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  • 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'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'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'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'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'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'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'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'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'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'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'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'會說,'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'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'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'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'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'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'在正確的圖表或我'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'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'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'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,'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'的打算,讓我得到一個值 你可以看到,她'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'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'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'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',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'要做到這一點的頭列,然後我們'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'的兩個結果。2減1是1,所以我們'。

  • 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'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'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''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'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'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'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'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'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'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'''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'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'只有9.6,它'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'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'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'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'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'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'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'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'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'。

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

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Chi-squared Test

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    Why Why 發佈於 2013 年 03 月 25 日
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