跟讀練習: 99 - 通過影片學習英語口語

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Every statistics course draws the same little square.

The truth is one of two things, and your decision is one of two things, so there are four boxes, two of which are mistakes,

and the two mistakes get names, type 1 and type 2, printed side by side as though they were two of a kind.

They are not, and the difference between them is the whole subject.

The box where nothing was going on and you called it real, the false alarm, carries a number you picked yourself before collecting a single observation,

and that number is 0.05.

The box below it, where something real was there, and you walked straight past it, has no number attached to it anywhere,

not on your screen, and not in the paper, and usually not in your head either.

So let's go and find the second number, because once you can see it, the sentence we have all written at some point,

no significant difference, stops meaning what you thought it meant.

Let's make this concrete with about the smallest real decision I can think of.

You change the color of a checkout button, you send some traffic to each version,

and you want to know whether the new one genuinely converts better or whether you are looking at noise wearing a costume.

The null hypothesis is the boring one, that the change did nothing, and it gets to be the starting point,

not out of fairness, but because it's the only hypothesis specific enough to make predictions.

If the button does nothing, the difference you measure is pure sampling wobble, and dividing that difference by its own standard error,

which is simply how much a number like this bounces around from one repeat of the experiment to the next, gives you a statistic whose distribution you already know.

It's a bell centered on zero, whose spread is exactly 1.

So from here on, one step along that axis means one standard error.

Now draw a line.

Pass the line you call the result real, short of it you don't.

And since you only care about the new button being better, one line on the right is all you need.

Put it where 5% of the bell is left stranded beyond it, which lands at 1.645 and shade that sliver in,

because area under a curve like this is probability, so the sliver is telling you how often you would cross the line in a world where the button did nothing.

That area is alpha, the type 1 error rate.

Alpha isn't measured, it's declared, and notice what that buys you, because you just computed it with no data, no knowledge of the true effect,

and without running the test at all.

So, try the same move on the other error.

You want the probability of missing a real effect,

which means the probability that your statistic lands short of the line in a world where the button does work,

and for that you need to know where the statistic sits in that world.

But the alternative hypothesis, as it is almost always written, only says the effect isn't And not zero is not a location.

No curve, so no area, so nothing to compute.

The only way forward is to stop being vague and name a specific effect out loud.

Say the lift is big enough that your statistic now averages three standard errors out instead of zero.

Then, there is a second bell, identical to the first, in every respect except where it's centered.

And now, the question has an answer.

Because beta is the piece of that second bell lying on the wrong side of your line,

the region where a real effect turns up looking ordinary enough to wave through.

With the line still at 1.645 and the alternative 3 standard errors out,

that shaded piece works out to about 9% of the second bell.

But 9% came with strings attached, because it was 9% for that effect.

Shrink the true lift and the second bell slides back toward the first.

The two overlap more and beta climbs.

So there is no such thing as the type 2 error rate of a test, only beta at an effect size somebody was willing to commit to,

which is exactly why alpha is printed on every table you have ever read and beta on almost none of them.

Alpha needs a null, and everybody has one of those lying around, while beta needs a guess about the truth, and nobody wants to write theirs down.

Now that both errors have pictures, watch what happens when you get nervous about false alarms, and pull the line further to the right.

The tail beyond it shrinks so alpha drops exactly as you wanted, but that line swept through the second bell as well,

and everything it passed over went from caught to missed, and the strip it swept is thin under the null and fat under the alternative,

since the alternative keeps most of its mass out in exactly that region, so beta climbs by a great deal more than alpha falls.

The numbers make the lopsidedness plain, with the alternative still 3 standard errors out.

At an alpha of 5%, you miss a real effect about 9% of the time.

Tighten alpha to 1%, which most people would call ordinary caution rather than paranoia, and you saved 4 points of false alarm,

and paid 16 points of miss, because the miss rate jumps to 25%.

Tighten to 1 in 1000, the kind of threshold people reach for when they want to sound rigorous,

and you now miss a real effect 54% of the time,

which makes a test that's strict worse than a coin flip at noticing the very thing it was built to notice.

And nothing about the world changed while we did that,

because nobody collected another observation and the button is exactly as good as it always was.

So the line is the only thing here you actually control.

And the cleanest way to see what you get for putting it somewhere is to flip beta over.

1 minus beta is the probability of catching a real effect when there is one, and that is the power of the test.

Because beta depended on which alternative you named, power inherits the same dependence.

So power isn't a number that belongs to your test the way alpha does.

It's a whole curve, with one value for every size of effect the world might be hiding from you.

So sweep the true effect from nothing up to enormous and plot what the test does at each point.

Choosing which point on that climb you need to be standing at is most of what designing a study actually is.

Far out on the right, the second bell has slid clean past the line, and power sits at essentially 100%,

because an effect that large is impossible to miss.

Walk back towards zero, and the curve sags, and the left-hand end is where it gets interesting.

Because when the true effect is exactly zero, the power does not drop to zero, it settles at 5%.

It settles at alpha.

That isn't a coincidence to memorize, is the definition unfolding, because when the alternative bell sits exactly on top of the null bell,

the chance of landing past the line is simply the tail area, and the tail area is what alpha was in the first place.

Which brings us to the sentence this whole video is really about.

Two teams run the same test on the same button at the same 5%, and the button really does help,

by a small amount, the sort of lift that is worth having, and that you would never spot by eye.

The first team routes a modest slice of traffic for a few days, and in their sample that true effect is worth one standard error.

The second team runs it across the whole site for a month, which is 16 times as much traffic,

and since the standard error falls like one over the root of the sample size, 16 times the data cuts that error to a quarter of what it was.

So the very same real effect is now worth 4 standard errors.

Both teams get a statistic that falls short of the line, and both write down the same sentence,

no significant difference, and since we stipulated that the button really works, both of them are wrong.

Only one of them was entitled to be.

For the first team, the two belts overlapped so heavily that their chance of catching that lift was 26%,

well under the 80% usually treated as the minimum worth running.

So being wrong was the likely outcome, expected about 3 times in 4,

and their sentence carries almost no information about the button at all.

For the second team, the chance of catching it was 99%.

So being wrong meant drawing a card that comes up about once in a hundred,

and their identical sentence is worth something precisely because it was so unlikely to get written.

Same words, same alpha, same underlying truth, and one of those sentences is nearly empty while the other is close to decisive.

A negative result never says there is no effect.

It says that if there is one, it was too small to be seen with the sample you had.

And how small that is, lives entirely in the number neither report printed.

Everything so far has been a trade, so it's fair to ask whether you can ever have both.

You can, but start with what doesn't work, because collecting more data does not lower alpha.

Alpha is wherever you put a line, so leave the line alone and quadruple your sample,

100

And your false alarm rate is still exactly 5% since the null bell is standard by construction

101

and doesn't care how much data went into building it.

102

What the extra data moves is the other bell.

103

We just watched the root and rule work against the first team and pointed the other way it works for you.

104

Because four times, the data doubles the distance between the two curves.

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And distance is exactly what you were short of.

106

Take that alternative sitting 3 standard errors out, where the line at 5% left you missing 9% of real effects,

107

then quadruple the sample so the separation becomes 6, and put the line at 3, which is exactly halfway between the two bells.

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Halfway makes the two tails mirror images of each other, so alpha and beta come out identical.

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both of them about 1 in 750.

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Neither error was traded away for the other.

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Both of them came down by more than a factor of 30, and the invoice for that came to 4 times the data.

112

The only other way to widen the gap is to make the effect itself bigger.

113

And that is usually a property of the world, rather than a knob on your desk.

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So the line is a trade and more data is an escape and both of those quietly assume you ran one test.

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Run several and alpha starts leaking in a way the single picture hides.

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Because alpha is a rate per test and rates accumulate.

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Run one test at 5% and you have a 1 in 20 chance of a false alarm, which most people accept without much thought.

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Run 20 independent tests over the same data set, 20 button variants, or 20 outcomes you happen to record, and the chance

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that at least one of them lights up in a world where nothing at all is happening is not 5%, it's 64%.

120

A room containing nothing but noise hands, you a significant result more often than not,

121

and every one of those results carries a p-value under 0.05, exactly as alpha promised.

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The standard repair is to divide the threshold by the number of tests you ran.

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So 20 tests each get an alpha of a quarter of a percent, and the chance of any false alarm anywhere comes back down to roughly 5%.

124

But look at what you just did to every one of those tests, because you moved each line further out.

125

And by now, we know exactly what that costs.

126

Against that same alternative, three standard errors out, power drops from 91% to 58%,

127

so a study that was properly powered for one comparison becomes underpowered for 20%, without anybody touching the data.

128

Every repair in this video has been somebody deciding which of the two errors to spend,

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which is why 0.05 deserves rather more suspicion than it normally gets.

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It isn't derived from anything, it's a convention that hardened into a habit, and adopting it without a thought silently announces

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that a false alarm is the mistake you would rather avoid in every situation for the rest of your career.

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Sometimes that is exactly right.

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If you are deciding whether a new drug reaches the market, a false alarm puts something useless on the shelf,

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and every study built on top of it inherits the mistake, so holding alpha very tight is defensible,

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provided you say out loud what you are buying it with, which is a higher chance that a compound that genuinely works dies in a trial too small to see it.

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And sometimes the posture is backwards.

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If you are watching for a rare structural failure, a false alarm costs you an inspection,

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and a wasted afternoon, while a miss costs you the failure itself.

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So the sensible design drives beta as low as it will go

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and simply pays for the drizzle of false alarms that comes with it.

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And sometimes the answer is to refuse the choice, which is what a two-stage design is for,

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where a cheap screen runs at a deliberately loose alpha so its beta is tiny, and almost nothing real slips past,

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and everything it flags goes on to an expensive test whose alpha is orders of magnitude tighter.

144

Neither stage escapes the trade.

145

What the pair of them does is spend the loose alpha, where testing is cheap, and the tight alpha,

146

where it is expensive, so that the errors surviving to the end are rare on both sides.

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So those two boxes were never two of a kind.

148

One is a promise you make before you look, the other is a consequence you inherit and can only pin down by naming what you were hoping to see,

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and the only question a test really puts to you is which of the two you would rather be wrong about.

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If you found this helpful, hit that like button, subscribe for more, and drop a comment if you have any questions.

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See you in the next one.

152

Bye-bye!

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流利口語所需的一切

AI 發音評分逐句打分

音標練習掌握每個音

詞彙學習建立你的詞庫

詞彙遊戲邊玩邊學

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本課的詞彙與口語要點

這段影片共有 152 個句子、2428 個單詞可供跟讀。講話部分時長為 15:41。說話人語速自然，每分鐘約 155 個詞，接近日常對話。 85% 的單詞屬於英語最常用的 3,000 詞，其餘的詞建議在練習前先學一下。

影片中的重點詞彙

影片中 15 個值得學習的單詞，附發音和釋義：

單詞	發音	釋義
alpha 名詞	/ˈæl.fə/	阿爾法 /阿爾法, 阿伐
beta 名詞	/ˈbeɪtə/	貝塔 /貝塔
alarm 名詞	/əˈlɑɹm/	警報 /警報
curve 名詞	/kɚv/	彎子 /彎子
null 名詞	/nʌl/	空值
tail 名詞	/ˈteɪ̯l/	йиба, 尾
probability 名詞	/ˌpɹɑ.bəˈbɪl.ə.ti/	可能性
climb 動詞	/ˈklaɪ̯m/	登
identical 形容詞	/ɪˈdɛntɪkl̩/	相同, 同一
sweep 動詞	/swiːp/	打掃 /打掃, 掃 /掃
hypothesis 名詞	/haɪˈpɒθɪsɪs/	假說 /假說, 假設 /假設
inherit 動詞	/ɪnˈhɛɹɪt/	繼承 /繼承, 繼承
ordinary 形容詞	/ˈɔɹdɪnɛɹi/	普通, 平常
repair 動詞	/ˈɹiːpɛɚ/	修理
collect 動詞	/ˈkɑlɪkt/	庋藏, 收藏

影片中出現的短語動詞

單詞	發音	釋義
come back 動詞		回來 /回來, 返回
come down 動詞		下來 /下來, 降
come out 動詞	/ˌkʌm ˈaʊt/	出, 出來 /出來
write down 動詞		寫下來 /寫下來, 寫下 /寫下

需要注意的發音

說話人用了 8 次縮略和弱讀形式，例如 isn't, doesn't, don't。請按聽到的簡短形式來說。

“th” 音: hypothesis /haɪˈpɒθɪsɪs/, threshold /ˈθɹɛʃ(h)oʊld/, thin /ˈθɪn/, theirs /ðɛɚz/
“sh” 和 “zh” 音: shade /ʃeɪd/, observation /ˌɑbzɚˈveɪʃn̩/, threshold /ˈθɹɛʃ(h)oʊld/, essentially /ɪˈsɛnʃəli/, structural /ˈstɹʌk(t͡)ʃəɹəl/
長單詞——注意重音位置: statistical /stəˈtɪs.tɪ.kəl/, probability /ˌpɹɑ.bəˈbɪl.ə.ti/, hypothesis /haɪˈpɒθɪsɪs/, ordinary /ˈɔɹdɪnɛɹi/, genuinely /ˈd͡ʒɛn.ju.ɪn.li/

如何用這段影片練習

先完整聽一遍影片，不要開口，記下不認識的單詞。
先用 0.75 倍速逐句跟讀，熟練之後再回到正常速度。
錄下自己的聲音並與原聲對比，特別注意 alpha, beta, alarm 這類單詞。

影片中的語法

說話人最常用的結構，並附上影片中的原話：

結構	影片中的用法
被動語態 be + 過去分詞 — 強調發生了什麼，而不是誰做的	is left · isn't measured · is printed
現在完成時 have/has + 過去分詞 — 過去發生但與現在仍有關聯的事	have ever read · has been
定語從句 who / which + 從句 — 補充說明人或事物	month, which is · with, which is · choice, which is

什麼是跟讀法？

跟讀法 (Shadowing) 是一種有科學依據的語言學習技巧，最初開發用於專業口譯員的培訓，並由多語言者Alexander Arguelles博士普及。這個方法簡單而強大：您在聽英語母語原聲的同時立即大聲重複——就像是一個延遲1-2秒緊跟說話者的影子。與被動聽力或語法練習不同，跟讀法強迫您的大腦和口腔肌肉同時處理並模模擬實的講話模式。研究表明它能顯著提高發音準確性，語調，節奏，連讀，聽力理解和口語流利度——使其成為雅思口語備考和真實英語交流最有效的方法之一。

影子跟讀法: 閱讀完整分步指南 →

跟讀練習: 99 - 通過影片學習英語口語

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