical logic For each form, find an example in a newspaper or news magazine, describe it and give your opinion of its veracity For each form, find an example in a newspaper or news magazine, describe it and give your opinion of its veracity What statistical argument are they making? What statistical argument are they making? Is there any data/evidence to back up the argument or are they simple assertions? Is there any data/evidence to back up the argument or are they simple assertions? Are there any Yes, but…s that should be considered? Are there any Yes, but…s that should be considered?


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