 ## 字幕列表 影片播放

• Hi. It's Mr. Andersen and welcome to my podcast on the Chi-squared test. Chi-squared

你好，我是安德森先生，歡迎收看我的Chi-squared測試播客。Chi-squared

• test if you look at the equation lots of students get scared right away. It's really simple

測試如果你看公式很多學生馬上就會害怕。它真的很簡單

• once you figure it out. So don't be scared away, but Chi-squared test especially in AP

一旦你想通了。所以不要被嚇跑了，但是Chi-squared測試尤其是在AP中的

• biology, especially in science is very important. And it's a way to compare when you collect

生物學，特別是在科學是非常重要的。而且它&#39;是一種比較的方法，當你收集

• data, is the variation in your data just due to chance or is it due to one of the variables

數據，你的數據的變化是僅僅由於偶然性，還是由於其中的一個變量造成的

• that you're actually testing. And so the first thing you should figure out is what are the,

你&#39;實際測試。所以你首先應該弄清楚的是什麼是。

• what do all these variables mean?

這些變量意味著什麼？

• So the first one, this right here stands for Chi-squared. And so this was developed way

所以，第一個，這個就在這裡代表Chi -squared。所以這是開發的方式

• in the early part of the 1900s by Carl Pearson. Pearson's Chi-squared test. So, what is this

在20世紀初，由卡爾-皮爾遜。皮爾遜&#39;的Chi-squared檢驗。那麼，這是什麼呢？

• then? That is going to be a sum. So we're going to add up a number of values in a Chi-squared

然後呢？那將是一個總和。所以，我們&#39;要加起來的值的數量在一個Chi平方的

• test. What does the O stand for? Well that's going to be for the data you actually collect.

測試。O代表什麼？嗯，這&#39;將是你實際收集的數據。

• And so we call that observed data. And then the E values are going to be the expected

所以我們稱之為觀測數據。然後E值將是預期的。

• values. And so if you're ever doing an experiment, you can actually figure out your expected

值。是以，如果你&#39;做一個實驗，你實際上可以計算出你的預期的

• values before you start. And then you just simply compare them to your observed values.

在你開始之前，數值。然後你只需簡單地將它們與你的觀察值進行比較。

• Let me give you an example of that with these coins over here.

我給大家舉個例子，這邊的這些硬幣。

• Let's say I flip a coin 100 times. And I get

讓我們&#39;說我拋硬幣100次。我得到

• 62 heads and I get 38 tails. Well is that due to just chance? Or is there something

62個頭，我得到38個尾巴。那麼，這是由於只是偶然？還是有什麼原因？

• wrong with the coin? Or the way that I'm flipping the coin? And so the Chi-squared test allows

硬幣有問題？還是我翻轉硬幣的方式？所以Chi-squared測試允許

• us to actually answer that. And so what I'm thinking in my head is something called a

我們實際回答。所以我腦子裡想的是一個叫作 "的東西"。

• Null Hypothesis. And so if we're flipping a coin 100 times. And I think I said 62 head

空心假說。所以如果我們&#39;擲硬幣100次。我想我說的62頭

• and 38 tails. Well that would be the observed value that we get in an experiment. But there'd

和38個尾巴。嗯，這將是我們在實驗中得到的觀察值。但有&#39;d

• also be expected values because you know it should be 50 heads and 50 tails. And so you

也是預期值，因為你知道它應該是50頭50尾。所以你

• used something called a null hypothesis in this case where you're saying there's not

在這種情況下，使用的東西稱為無效假設，你說有&#39;s不

• statistical significant difference between the observed values and the expected frequencies

觀測值與預期頻率之間的顯著性差異。

• that we expect to get and what do we actually find.

我們期望得到的和我們實際發現的。

• And so it's cool, Chi-squared, because we

所以它很酷，Chi-squared，因為我們的。

• can actually measure our data, or look at our data and see is there a statistical difference

可以實際測量我們的數據，或者看我們的數據，看看是否有統計學上的差異。

• between those two. The best way to get good at Chi-squared is actually to do some problems.

這兩者之間。想要學好Chi平方，其實最好的方法就是做一些題。

• Before we get to that there's two terms that I have to define. One is degrees of freedom

在我們討論這個問題之前，有兩個術語我必須要定義一下。一個是自由度

• and then one is critical values. And so the whole point of a Chi-squared test is either

然後一個是臨界值。所以Chi-squared檢驗的全部意義是要麼

• to accept or reject our null hypothesis. And so you have to either exceed or don't exceed

以接受或拒絕我們的零點假設。是以，你必須要麼超過或不超過。

• your critical value. But first of all we have to figure out where that number is in this

你的臨界值。但首先我們要弄清楚這個數字在哪裡，在這個

• big chart right here.

大圖就在這裡。

• First thing is something called degrees of freedom. So since we're comparing outcomes,

第一件事是一種叫做自由度的東西。所以既然我們&#39;比較結果。

• you have to have at least two outcomes in your experiment. So in this case if we have

你必須在實驗中至少有兩個結果。所以在這種情況下，如果我們有

• heads and tails, we have two outcomes that we could get, so we'll say that's 2. And then

頭和尾，我們有兩個結果，我們可以得到，所以我們&#39;會說，&#39;是2。然後

• we simply subtract the number 1 from that to get the degrees of freedom. And so in this

我們只需從中減去數字1就可以得到自由度。所以在這個

• case we have two outcomes minus 1 and so we would have 1 degree of freedom. Now you might

的情況下，我們有兩個結果減1，所以我們將有1個自由度。現在你可能會

• think to yourself why isn' there a zero on this chart? Well, if you just have one outcome

想到自己為什麼不&#39；這個圖上有一個零？那麼，如果你只有一個結果

• you have nothing to compare it to. So that's an easy way to think about that. So we figured

你沒有什麼可以比較的。所以，這&#39;是一個簡單的方式來思考這個問題。所以我們想

• out that there is one degree of freedom in this case. The next thing you're looking at

出，在這種情況下有一個自由度。接下來你&#39;看的是

• is for a critical value. And the critical value that we'll always use in the class is

是為一個臨界值。而我們在類中會一直使用的臨界值是

• the 0.05 value. And so that's going to be this column right here. So the first thing

0. 05值。所以這&#39;將是這一列就在這裡。所以第一件事

• you do is find the 0.05 value and you don't worry about all of the other numbers. So that's

你要做的是找到0.05的值，你不&#39;擔心所有的其他數字。所以這

• 3.841 is something I just know because it means that I'm in the right chart or I'm in

3.841是我只知道的東西，因為它意味著我&#39;在正確的圖表或我&#39;在。

• the right column.

右欄。

• A way that I explain this to kids is that you can think of that as being 95% sure that

我向孩子們解釋的一個方法是，你可以把它看成是95％的肯定。

• you're either accepting or rejecting your null hypothesis. And you can see that our

你&#39;要麼接受要麼拒絕你的零點假設。你可以看到，我們的

• critical values get higher over here. So you can think as we move this way, if we really

這裡的臨界值會越來越高所以你可以想，當我們這樣移動時，如果我們真的...

• want to be sure we'd have to exceed a higher critical value. So what's our null hypothesis

想要確定我們&#39;d必須超過一個更高的臨界值。所以我們的零點假設是什麼？

• again. Null hypothesis's no statistical difference between observed and expected and so we either

再次。Null hypothesis&#39;的觀察到的和預期的沒有統計學上的差異，所以我們要麼是。

• accept or reject that value. So in this case our critical value would be 3.841. And so

接受或拒絕該值。所以在這種情況下，我們的臨界值將是3.841。所以

• when you calculate Chi-squared, if you get a number that is higher than 3.841 then you

當你計算Chi-squared時，如果你得到的數字高於3.841，那麼你就

• reject that null hypothesis. And so there actually is something aside from just chance

拒絕這個零假設。是以，實際上有一些東西 除了只是機會

• that is causing you to get more heads than tails. And if you don't exceed the critical

是導致你得到更多的頭比尾。如果你不超過臨界值

• value then you accept that null hypothesis. And this is usually what ends up happening,

值，那麼你就接受這個零點假設。而這通常是最終的結果。

• unless you have a variable that's impacting your results. Let's apply this in a couple

除非你有一個變量，&#39;的影響你的結果。讓我們把這個應用在幾個例子中吧

• of different cases.

的不同情況。

• So this is my wife here. I asked her to flip a coin and so I asked the statistics teacher

所以這是我老婆在這裡。我讓她拋硬幣，所以我問統計學老師。

• how much data do you have to get before you can actually apply the Chi-squared test? And

你要得到多少數據才能真正應用Chi-squared檢驗？還有

• Mr. Humberger said something magic about 30. And so I want to exceed that number in each

杭博格先生說過一個神奇的數字，大約是30。所以我希望在每一個環節都能超過這個數字。

• of these experiments and so this is my wife down here. This is her hand. And what she's

這些實驗，所以這是我的妻子在這裡。這是她的手。而她

• going to do is she's going to, let me get a value you can see, she's going to flip 50

要做的是她&#39;的打算，讓我得到一個值 你可以看到，她&#39;的打算翻轉50。

• coins. You can see she's really fast so she's flipping 50 coins and then she's sorting them

幣。你可以看到她的速度非常快，所以她翻轉了50枚硬幣，然後她把它們分揀出來

• out. And so if we look at that, the first thing, even before you collect the data is

出。是以，如果我們看一下，第一件事， 甚至在你收集數據之前，是：

• we could look at the expected values. And so we've got heads or tails. And so if you

我們可以看看預期值。所以我們&#39;已經得到了頭或尾。所以，如果你

• flip 50 coins how many do we expect to come up as heads? The right answer would be 25.

拋出50枚硬幣，我們預計有多少枚會出現人頭？正確答案是25個。

• And how many would we expect to come up as tails? 25 as well. Now let's say your data

又有多少會以尾巴的形式出現呢？25個也是。現在，讓我們&#39;說你的數據

• is not as even as that. If you're looking at fruit flies it might be 134 or 133. Well

是沒有那麼均勻的。如果你&#39;在看果蠅，可能是134或133。嘛

• let's say I flip 51 coins for example instead of 50 then my expected values would be 25.5

比如說我拋出51枚硬幣，而不是50枚，那麼我的期望值將是25.5

• and 25.5. So expected values since they're just due to probability don't have to be a

和25.5。所以，預期值既然只是由於概率不&#39;，那麼就不一定是一個

• whole number.

整數。

• If we look at our observed values, well let's look down here. How many heads did we get?

如果我們看一下我們的觀測值，好吧，讓我們看下這裡。我們有多少人頭？

• 28 heads. And how many tails did we get? So that would just be 22. Okay. So now we're

28個頭。那我們得到了多少個尾巴？所以，這將只是22。好了，現在我們

• going to apply Chi-squared and come up with a critical value. And so, what does that mean?

要應用Chi -squared 並拿出一個臨界值。那麼，這意味著什麼？

• Well let me get this out of the way. So we're going to take our equation which is O minus

好吧，讓我把這個問題說清楚。所以，我們要把我們的公式 這是O減去。

• E squared over E, and we're going to do that for the heads column and then we're going

E的平方在E上，我們&#39;要做到這一點的頭列，然後我們&#39;要。

• to do it for the tails column. So we've also got O minus E squared over E for the tails

來做尾部列。所以，我們也得到了O減E的平方在E上的尾數。

• column. And so our observed value is going to be 28. So it's 28 minus 25, which is expected,

列。所以我們的觀測值將是28。所以是28減去25，這是預料之中的。

• squared over 25. Now this sum means that we're going to add these two values together so

25的平方。現在這個總和意味著我們要把這兩個值加在一起，所以。

• I'm going to put a plus sign right here. Now we're going to do the tails side. So what's

我在這裡放一個加號。現在我們要做的是尾部。所以，什麼

• our observed? It's 22 minus 25 squared over 25. So you can do this in your head. 28 minus

我們的觀察？這是22減25的平方超過25。所以，你可以在你的腦袋裡做這個。28減

• 25 is 3, square that is 9. 9 over 25 plus 22 minus 25 is negative 3 squared. It's 9

25是3，平方就是9，9過25加22減25是負3的平方。它的9

• over 25. And so our answer is 18 over 25 which equals 0.72.

超過25。所以我們的答案是18大於25，等於0.72。

• Okay. So that's our Chi-squared value for

這就是我們的Chi-squared值。

• this data that we just collected. Now let's go over here to our critical values. Well

這個數據，我們剛剛收集。現在讓我們到這裡來看看我們的臨界值。好了

• we said that we had 1 degree of freedom, because there's two outcomes. 2 minus 1 is 1. So we're

我們說我們有1個自由度，因為有&#39;的兩個結果。2減1是1，所以我們&#39;。

• in this right here, this row right here. And then here is our magical 0.05 column and so

在這裡，這一行就在這裡。然後這裡是我們神奇的0. 05欄，所以。

• our critical value is 3.841. And so if we get a number higher than that we reject our

我們的臨界值是3. 841所以，如果我們得到的數字比這個高，我們拒絕我們的。

• null hypothesis. We didn't, so we got a value that is lower than that, 0.72 so that means

零假設。我們沒有&#39;t，所以我們得到了一個比這個值更低的值，0.72，所以這意味著。

• we have to accept our null hypothesis. That means that my wife did a great job. There's

我們必須接受我們的零假設。這意味著我的妻子做得很好。There&#39;s

• nothing wrong with the coins. There's not way more heads then there should be and so

幣沒有什麼問題。有&#39;'s不方式更多的頭，然後有應該是，所以。

• we have to accept the null hypothesis that there's no statistical difference between

我們必須接受零假設，即沒有&#39；之間的統計學差異。

• what we observe and what we expect to see.

我們觀察到的和我們期望看到的。

• So now let's try a little more complex problem. Now we've got dice. So we've got 36 dice.

所以，現在讓我們試試更復雜一點的問題。現在，我們已經得到了骰子。所以我們有36個骰子。

• So let me get this out here. So our expected values, well there are six things you could

所以讓我在這裡把這個說出來。是以，我們的預期值， 好了，有六件事情，你可以。

• get. So we could get a 1, 2, 3, 4, 5 or 6. And so let's play this out. So expected values,

得到。所以我們可以得到1、2、3、4、5或6。所以讓我們&#39;玩這個了。所以預期值。

• since I have 36 dice here, we would expect to get 6 of each of those numbers coming up.

因為我這裡有36個骰子，我們希望能從這些數字中各得到6個。

• So I'm just taking 36 total dice divided by 6 so I got 6. But let's see what we get for

所以我&#39;只是把36個總骰子除以6，所以我得到了6個。但讓我們看看我們得到了什麼。

• observed values. Oh, it looks like we're getting a lot of sixes. So if we look at the observed

觀測值。哦，看起來我們&#39;得到了很多6。所以，如果我們看一下觀察到的

• values for one here we get 2 ones. We look at the twos, we get 4 of those. For the threes

這裡的1的值，我們得到2個1。我們看看二，我們得到4個二。對於3

• it looks like 8 threes. For the fours we get 9. For the fives we just get 3. And then for

它看起來像8個三。四個四，我們得到9個。5號的我們只得到3個。然後是

• the sixes, look at all the sixes, so we get 10 right here. Okay. Now we have to figure

六，看看所有的六， 所以我們得到10在這裡。好了，現在我們要算出現在我們要計算

• out a Chi-squared value. So let me get this out of the way.

出一個Chi-squared值。所以讓我把這個問題說清楚。

• And I'm going to stop talking and do the math

我就不說了，先算算賬吧。

• and speed up the video a little bit. And so hopefully I don't screw up any of this. So

並加快視頻一點點。所以希望我不&#39;搞砸了任何這一點。所以...

• that is 58 over 6 which is 9.6. So that is our Chi-squared value. It's 9.6 in this case.

那就是58大於6，也就是9.6。所以這就是我們的Chi平方值。它&#39;9.6在這種情況下。

• Since we added all these up. So now we've got to go over here to our chart. And so first

既然我們把這些都加起來了。所以現在我們&#39;''已經得到了在這裡去我們的圖表。所以首先

• of all we have to figure out how many degrees of freedom do we have. Well, since there are

我們必須弄清楚我們有多少自由度。好吧，既然有

• 6 different outcomes and we take 6 minus 1, so we've got 5. We're in this column of the

6種不同的結果，我們取6減1，所以我們&#39;已經得到5。我們在這一列的。

• 0.05 right here so if I read across our critical value is 11.070. And so if we look at that,

0. 05就在這裡，所以如果我讀過我們的臨界值是11. 070。所以如果我們看一下，

• did our value go higher than that, no it's only 9.6, it's lower than that, so in this

我們的價值是否比這更高，不，它&#39;只有9.6，它&#39;比這更低，所以在這個。

• case since it's 9.6, even though we had all of those sixes we still need to accept our

的情況下，因為它的9.6，即使我們有所有這些六，我們仍然需要接受我們的。

• null hypothesis that there's no statistical significance between or difference between

null hypothesis that there&#39;s no statistical significance between or difference between

• what we observed and then what we expected.

我們觀察到的，然後是我們預期的。

• So now let's leave you with this question. So in the animal behavior podcast as I talk

所以現在讓我們&#39;留給你這個問題。所以，在動物行為播客中，當我談到

• about that, we're looking at pill bugs and if they spend more time in the wet or if they

關於這一點，我們&#39;正在尋找藥丸蟲，如果他們花更多的時間在潮溼或如果他們

• spend more time in the dry. And so if you look at the values right here, this is recording

花更多的時間在乾燥。所以，如果你看這裡的值，這是錄音

• how much time they spend in the wet and how much time they spend in the dry. So what I've

他們花多少時間在潮溼和多少時間在乾燥。所以我&#39;ve

• done is we would expect since there are 10 pill bugs we'd have 5 on each side. But since

做的是我們會期望因為有10個藥蟲，我們&#39;會有5個在每邊。但由於

• it looks like they're spending more time on the wet, you can even see them in the video

它看起來像他們&#39;花更多的時間在溼的，你甚至可以看到他們在視頻中

• here spending more time in the wet, I take the average of the wet and the average of

在這裡花了更多的時間在潮溼的，我採取的平均溼和平均的。

• the dry column. And that gives me my wet and my dry and so now I'm not going to show you

幹柱。這給了我我的溼和我的幹，所以現在我&#39;不打算告訴你。

• how to do this one, but try to apply Chi-squared to figure out if there's a statistical difference

如何做到這一點，但嘗試應用Chi-squared來計算，如果有&#39;的統計學差異。

• between the expected values of what we expect and what we observed. And you can put your

我們所期望的和我們觀察到的預期值之間。你可以把你的

• answer down in the comments. And so I hope that's helpful.

在評論中回答下來。所以希望對大家有所幫助&#39;。

Hi. It's Mr. Andersen and welcome to my podcast on the Chi-squared test. Chi-squared

A2 初級 中文 硬幣 自由度 平方 數據 假設 數字

# Chi-squared Test

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Why Why 發佈於 2013 年 03 月 25 日