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Chap 1. Statistics and Data

Chap 1. Statistics and Data. Why do we Study Statistics? Data Variables Experimental Study Observational Study. 1. 2. 3. 5. 4. Why do we Study Statistics?. Data. Variables. Controlled Experiments. Observational Study. INDEX. 1. Why Do we Study Statistics?.

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Chap 1. Statistics and Data

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  1. Chap 1. Statistics and Data Why do we Study Statistics? Data Variables Experimental Study Observational Study

  2. 1 2 3 5 4 Why do we Study Statistics? Data Variables Controlled Experiments Observational Study INDEX

  3. 1. Why Do we Study Statistics? The Value of Statistics We use statistics in almost everywhere such as economics, business administration, law, medical science, humane studies and natural science. We live in statistics. ‘The specific advertisement raises the revenue?’ ‘A famous actor makes a larger audience share?’ ‘A sexism exists in labor market?’ ‘what is the effect of FDI on economic growth rate?’ …

  4. 1. Why Do we Study Statistics? Idiot Statistics (I) “A .3 hitter made three poor shows of batting, so he is gonna make a hit.’ - Game commentary – “Since you had only two daughters, this time is for son. One more please…”– a husband’s mother -

  5. 1. Why Do we Study Statistics? Idiot Statistics (II) “They could make over 800% profitability just for 3 months, according to the fundamental investment principle.” - Appraisal for the first winner of the Mock Investment in Stocks Contest -

  6. Why Do we Study Statistics? Idiot Statistics (III) “ Low relation in SAT score and GPA in college. So SAT score is not so helpful for predicting the achievement in college.” - the office of XX academic affairs -

  7. 1 2 3 5 4 Variables Controlled Experiments Observational Study INDEX Why do we Study Statistics? Data

  8. 2. Data Relation between Population and Sample Sampling Sample Population Statistic Parameter Inference • Statistics includes not only the descriptive statistics but the inference statistics.

  9. 2. Data Kinds of Data • Cross-Section Data - Different subjects are compared to one another at one point in time. • Time-Series Data - Changes of one subjects are compared to over time. • Longitudinal Data - Subjects are followed over time, and compared with themselves at different points in time. • Panel Data - Observations on multiple phenomena are observed over multiple time periods

  10. 1 2 3 5 4 Data Controlled Experiments Observational Study INDEX Why do we Study Statistics? Variables

  11. 3. Variables 변수의 유형 Coding Random Variable Quantitative Variable Qualitative Variable • Quantitative Variable : answered by giving a number Ex) age, family size, family income • Qualitative Variable : not a number by itself, but become a random variable after coding to a number Ex) marital status (single, married, widowed, divorced, separated), employment status

  12. 1 2 3 5 4 Data Variables Observational Study INDEX Why do we Study Statistics? Controlled Experiments

  13. 4. Controlled Experiments Principles of Experimental Studies • Randomized Control • Assignment to the treatment group or the control group • What if make groups w.r.t the relevant variables; family income, personality, or social habits? • Toss a coin! • Double blindness • The subjects did not know whether they got the treatment of the placebo, and neither did those who evaluated the responses.

  14. 4. Controlled Experiments National Foundation for Infantile Paralysis Experiment 1st grade 2nd grade 3rd grade Control Group Consent of parents Treatment Group (vaccine) No consent • Are subjects assigned to treatment of control at random? No! • Is double blindness considered? No!

  15. 4. Controlled Experiments Randomized double blind experiment Children consented to vaccination No consented children No consent (exclusion) Random assignment Treatment group (vaccine) Control group (placebo) • Only the children consented by parents are assigned to treatment or control at random • After controlling grades, placebo makes double blind

  16. 4. Controlled Experiments The Salk Vaccine Field Trial Randomized controlled double blind Not randomized controlled rate Sample size rate Sample size Treatment 200,745 28 Grade 2(vaccine) 221,998 25 Control 201,229 71 Grade 1&3(control) 725,173 54 123,605 44 No concent 338,778 46 Grade 2(no concent) Size of groups and rate of polio cases per 100,000 in each group source: J.M.Tanner, et al., Statistics , 3rd ed., Wadworth & Brooks, p.12, Table1. Without randomized control, ‘consent of parents’ is a confounding factor. It offsets the positive effect of vaccine partly.

  17. 4. Controlled Experiments A specific for growth model Control group ??? Slow-growing kids Fast-growing kids exclusion Treatment group (specific for growth) • Is it meaningful to compare before and after having a specific for growth? • Does a specific for growth affect slow-growing kids to grow?

  18. 4. Controlled Experiments Revised model– a specific for growth Slow-growing kids Fast-growing kids exclusion Random assignment Treatment group (a specific for growth) Control group (placebo) • Random assignment to control or treatment among slow-growing kids • Placebo effect

  19. 1 2 3 4 5 Data Variables Controlled Experiments INDEX Why do we Study Statistics? Observational Study

  20. 5. Observational Study Observational Study VS Controlled Experiments In an observational study it is the subjects who assign themselves to the different groups: the investigators just watch what happens Ex ) Studies on the effects of smoking Nobody is going to smoke for ten years just to please a statistician. The investigators compare smokers with nonsmokers to determine the effect of smoking.

  21. 5. Observational Study If the treatment group is different from the control group with respect to other factors, their effects are confounded with the effect of the treatment. Confounding Factor

  22. 5. Observational Study Control for Confounding factors To control for confounding factors, make comparisons separately for smaller and more homogeneous groups. Ex) simple comparison between smokers’ and nonsmokers’ mortality: men are more likely than women to have heart disease Male smokers to male nonsmokers Compare separately female smokers to female nonsmokers Older people have different smoking habits, and are more at risk for lung cancer Compare separately Male smokers to nonsmokers at same age Female smokers to nonsmokers at same age

  23. 5. Observational Study Simpson’s paradox The successes of several groups seem to be reversed when the groups are combined. We need to control for the confounding factors.

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