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T test n F test区别

T test n F test区别
T test n F test区别

你要检验两独立样本均数差异是否能推论至总体,而行的t检验

两样本(如某班男生和女生)某变量(如身高)的均数并不相同,但这差别是否能推论至总体,代表总体的情况也是存在著差异呢?

会不会总体中男女生根本没有差别,只不过是你那麼巧抽到这2样本的数值不同?

为此,我们进行t检定,算出一个t检定值。

与统计学家建立的以「总体中没差别」作基础的随机变量t分布进行比较,看看在多少%的机会(亦即显著性sig值)下会得到目前的结果。

若显著性sig值很少,比如<0.05(少於5%机率),亦即是说,「如果」总体「真的」没有差别,那麼就只有在机会很少(5%)、很罕有的情况下,才会出现目前这样本的情况。虽然还是有5%机会出错(1-0.05=5%),但我们还是可以「比较有信心」的说:目前样本中这情况(男女生出现差异的情况)不是巧合,是具统计学意义的,「总体中男女生不存差异」的虚无假设应予拒绝,简言之,总体应该存在著差异。

每一种统计方法的检定的内容都不相同,同样是t-检定,可能是上述的检定总体中是否存在差异,也同能是检定总体中的单一值是否等於0或者等於某一个数值。

至於F-检定,方差分析(或译变异数分析,Analysis of Variance),它的原理大致也是上面说的,但它是透过检视变量的方差而进行的。它主要用于:均数差别的显著性检验、分离各有关因素并估计其对总变异的作用、分析因素间的交互作用、方差齐性(Equality of Variances)检验等情况。

4,T检验和F检验的关系

t检验过程,是对两样本均数(mean)差别的显著性进行检验。惟t检验须知道两个总体的方差(Variances)是否相等;t检验值的计算会因方差是否相等而有所不同。也就是说,t检验须视乎方差齐性(Equality of Variances)结果。所以,SPSS在进行t-test for Equality of Means的同时,也要做Levene's Test for Equality of Variances 。

1.

在Levene's Test for Equality of Variances一栏中F值为2.36, Sig.为.128,表示方差齐性检验「没有显著差异」,即两方差齐(Equal Variances),故下面t检验的结果表中要看第一排的数据,亦即方差齐的情况下的t检验的结果。

2.

在t-test for Equality of Means中,第一排(Variances=Equal)的情况:t=8.892, df=84, 2-Tail Sig=.000, Mean Difference=22.99

既然Sig=.000,亦即,两样本均数差别有显著性意义!

3.

到底看哪个Levene's Test for Equality of Variances一栏中sig,还是看t-test for Equality of Means中那个Sig. (2-tailed)啊?

答案是:两个都要看。

先看Levene's Test for Equality of Variances,如果方差齐性检验「没有显著差异」,即两方差齐(Equal Variances),故接著的t检验的结果表中要看第一排的数据,亦即方差齐的情况下的t检验的结果。反之,如果方差齐性检验「有显著差异」,即两方差不齐(Unequal Variances),故接著的t检验的结果表中要看第二排的数据,亦即方差不齐的情况下的t检验的结果。

4.

你做的是T检验,为什么会有F值呢?

就是因为要评估两个总体的方差(Variances)是否相等,要做Levene's Test for Equality of Variances,要检验方差,故所以就有F值。

另一种解释:

t检验有单样本t检验,配对t检验和两样本t检验。

单样本t检验:是用样本均数代表的未知总体均数和已知总体均数进行比较,来观察此组样本与总体的差异性。

配对t检验:是采用配对设计方法观察以下几种情形,1,两个同质受试对象分别接受两种不同的处理;2,同一受试对象接受两种不同的处理;3,同一受试对象处理前后。

F检验又叫方差齐性检验。在两样本t检验中要用到F检验。

从两研究总体中随机抽取样本,要对这两个样本进行比较的时候,首先要判断两总体方差是否相同,即方差齐性。若两总体方差相等,则直接用t检验,若不等,可采用t'检验或变量变换或秩和检验等方法。

其中要判断两总体方差是否相等,就可以用F检验。

若是单组设计,必须给出一个标准值或总体均值,同时,提供一组定量的观测结果,应用t检验的前提条件就是该组资料必须服从正态分布;若是配对设计,每对数据的差值必须服从正态分布;若是成组设计,个体之间相互独立,两组资料均取自正态分布的总体,并满足方差齐性。之所以需要这些前提条件,是因为必须在这样的前提下所计算出的t统计量才服从t分布,而t检验正是以t分布作为其理论依据的检验方法。

简单来说就是实用T检验是有条件的,其中之一就是要符合方差齐次性,这点需要F检验来验证。

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全新版大学英语听说教程test听力原文

全新版大学英语听说教程 t e s t听力原文 This manuscript was revised by the office on December 10, 2020.

大学英语(第二版)听说教程 听力原文 Test 1 Part A Directions: You are going to hear eight short conversations between two speakers. Each will be read only once. After each conversation, a question will be asked about what you have heard. Listen once and choose the right answer to the question you hear. (8 points) 1.M: You like music, don’t you, Sally W: Yes. Classical and light music. But now what you hear everywhere is only noisy music. I can’t stand it. Q: What does the woman mean 2.W: I think I’ll wear my red blouse to the party tonight. M: Why don’t you wear the blue one I think you look in better in it. Q: What does the man mean 3.W: How do you like the pie you’ve had M: Never have I had such a delicious pie. Q: What does the man mean 4.W: Oh, Peter. I’m hungry. I can’t walk any further. M: How about getting something to eat in the restaurant just round the corner by the parking lot Q: Where are the two speakers 5.W: Nice day, isn’t it Want to join us for a swim M: Would you mind waiting for a minute while I get prepared Q: What does the woman mean 6.W: Hi, Tony. Haven’t seen you for some time. How have you been M: I have a car accident last week, but only some minor injuries. Q: What happened to Tony 7.W: Maggie, could you forward this mail to Professor Wang M: Sorry, Phil. My computer has broken down. But I’ll do it as soon as I have it fixed. Q: What does the woman mean 8.W: I’ve been under the weather for quite a few days. I thought my cold was going away. But it seems to get worse now. M: You’ve been complaining too much. Why didn’t you make an appointment with the doctor earlier Q: What does the man mean Part B Directions: You’ll hear two conversations. Each will be read once. Listen carefully and choose the right answers to the questions you hear. (7 points)

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