在新SAT數(shù)學(xué)里，統(tǒng)計(jì)這一塊進(jìn)行了比較大的變動(dòng)，增加了一些同學(xué)們不太熟悉的知識(shí)點(diǎn)，包括margins of error/confidence interval，random sampling & random assignment 等。1月份考試將近，今天我們來(lái)講講random sampling & random assignment在SAT數(shù)學(xué)考試中的考法和應(yīng)用。
定義
什么是random sampling？ 如果說(shuō)你從1000人中隨機(jī)抽取100人來(lái)做實(shí)驗(yàn)，那就是 random sampling。
什么是random assignment？如果你將不同實(shí)驗(yàn)方案隨機(jī)分配給上述那100人中進(jìn)行實(shí)驗(yàn)，那就是random assignment。
應(yīng)用
那么random sampling和random assignment在統(tǒng)計(jì)題目中意味著什么呢？我們來(lái)看一個(gè)例子：
Hilary recruits residents from her town who have physical exams scheduled in the next month with the local doctor's office. She randomly assigns the volunteers to either a Vitamin D supplement pill or a placebo pill. Participants do not know which pill they are taking. They have their blood pressures measured before the study begins and at the end of the study.
Suppose Hilary finds that the group who took the Vitamin D supplements had a significant decrease in blood pressure, while the placebo group showed no significant change in blood pressure.
這個(gè)時(shí)候題目一般會(huì)問(wèn)兩個(gè)問(wèn)題：
1、根據(jù)我們剛剛的實(shí)驗(yàn), 我們是否能夠?qū)⒔Y(jié)論拓展到整個(gè)群體「Can the results be generalized to the entire population?」
2、根據(jù)我們剛剛的實(shí)驗(yàn)，我們是否得出the difference in blood pressures is caused by the Vitamin D「Can conclusions about cause and effct be drawn？」
以上的問(wèn)題也就是SAT數(shù)學(xué)關(guān)于random sampling & random assignment的考點(diǎn)，各位同學(xué)只要會(huì)回答上邊兩個(gè)問(wèn)題，即可應(yīng)付考試。那么如何去理解呢？同學(xué)們需要記住下邊兩個(gè)結(jié)論:
- Was the sample of subjects in the study selected at random from the entire population in question? If so, the results can be generalized to the entire population in question. However, check to make sure that the conclusion is referring to the same population as that in the study.
- ** Were the subjects randomly assigned to treatments?** If so, conclusions about cause and effect can be drawn.
簡(jiǎn)單總結(jié)就是：Random Sampling 可推出 the results can be generalized to the entire population；Random Assignment 可推出 結(jié)論因果關(guān)系成立。
根據(jù)我們剛剛的實(shí)驗(yàn)，我們樣本來(lái)自volunteer，并不是隨機(jī)從總體里選的，那么最后的結(jié)論就不能generalize to the entire population。然而我們?cè)谧鰧?shí)驗(yàn)的時(shí)候，的確符合random assignment，所以最后的結(jié)論就能夠得出因果關(guān)系。
真題練習(xí)
Researchers in Australia carried out an experiment to determine if the color of a coffee mug affects how people rate the flavor intensity of the coffee.
Volunteers were randomly assigned to taste coffee in mugs that differed only by color: some white and some clear. The same type of coffee was used in both mugs. The researchers concluded that the mean flavor intensity rating was significantly higher for those who drank coffee in a white mug than for those who drank coffee in a clear mug. Based on this study which of the following statements is correct?「11月亞太真題」
A) The color of the mug was the cause of the difference in mean intensity rating for these volunteers, and this conclusion can be generalized to all coffee drinkers.
B) The color of the mug was the cause of the difference in mean intensity rating for these volunteers, but it is not reasonable to generalize this conclusion to all coffee drinkers.
C) It is not reasonable to conclude that the color of the mug was the cause of the difference in mean intensity rating for these volunteers.
D) It is not possible to draw any conclusions from this experiment because volunteers were used.
解析
同學(xué)們應(yīng)對(duì)這樣的題目，一定要結(jié)合考點(diǎn)來(lái)解答，這樣才能得到一個(gè)準(zhǔn)確無(wú)誤的答案。根據(jù)我們剛剛的總結(jié)：Random Sampling → the results can be generalized to the entire population；Random Assignment → 結(jié)論因果關(guān)系成立。
題中使用的sample是volunteers，這并不是一個(gè)隨機(jī)抽取的樣本，所以結(jié)論不能generalize to the entire population。同時(shí)這個(gè)實(shí)驗(yàn)的確是random assignment，所以結(jié)論中的因果關(guān)系是成立的。因此，答案選B。
總結(jié)
雖然Random Sampling & Random Assignment這兩個(gè)知識(shí)點(diǎn)看起來(lái)很生澀，有的同學(xué)不太熟悉，但SAT數(shù)學(xué)在這兩個(gè)知識(shí)點(diǎn)上考的變化并不大，就是圍繞上文的兩個(gè)考點(diǎn)來(lái)出題。事實(shí)上我們只需要緊扣上文中提到的兩個(gè)考點(diǎn)和對(duì)應(yīng)的結(jié)論，即可應(yīng)付考試。祝同學(xué)們都能夠取得數(shù)學(xué)800，加油！
