https://blog.biocomm.ai/2025/07/31/coherent-and-incoherent-light-scattering-by-single-atom-wave-packets-mit/
https://www.researchgate.net/publication/385292368_Coherent_and_incoherent_light_scattering_by_single-atom_wavepackets
2025年4月9日 星期三
2025升中乙部抽獎形勢
又到乙部派位時間。通常傳媒會用不經大腦的標嚇人。
這個4.6人爭一個英中位是用該網參加抽獎人數去算。
例如中西區就是用
參加抽獎總人數/乙部英中位來算出一個位2個人爭。
但實際上抽獎方法是該網總評分前1/3的學生，即Band 1學生，先派位。
待所有Band 1 生抽完後其他組別才派位。
所以實際上，
中西區band 1 學生每人有1.48個英中位選擇。
灣仔區每人有1.67個位。
九龍城區每人有1.15個位
從下表可見除了上面3個校網及離島網外大部份校網都是約2個band 1生 爭1個英中位。
都是那一句好校網贏在起跑線
2023年12月26日 星期二
從生產力看雅萬高鐵定價—公共財(Public Goods)
雅萬高鐵定價
高鐵二等單程票價20萬印尼盾（USD12.92）。
雅萬巴士單程票價78000盾（USD5.00）。
乘高鐵比巴士多付USD 7.92。-------------------------------------------------------------------（1）
下為印尼部份工種平均月薪：
印尼法例每周工作5天，每天工作8小時，共40小時。1年52周，有工作日260日，
減去
法定假期27日，年假12日，即一年工作（260-27-12）x8小時＝1768小時。
這教師每小時生產力收入 USD 7541.4/1768＝USD 4.265
高鐵全程40分鐘，巴士約3小時。乘高鐵節省2.25小時以上。
節省的時間換算成生產力收入 ：USD 4.265x2.25 ＝USD 9.60 --------------------------------------（2）
這教師乘坐高鐵單程可省下的生產力是：
（2）–（1）
9.60 – 7.92 ＝USD 1.68
換個算法，月薪8,030,000印尼盾以上的人會選擇乘雅萬高鐵來往雅加達—萬隆。
這個票價定價方法與一般的用者自付，自負盈虧的定價方法不同。
基建是公共財(public goods)整條鐵路建設及營運初期會要政府投入資金。
通常是從富裕地區的稅收津貼鐵路。
利用鐵路提升沿途地區發展直至落後地區經濟追上發達地區後就可轉為自負盈虧。
這方法適用於連貫經濟落差大地區的鐵路或收費高速公路。
在發達地區如香港則可利用鐵路站上蓋物業項目收益去支持鐵路建設。
另有中國高鐵定價文章： 高鐵定價與GPA關係
All Rights Reserved©2023 fengshuileung
2023年5月10日 星期三
2023年4月11日 星期二
2022年3月5日 星期六
全民檢測成效成疑，尷尬的數學真相
近日全民檢測新冠病毒甚囂塵上。大部人誤會全民檢測後就可截斷傳播鍊，大家重回正常生活。但從統計學角度這只是一廂情願而已。
下為 EU 對 Rapid Antigen Test 的要求：
[Sensitivity and specificity of nucleic acid testing in close contacts of COVID-19 cases in Guangzhou] 核酸測試靈敏度研究
以下為試劑在不同靈敏度及總體感染量下的估計誤測數及預計隔離人數：
1.
以有感染為陽性。
Sensitivity 90%，即有10%陽性被測不出，被錯認為陰性。Specificity 98%，即有2%陰性被錯認為陽性。
假設本地受感染率為15%，以700萬人計，真陽性應為105萬人。
無感染為595萬人。
陽性但驗不出的有10萬5千人。受感染又驗出陽性的有94萬5千人。
無染疫但卻被劃成陽性的有11萬9千人。
故此陽性準確率是94.5/(94.5+11.9)=88.82%
陰性準確率為583.1/(583.1+10.5)=98.23%
如凡驗出陽性要隔離，則隔離人數為 (94.5+11.9)=106.4萬人。
如只能提供10萬個隔離位則有88.7萬真陽性的人要在家隔離。
另外亦有10.5萬陽性的人走漏進入社區。
2.
以有感染為陽性。
Sensitivity 90%，即有10%陽性被測不出，被錯認為陰性。Specificity 98%，即有2%陰性被錯認為陽性。
假設本地受感染率為10%，以700萬人計，真陽性應為70萬人。
無感染為617.4萬人。
陽性但驗不出的有7萬人。受感染又驗出陽性的有63萬人。
無染疫但卻被劃成陽性的有12萬6千人。
故此陽性準確率是63/(63+12.6)=83.33%
陰性準確率為617.4/(6617.4+7)=98.87%
如凡驗出陽性要隔離，則隔離人數為 (63+12.6)=75.6萬人。
如只能提供10萬個隔離位則有54.7萬真陽性的人要在家隔離。
另外亦有7萬陽性的人走漏進入社區。
3.
以有感染為陽性。
Sensitivity 95%，即有5%陽性被測不出，被錯認為陰性。Specificity 98%，即有2%陰性被錯認為陽性。
假設本地受感染率為10%，以700萬人計，真陽性應為70萬人。
無感染為630萬人。
陽性但驗不出的有3.5萬人。受感染又驗出陽性的有66.5萬人。
無染疫但卻被劃成陽性的有12萬6千人。
故此陽性準確率是66.5/(66.5+12.6)=84.07%
陰性準確率為617.4/(617.4+3.5)=99.44%
如凡驗出陽性要隔離，則隔離人數為 (66.5+12.6)=79.1萬人。
如只能提供10萬個隔離位則有58.1萬真陽性的人要在家隔離。
另外亦有3.5萬陽性的人走漏進入社區。
4.
以有感染為陽性。
Sensitivity 97%，即有3%陽性被測不出，被錯認為陰性。Specificity 98%，即有2%陰性被錯認為陽性。
假設本地受感染率為10%，以700萬人計，真陽性應為70萬人。
無感染為630萬人。
陽性但驗不出的有2.1萬人。受感染又驗出陽性的有67.9萬人。
無染疫但卻被劃成陽性的有12萬6千人。
故此陽性準確率是67.9/(67.9+12.6)=84.35%
陰性準確率為617.4/(617.4+2.1)=99.66%
如凡驗出陽性要隔離，則隔離人數為 (67.9+12.6)=80.5萬人。
如只能提供10萬個隔離位則有59.5萬真陽性的人要在家隔離。
另外亦有2.1萬假陰性真陽性的人走漏進入社區。
5.
以有感染為陽性。（以核酸測試最高 Sensitivity算）
Sensitivity 99%，即有1%陽性被測不出，被錯認為陰性。Specificity 98%，即有2%陰性被錯認為陽性。
假設本地受感染率為10%，以700萬人計，真陽性應為70萬人。
無感染為630萬人。
陽性但驗不出的有0.7萬人。受感染又驗出陽性的有69.3萬人。
無染疫但卻被劃成陽性的有12萬6千人。
故此陽性準確率是69.3/(69.3+12.6)=84.62%
陰性準確率為617.4/(617.4+0.7)=99.89%
如凡驗出陽性要隔離，則隔離人數為 (69.3+12.6)=81.9萬人。
如只能提供10萬個隔離位則有60.84萬真陽性的人要在家隔離。
另外亦有0.7萬假陰性真陽性的人走漏進入社區。
6.
下為最樂觀估計。
目前尚有277萬人一針未打。假定只有一針未打才會染疫。
以有感染為陽性。
Sensitivity 97%，即有3%陽性被測不出，被錯認為陰性。Specificity 98%，即有2%陰性被錯認為陽性。
假設此群組受感染率為15%，以27萬人計，真陽性應為41.55萬人。
無感染為235.45萬人。
陽性但驗不出的有1.25萬人。受感染又驗出陽性的有40.3萬人。
無染疫但卻被劃成陽性的有4萬7千人。
故此陽性準確率是89.54%
陰性準確率為99.46%
如凡驗出陽性要隔離，則隔離人數為 45萬人。
如只能提供10萬個隔離位則有31.35萬真陽性的人要在家隔離。
另外亦有1.25萬假陰性真陽性的人走漏進入社區。
以上只是一次全檢的推算。
要注意的是在家隔離的人因個人及緊密接觸者皆會著重防疫故在轉陰前傳染他人機會是較低。
反為假陰性的數萬人會在正常社交中較大機會傳染他人。
By WK Leung MHKIE, RPE, CEng, MIMarEST, CMarEng
All Rights Reserved©2022 fengshuileung
同類文章
其他有關 COVID 19 文章
2021年6月28日 星期一
Triplet control prevents ‘lasing death’ in perovskite lasers
https://physicsworld.com/a/triplet-control-prevents-lasing-death-in-perovskite-lasers/
On paper, perovskites make great building blocks for lasers. In their quasi-two-dimensional form, these organic–inorganic materials exhibit tunable colour and excellent stability. The fact that they can fabricated from low-cost starting components in simple solution-based processes makes them attractive for manufacturers, too. There’s just one tiny flaw: perovskite-based lasers abruptly stop working after only a few minutes of constant operation at room temperature. Now, however, a team of researchers in China and Japan say they have overcome this so-called “lasing death” by suppressing long-lived energetic states known as triplet excitons.
Both 2D and quasi-2D perovskites are promising alternatives to silicon in optoelectronics devices. While 2D perovskites are made up of stacked sheets of alternating organic and inorganic layers, their quasi-2D variants contain small regions in which organic and inorganic materials alternate in all directions (as is the case in their 3D counterparts). The quasi-2D versions also contain two different types of organic materials.
In organic semiconductors such as those that make up quasi-2D perovskites, charge carriers – electrons and holes – come together to form an energetic state called an exciton. This entity may exist in a so-called singlet state (which has no net spin because the contributing electron spins point in opposite directions) or in a triplet state (in which the spins point in the same direction). In both cases, the energy in the exciton can then be released as light via a process known as radiative recombination. Triplets generally have a lower energy than singlets, however, and emit hardly any light.
Long triplet lifetimes
Recently, researchers led by Chuanjiang Qin of the Chinese Academy of Sciences and Chihaya Adachi at Kyushu University in Japan found evidence that triplet excitons have lifetimes of nearly a microsecond in these materials. These long lifetimes led them to focus on these excitons as a possible cause of lasing death.
As well as emitting very little or no light, triplet states also tend to interact with light-emitting singlets in a way that causes both to lose their energy without producing light, Qin explains. Eliminating any triplets in perovskites would therefore prevent interference with lasing.
In their latest work, the researchers studied FAPbBr3-based (where FA is formamidinium) quasi-2D perovskites with two different organic cations, phenylethylammonium bromide (PEABr) and 1-naphthylmethylamine bromide (NMABr). The PEABr-based perovskite contains an organic cation with high triplet energy, and the NMABr-based perovskite has an organic cation with low triplet energy.
Holding triplets in a low energy state
To eliminate triplets in these quasi-2D perovskites, the researchers incorporated an organic layer into the materials, which confines the triplets to a low-energy state. Since the excitons want to move to lower energies, the long-lived triplet excitons transfer from the active (that is, light-emitting) portion of the perovskites to the organic layer, they explain. This reduces light losses and allows for lasing under constant optical excitation (also known as optically pumped continuous-wave, or CW lasing) without interruption.
Qin, Adachi and colleagues also discovered that they could make their material lase continuously simply by placing it in air. This is because oxygen can destroy triplets – a result that further suggests that light losses caused by triplets may indeed be the culprits in lasing death.
Unchanged lasing intensity
The researchers quantified their material’s performance by measuring the amplified spontaneous emission (ASE) intensity of the two films as they were optically powered. They found that the ASE, or lasing, remained virtually unchanged after an hour at room temperature in air with a relative humidity of 55%. The lasing spectrum also maintained its narrowness (full width at half maximum) without shifting. The team stress that these measurements were taken without the films being encapsulated in glass, and without a protective layer over their tops, as was the case in previous ASE stability measurements of 3D perovskites such as MAPbBr3.
According to the researchers, the excellent stability of their material comes from the protection provided by the larger cations on its surface. “We have demonstrated the key role of triplets in the lasing process of these types of perovskites and the importance of managing triplets to achieve continuous lasing,” Adachi states in a Kyushu University press release. “These new findings will pave the way for the future development of a new class of electrically operated lasers based on perovskites that are low cost and easily fabricated.”
2021年6月27日 星期日
2021年5月19日 星期三
Why do Indonesians prefer to have a vacation to Singapore, where the daily price is more expensive than Australia?
Why do Indonesians prefer to have a vacation to Singapore, where the daily price is more expensive than Australia?
- Airfare cost to Singapore is cheaper than to Australia. Flight to Singapore can cost as low as IDR 800,000 roundtrip (About USD 75)
- It only takes 1 hour flight to reach Singapore while flight from Jakarta to Sydney takes 6 hours
- Indonesians don't need visa to visit Singapore, while it cost $100 to have Australia's tourist visa
- Singapore is small so that tourist can explore it in 1 till 3 days. This can be an efficient option for Indonesians since leave days in Indonesia is really short
- Public transportation in Singapore is well connected and quite affordable, making it easier to be explore comparing to big cities in OZ like Melbourne, Sydney, and Perth
- Singapore has great culinary scene with great variety of halal foods, which suitable with Muslim travelers from Indonesia
- Few Indonesians have relatives in Singapore and many upper class Indonesians have apartment in Singapore
- Malay language are still used in Singapore, making Indonesians that don't understand English more comfortable when exploring Singapore
- Singapore climate is same as Indonesia, so that Indonesian tourists don't need special clothes to be prepared
- Sometimes gadgets/electronic appliances prices in Singapore cheaper than in Indonesia. The specification often more advance. Therefore many Indonesians go there to buy that stuff
2021年5月16日 星期日
F = ma & Ohm's law CONFLICT
By Rushi Shroff
Now lets try to really understand Ohm's law, which says that the current in a wire is proportional to the voltage. This law isn't really a law at all, not like the force law of gravity or the law of conservation of energy or momentum. In fact it is really rather astonishing that it should be true at all. Why? The voltage produces an electric field in the wire, which produces a force on the electrons. Now this force produces an acceleration (remember Newton: F=MA) not a velocity, thus we would expect the current to grow larger and larger, as the electrons continue to accelerate, moving ever faster. Instead Ohm's law is saying that this constant electric field is producing a constant current, hence constant velocity. Something funny is going on here. To understand this we need to take a closer look at the goings on in the wire. Remember I said that the electrons are like a gas, filling the wire. Well, these electrons are constantly bumping into things, and bouncing off of them. Think of it as follows: Imagine you are in a Ferrari, and you can go from 0 to 100 in 6 seconds. However, you happen to be on a road where there is a stop sign every three seconds. How fast, on the average do you travel? In three seconds, you've accelerated from 0 to 50. Your average speed during those three seconds was 25MPH. Then you had to slam on the brakes, screech to a halt, and start all over again. Thus even though your Ferrari can do 100 in 6 seconds, your average speed is only 25MPH. Hell, you're not even breaking the speed limit (at least on average.)
In the general case, we need to relate
the distance you cover, say L,
to your acceleration, A,
and the amount of time, T you are moving.
At the end of time T,
your velocity V = A * T.
The distance you've covered is your average velocity over that time,
which is V/2, times the time T,
so L = V/2 * T = 1/2 * A * T * T.
Thus if we solve for T we get that
T = Square Root (2 * L / A).
Finally this means that the current,
with is the average velocity of the electrons is 1/2 * A * T = √(L * A / 2).
Take a breath for a moment and let's see what we've discovered.
The current is proportional to some constant,
namely Square Root (L/2) times Square Root(A).
And A, the acceleration, is proportional to the electric field, which is proportional to the voltage.
Oops. We must have made a mistake somewhere, because that is not Ohm's law. Ohm's law says the current is proportional to the voltage, not the square root of the voltage.
What's wrong? Well in a gas, each molecule is constantly moving, because of the thermal energy of the gas. Furthermore, the velocity due to this thermal energy is very large compared to the drift velocity we calculated above.
In fact it is about 10^9 mm/sec or almost 10 orders of magnitude (10^10) times bigger.
Thus their motion is totally random, and very fast.
Therefore the time between collisions is L / thermal velocity, not L / drift velocity.
The fact that this is 10 orders of magnitude greater than the drift velocity means the drift velocity contributes almost nothing to the time.
Thus the average velocity between collisions is 1/2 A * T where T does not depend on A at all. Thus the current is proportional to A which is proportional to the voltage, and voila, we have Ohm's law.
n fact we can squeeze even more information out of this observation. The amount of current flowing down a section of wire is:
the distance you cover, say L,
to your acceleration, A,
and the amount of time, T you are moving.
At the end of time T,
your velocity V = A * T.
The distance you've covered is your average velocity over that time,
which is V/2, times the time T,
so L = V/2 * T = 1/2 * A * T * T.
Thus if we solve for T we get that
T = Square Root (2 * L / A).
Finally this means that the current,
with is the average velocity of the electrons is 1/2 * A * T = √(L * A / 2).
Take a breath for a moment and let's see what we've discovered.
The current is proportional to some constant,
namely Square Root (L/2) times Square Root(A).
And A, the acceleration, is proportional to the electric field, which is proportional to the voltage.
Oops. We must have made a mistake somewhere, because that is not Ohm's law. Ohm's law says the current is proportional to the voltage, not the square root of the voltage.
What's wrong? Well in a gas, each molecule is constantly moving, because of the thermal energy of the gas. Furthermore, the velocity due to this thermal energy is very large compared to the drift velocity we calculated above.
In fact it is about 10^9 mm/sec or almost 10 orders of magnitude (10^10) times bigger.
Thus their motion is totally random, and very fast.
Therefore the time between collisions is L / thermal velocity, not L / drift velocity.
The fact that this is 10 orders of magnitude greater than the drift velocity means the drift velocity contributes almost nothing to the time.
Thus the average velocity between collisions is 1/2 A * T where T does not depend on A at all. Thus the current is proportional to A which is proportional to the voltage, and voila, we have Ohm's law.
n fact we can squeeze even more information out of this observation. The amount of current flowing down a section of wire is:
current density (I) =
The number of atoms per unit volume (N)
times
the number of free electrons per atom (f)
times
the charge per electron (q)
the number of free electrons per atom (f)
times
the charge per electron (q)
times
the average velocity of the electron (1/2 A * T)
the average velocity of the electron (1/2 A * T)
thus: I = 1/2 * N * f * q * A * T
now acceleration A = Force / mass of electron (m) = E / m
and time T = distance between collision L / thermal Velocity V
so I = (N * f * L * q^2 / 2 m V) * E
What have we here? Well, we can see that the stuff in the parentheses, which are all things that depend on the material the wire is made of, is a first order formula for the conductivity. Conductivity is the inverse of resistance, so if we stick all that stuff on the other side of the equation we get:
E (voltage) = (2 m V / N * f * L * q^2) I .... Ohm's law
Which correctly predicts that the resistance should increase as the thermal velocity of the electrons gets larger, or in other words, resistance goes up with temperature, a well know fact.
Now the resistance of a metal like copper is essentially zero, but the resistance of the bulb is substantial. Thus there are a lot more collisions taking place in the filament than in the wire, and guess what, the filament gets hot. The electrical force is being converted into heat, and eventually light by the resistance of the filament, in other words, the flashlight produces light.
2021年5月7日 星期五
旅遊及款待科 2021 DSE 貼題
又到估題時間，今次疫情對整個旅遊款待行業影響極大，長題涉及行業在此環境下如何打開局面，如何善用旅遊氣泡，如何推廣本地旅遊內需；在疾情結束後如何吸引顧客，如何向顧客推廣使香港成為對方疫後出遊的首選？
今屆貼：
1.
Staycation - hotel operation., 如何保障人客員工健康防止感染。例如無接觸感應，環境消毒機械人。
2.
疫下很多時要避免面對面接觸，customer relations 怎去維持，
RATER model.
3.
本地遊：發展大嶼山的旅遊優勢，遠足，野營，單車之旅，水上活動...
例如水口泥灘生態遊，鳳凰山觀日出，大澳鹽田等。路線設計，硬件需求。
4.
Disneyland- Theme park-type of theme & characteristic.
5. Doxy index of irritation.
2021年1月17日 星期日
Example of atom excitation
The left picture is a green amber bracelet under normal fluorescent light.
The one on the right is the same piece under "white" LED light.
Amber is natural resin which is unsaturate-hydrocarbon.
When the the photon energy is high enough the hydrogen atom's electron will be raised from the ground state into higher level. When the electron drop back to ground state the absorbed energy is released in the form of light.
2021年1月12日 星期二
2020年12月30日 星期三
Differentiation max/min example 3
看完下面6 parts視頻你已可掌握DSE的Differentiation.
視頻教學：
Differentiation 入門 part 1 part 1 to part 6
如AP cost 是 4700/km
2020年12月29日 星期二
2020年12月28日 星期一
2020年5月20日 星期三
2020旅遊與款待科貼題
1.Doxy index of irritation 及 social culture impact.
可能會要考生舉例
或題目提供一個地點的資料要求考生評論。
2.MICE對經濟的直接及間接好處。
設計大型會議(數百人)的餐單。或會議場所要提供的或代客安排事項，例如catering ，WIFI hotspots，交通，臨時接待員工等。
3.GAP model，5 gaps 成因及解決方案。
服務品質控制，
客戶忠誠度成因及提升客戶忠誠度方法。不同因素要用不同方法，（用家滿足感）。
4.各種交通工具例如高鐵，飛機，遊輪在旅遊與款待業的位置。
另類旅遊（深度遊）如生態旅遊，探索旅遊，古跡旅遊，文化旅遊，與其它旅遊的異同如景點，經濟貢獻（當地小店vs國際名店），客源，接待人手要求..,,,。
並以大嶼山為例。
5.主題公園，公園主題及選址在地理上的考慮，如交通人口經濟潛在客源期望的體驗等。
主題公園成功的因素，怎樣才算成功呢？
可能會要考生舉例
或題目提供一個地點的資料要求考生評論。
2.MICE對經濟的直接及間接好處。
設計大型會議(數百人)的餐單。或會議場所要提供的或代客安排事項，例如catering ，WIFI hotspots，交通，臨時接待員工等。
3.GAP model，5 gaps 成因及解決方案。
服務品質控制，
客戶忠誠度成因及提升客戶忠誠度方法。不同因素要用不同方法，（用家滿足感）。
4.各種交通工具例如高鐵，飛機，遊輪在旅遊與款待業的位置。
另類旅遊（深度遊）如生態旅遊，探索旅遊，古跡旅遊，文化旅遊，與其它旅遊的異同如景點，經濟貢獻（當地小店vs國際名店），客源，接待人手要求..,,,。
並以大嶼山為例。
5.主題公園，公園主題及選址在地理上的考慮，如交通人口經濟潛在客源期望的體驗等。
主題公園成功的因素，怎樣才算成功呢？
2020年3月16日 星期一
Time lag in base popuplation change, misleading statistics COVID-19
The following is the fatal rate of COVID-19 in China.
Graph A
The above graph (A) shows a convex curve rising from 2% to the current 4%.
The graph (B) below shows a concave curve desending from 14% to 4%.
Graph B
Graph A shows a low inital fatal rate of just 2%.
Graph B says otherwise, a 14% initially.
The hugh difference is the base population of confirmed case.
In graph (A) both the base and the fatal figure starts from Jan 28, 2020.
The fatal figure in graph (B) starts from Feb 7, the base figure starts from Jan 28, 2020.
As the health authority estimated the median of number days a confirmed case fails is 10 to 14 days, so a 12 days lag from the fatal data is used in the base figure.
From graph A the fatal rate is not yet flatten out.
However ,graph B shows that the fatal rate starts to flat out at 4% from Feb 27 onwards.
So the spread of virus may not under contain but the treatment or measure taken to cure the infected patients have kept the fatal rate under control.
On the other hand one should take a deeper look into the seemingly tough 4% line., be it due to age, chronic disease or whatever reason.
So graph A is good for show to your voter at the initial outbreak stage
but graph B is more useful in public health decision making and more presentable to voters.
All Rights Reserved© fengshuileung2020
Graph A
The graph (B) below shows a concave curve desending from 14% to 4%.
Graph B
Graph A shows a low inital fatal rate of just 2%.
Graph B says otherwise, a 14% initially.
The hugh difference is the base population of confirmed case.
In graph (A) both the base and the fatal figure starts from Jan 28, 2020.
The fatal figure in graph (B) starts from Feb 7, the base figure starts from Jan 28, 2020.
As the health authority estimated the median of number days a confirmed case fails is 10 to 14 days, so a 12 days lag from the fatal data is used in the base figure.
From graph A the fatal rate is not yet flatten out.
However ,graph B shows that the fatal rate starts to flat out at 4% from Feb 27 onwards.
So the spread of virus may not under contain but the treatment or measure taken to cure the infected patients have kept the fatal rate under control.
On the other hand one should take a deeper look into the seemingly tough 4% line., be it due to age, chronic disease or whatever reason.
So graph A is good for show to your voter at the initial outbreak stage
but graph B is more useful in public health decision making and more presentable to voters.
All Rights Reserved© fengshuileung2020
天賦基因測試準確性99%?
天賦基因測試準確性99%?
天賦基因測試搶算命佬生意
近日虎媽熱門話題中“天賦基因測試”一定有一席位。
這是直接搶算命佬生意。
下走可以斷言任一有料算命佬一算就算到一個八字
有無書緣，
聰不聰明，
要怎去教，
要讀什麼類型學校，要不要留學...等等，
根本不需做什麼測試
測試準確性達99%可以是數字遊戲
更有宣傳稱測試準確性達99%。
這就引出下走要討論
統計學中有所謂的準確率數字遊戲。
統計學的陷阱
搗蛋的陰性大多數性
有修社會科學，醫科或政政的同學不妨細看一下。
以本地中學為例，有1/3學位是band 1，而此等學位又有約1/3是學校自主收生。
可以據此假設真正讀到書的學霸約占10%。
一：
假設有一測試
如對象是有某特質之人，這測試有99%成功測出其有此特質。Sensitivity 99%
如對象是無此特質之人，這測試有99%成功測出其無此特質，亦即有1%誤認為有此特質。Specificity 99%
以測試一千人為例
有此特質的有100人，
測試顯示出有此特質的有99人。
無此特質之人有900人，
誤測出為有此特質的有9人。
測試認為是有此特質的是 99+9=108人
準確率為99/108
=0.917
二：
再來一個假設
如對象是有此特質之人這測試有99%成功測出其為有此特質。
如對象無此特質之人這測試有98%成功測出其為無此特質，亦即有2%誤認為有此特質。
以測試一千人為例
有此特質的有100人，
測試顯示出有此特質的有99人。
無此特質之人有900人，
誤測出為有此特質的有18人。
測試認為是有此特質的是99+18=117人
準確率為99/117
=0.846
三：
再推算下去
如對象是有此特質之人這測試有99%成功測出其為有此特質。
如對象是無此特質之人這測試有95%成功測出其為無此特質，亦即有5%誤認為有此特質。
以測試一千人為例
有此特質的有100人，
測試顯示出有此特質的有99人。
無此特質之人有900人，
誤測出為有此特質的有45人。
測試認為是有此特質的是99+45=144人
準確率為99/144
=0.688
你是有此特質，個測試可以測出你是有此特質的準確度有多高不重要，
你無此特質，而個測試誤測出你是有此特質的機率有幾高才重要。
在統計學，上面第一例的 0.917 準確率很多時已經不可以被認為是嚴謹結論，
更不必論例二、三了。
這種誤解不但出現在社科，更常出現在醫學上的統計，如疾病試劑藥苗效果等。
Disclaimer :
本文純屬學術討論，內容數據並非真實，並無意圖影射或針對任何人或企業或技術，如有雷同實屬巧合。
All Rights Reserved ©2019 fengshuileung
2020年1月29日 星期三
劍橋大學：全球民眾有關不滿民主制度創新高
劍橋大學民調：有關全球民眾有關不滿民主制度創新高：
報告
https://www.bennettinstitute.cam.ac.uk/media/uploads/files/DemocracyReport2020.pdf
報告
https://www.bennettinstitute.cam.ac.uk/media/uploads/files/DemocracyReport2020.pdf
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