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Economics and statistics
创建日期：2024-09-03 14:48:12
所属分类：统计学statistics
标签： Ecstatistics
Economics and statistics

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Economics and statistics

Problem Set 2

1.    For the following examples, what do you think the level of randomization should be?

Hint: When answering this question, first think about whether individual level randomization is possible. To determine that, you need to think through any potential concerns about logistics, fairness, balance, spillovers as well as the level of the outcome of interest. If individual level randomization is not possible, what are other potential levels you can use and why?

a.    In a field study, in a  large amusement park, participants rode a roller coaster, were photographed during the ride, and later chose whether to purchase a print of the photo. The researcher wants to measure the effect of pricing strategy (a fixed price of $10 vs pay want you want) on profits.

b.   Uber wants to measure the effect of increasing driver’spay (paying drivers 10% more per ride vs. paying current amounts) on driver’s hours worked.

c.    Oberweiss, an ice-cream cream chain, wants to know the effect of offering free samples on ice-cream sales.

2.   A  researcher plans to ask six subjects to donate either 30 or 60 minutes of their  time. Researcher considers the following three methods for randomization:

*Coin flip : ask 30 minutes of time if coin comes up heads, ask 60 minutes otherwise

*Ordered : ask the 3 subjects who arrived at the lab first for 60 minutes of their time and the last 3 subjects for 30 minutes of their time

*Lottery : write 30 on 3 slips of paper and 60 on another 3 slips of paper; put the slips into envelope,sealand shuffle the envelopes, randomly pick one envelope (without replacement) before talking to a subject and ask the number written on the slip.

a. Discuss the advantages and/or disadvantages of these methods. Which of these methods do you recommend to the researcher?

b. What is the distribution of the average assigned number of minutes if the coin flip method is used?  What is the distribution of the average assigned number of minutes if the lottery method is used?

c.  How will your answer to part (a) change if there are 600 subjects instead of 6 subjects?

3.   Suppose you are interested in understanding how 7-hour workdays compared to 8-hour workdays affect the productivity of your workers using an experiment. That is, you will randomly assign 100 workers to have 7-hour workdays (treatment) and 100 workers to have 8-hour workdays (control). You have data on your employees’ gender, age, years of experience, and current productivity.

a.   Would you choose to do a complete random assignment or a stratified random assignment? Explain your reasoning.

b.   If you can only stratify on one variable, which variable would you choose to stratify on? Why? Do you  need to do any  modifications on this variable before doing the stratification?

c.    If you can choose more than one variable to stratify on, which additional variable(s) would you choose to stratify on? Why? Do you need to do any modifications on these variable(s) before doing the stratification? Are there any concerns about choosing many variables to stratify on?

d.   Would  your  answer  to  part  (a)  be  different if  you  were randomly assigning 1000 workers  to  have  7-hour  workdays  (treatment)  and 1000 workers  to  have  8-hour workdays (control)? If yes, why/how?

4.   Your research team is interested in looking at the impact of providing students a tutor. These tutors work with children in grades 2, 3 and 4 who are identified as falling behind their peers. Through  a  pilot  survey,  we  know that  the  average  test  scores  of  these  students  before receiving tutoring is 26 out of 100, with a standard deviation of 20.

Note:  For  this  question,  please   use  the  formulas  that  we   learned  in  class  and  do  the calculations yourself instead of using the software. You are allowed to use excel or online calculators to calculate the relevant values of the student’st-distribution. Show all your work. It is ok if your answers are not round numbers.

a.    If you have 1000 students and you randomly assign half of them to the control group and half of them to the treatment group, what is the minimum detectable effect you can measure when the level of significance is 0.05 and power you want is 80%?

b.   If you have 2000 students and you randomly assign half of them to the control group and half of them to the treatment group, what is the minimum detectable effect you can measure when the level of significance is 0.05 and power you want is 80%?

c.    Based on  parts a and  b, will you need larger or smaller samples to measure smaller effect sizes?

d.   If you have 1000 students and you randomly assign 3/4th of them to the control group and 1/4th of them to the treatment group, what is the minimum detectable effect you can measure when the level of significance is 0.05 and power you want is 80%?

e.    Based on your answer in parts a and d, will you prefer unequal assignment allocations or equal

assignment allocations? When might a researcher prefer unequal assignment allocations?

f.    Suppose you control for some  student characteristics  which reduces the  residual standard deviation to 10. If you have 1000 students and you randomly assign half of them to the control group and half of them to the treatment group, what is the minimum detectable effect you can measure when the level of significance is 0.05 and power you want is 80%?

g.    Based on your answer in parts a and f, will you be able to detect smaller effect sizes when the standard deviation is lower or higher?

h.   Your research team decides to randomize at the school level instead of at the individual level. So, you are doing a clustered randomization. Suppose you have 20 schools in total and each school has 200 students. You randomly assign half of the schools to control and half of them to treatment. Continue to assume a standard deviation of 20.

i.     What  is  the  minimum  detectable  effect  you  can  measure  when  the  intracluster correlation is 0.05 and the level of significance is 0.05 and power you want is 80%?

ii.   What  is  the  minimum  detectable  effect  you  can  measure  when  the  intracluster correlation is 0.20 and the level of significance is 0.05 and power you want is 80%?

iii.  What  is  the  minimum  detectable  effect  you  can  measure  when  the  intracluster correlation is 0.50 and the level of significance is 0.05 and power you want is 80%?

iv.   Based  on  previous  parts, will you  be  able to detect smaller effect sizes when the intracluster correlation is lower or higher?


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关键词一 关键词二 关键词三 关键词四 关键词五 和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 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MATH20602 COMP532 MAS275 COMP5318 COMP4002 FIT5086 MAST20004 FIT3152 FIT5129 CIS2380 CS521 COMP 1005 EECMS CITS5501 ECE 462 ECON 6002 ENG 4051 CSC 648 CMT654 MECHENG 713 PHYS1002 AMME 2000 FP0060 DDES3200 MECHENG 743 BINF90002 FIT2081 ISYS90081 ELECTENG 722 BUS 360 ECOS3010 BUS2810 ETF2100 ENG2048 STAT5002 COMP2017 CEME 2003 MATS3004 COMP9319 PHYS1001 COMP5349 AMME2261 COMP-381 FIT3173 COSC2757 ENG4025 QBUS2820 COMP9414 MATH2021 EOSC118 MFIN6690 PMATH 321 CSE-141L MATH575A COMPSCI5002 COMP1511 management comp2123 FINS3616 COMP 3331 COMS30034 DTSC 71 AcF 702 AcF702 DTSC71 MAT021 ELE8083 ACFI213 EG-127J 127J FIT5163 FIT2001 ELE00113M CMT310 CS 245 ENGL 1101 MTH6115 EE497 CS 325 Math 124A MTH5130 MBA502 MGT 5380 ARCH 1261 F033800 20LLP109 ELE4009 FINANCIAL COMP3331 Computer ECE4179 20T3 COMP9311 COMP9311 UNSW MFIN6210 ACCT 5930 EE590 ENG2029 ECO100 SIT315 ACCT3610 COMP3600 STK2100 FIT2004 COMP30020 ACTL1101 Stat 101B BANA 200 COSC2473 ENGG1400 AI COMP90043 MMF 1914H PHYS 127 CS584 CIVL2010 ECMT2150 CS 333 CP1406 KIT308 Economics 701 ECON3740 ECE 5759 BFC3340 FINC2012 COMP4500 MATH3871 FIT3080 18-819C Economic ECO202Y5Y PHY100 FINC-780 Econ 100B EC602 IE582 EE450 COMP9517 WRDS 150B ECON 570 LECTURE 2 ECA5101 ECE 4420 ADAD9311 FIT3031 CS 544 MF 703 CS 6140 KIT501 ENGSCI 344 CSC171 IE 332 FINM8007 21S2 COSC 1114 FE545 E471 SIT102 CSC108 MAT301 IAE 101 COP3503 STAT2004 EC 303 CS1026 STAT1203 MATH3171 ISOM5160 IFN657 FIT2014 ACCT2102 DSCI550 STATS 330 ELEC421 COMP3670 QBUS6840 MEES:698B MAST30027 MIET1077 Economics IFT 6758 FIT5122 BUSN5101 CptS 111 HRMT5502 Math2018 PP 312 INFS3200 CZ3005 CSSE1001 SENG 2011 MKTG 553Q BUFN 640 COMP507 ETF5952 DATA 311 ECE4043 BANK3011 finance M3H623544 HW1 INFS 7410 AI6103 STAT3888 INFS3208 ACCT7103 ECOS3013 PSYCH 20B F79MA STAT3006 ENGG952 2X MGSC 7000 ECE4132 MSF 526 MATH 3033 CDS 511 EEEE4120 EEET2465 ECA5103 MATH2070 ELEC3104 BU51019 EEE8147 ENGR20003 COSC 1107 ETF3200 FNCE 435 MSFI 435 ISyE6420 GENG4405 HW ETC5523 IE 7315 MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A 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