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问卷假设检验 t检验_真实问题的假设检验

發(fā)布時間：2023/11/29 编程问答 32 豆豆

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問卷假設(shè)檢驗 t檢驗

A statistical Hypothesis is a belief made about a population parameter. This belief may or might not be right. In other words, hypothesis testing is a proper technique utilized by scientist to support or reject statistical hypotheses. The foremost ideal approach to decide if a statistical hypothesis is correct is to examine the whole population.

統(tǒng)計 假設(shè)是關(guān)于總體參數(shù)的一種信念。這種信念可能是正確的，也可能不是正確的。換句話說，假設(shè)檢驗是科學(xué)家用來支持或拒絕統(tǒng)計假設(shè)的一種適當技術(shù)。決定統(tǒng)計假設(shè)是否正確的最理想的方法是檢查整個人口。

Since that’s frequently impractical, we normally take a random sample from the population and inspect the equivalent. Within the event sample data set isn’t steady with the statistical hypothesis, the hypothesis is refused.

由于這通常是不切實際的，因此我們通常從總體中隨機抽取一個樣本并檢查等效樣本。如果事件樣本數(shù)據(jù)集的統(tǒng)計假設(shè)不穩(wěn)定，則拒絕該假設(shè)。

假設(shè)類型 (Types of hypothesis)

There are two sorts of hypothesis and both the Null Hypothesis (Ho) and Alternative Hypothesis (Ha) must be totally mutually exclusive events.

假說有兩種， 空假說 (Ho)和替代假說 (Ha)必須是完全互斥的事件。

? Null hypothesis is usually the hypothesis that the event won't happen.

?空假設(shè)通常是事件不會發(fā)生的假設(shè)。

? Alternative hypothesis is a hypothesis that the event will happen.

?替代假設(shè)是事件將發(fā)生的假設(shè)。

為什么我們需要假設(shè)檢驗？ (Why we need Hypothesis Testing?)

Suppose a company needs to launch a new bicycle in the market. For this situation, they will follow Hypothesis Testing all together decide the success of the new product in the market.

假設(shè)一家公司需要在市場上推出一款新自行車。對于這種情況，他們將一起進行假設(shè)檢驗，共同決定新產(chǎn)品在市場上的成功。

Where the likelihood of the product being ineffective in the market is undertaken as the Null Hypothesis and the likelihood of the product being profitable is undertaken as an Alternative Hypothesis. By following the process of Hypothesis testing they will foresee the accomplishment.

將產(chǎn)品在市場上無效的可能性作為零假設(shè)，而將產(chǎn)品獲利的可能性作為替代假設(shè)。通過遵循假設(shè)檢驗的過程，他們將預(yù)見其成就。

如何計算假設(shè)檢驗？ (How to Calculate Hypothesis Testing?)

· State the two theories with the goal that just one can be correct, to such an extent that the two occasions are totally unrelated.

·陳述兩種理論，目標是只有一種是正確的，以至于兩種情況完全無關(guān)。

· Now figure a study plan, that will lay out how the data will be assessed.

·現(xiàn)在制定一個研究計劃，該計劃將列出如何評估數(shù)據(jù)。

· Now complete the plan and genuinely investigate the sample dataset.

·現(xiàn)在，完成計劃并真正調(diào)查樣本數(shù)據(jù)集。

· Finally examine the outcome and either accept or reject the null hypothesis.

·最后檢查結(jié)果，并接受或拒絕原假設(shè)。

另一個例子 (Another example)

Assume, a person has gone after a job and he has expressed in the resume that his composing speed is 70 words per minute. The recruiter might need to test his case. On the off chance that he sees his case as adequate, he will enlist him, in any case, reject him. Thus, after the test and found that his speed is 63 words a minute. Presently, he can settle on whether to employ him or not. In the event that he meets all other qualification measures. This procedure delineates Hypothesis Testing in layman’s terms.

假設(shè)一個人去找工作了，他在簡歷中表示自己的寫作速度是每分鐘70個單詞。招聘人員可能需要測試他的情況。在他認為自己的案子足夠的偶然機會上，他將征召他，無論如何，拒絕他。這樣，經(jīng)過測試，發(fā)現(xiàn)他的速度是每分鐘63個字。目前，他可以決定是否雇用他。如果他符合所有其他資格評定標準。此過程以外行的術(shù)語描述了假設(shè)檢驗。

In statistical terms Hypothesis, his composing speed is 70 words per minute is a hypothesis to be tested so-called null hypothesis. Clearly, the alternating hypothesis his composing speed isn’t 70 words per minute. So, normal composing speed is the population parameter and sample composing speed is sample statistics.

用統(tǒng)計學(xué)的假設(shè)來說，他的寫作速度是每分鐘70個單詞，這是一個需要檢驗的假設(shè)，即所謂的零假設(shè)。顯然，他的寫作速度不是每分鐘70個單詞。因此，正常合成速度是總體參數(shù)，樣本合成速度是樣本統(tǒng)計量。

The conditions of accepting or rejecting his case are to be chosen by the selection representative. For instance, he may conclude that an error of 6 words is alright to him so he would acknowledge his claim between 64 to 76 words per minute. All things considered, sample speed 63 words per minute will close to reject his case. Furthermore, the choice will be he was producing a fake claim.

selection選代表應(yīng)選擇接受或拒絕其案件的條件。例如，他可能會得出結(jié)論，認為6個字的錯誤對他來說是可以的，因此他將承認他的要求是每分鐘64到76個字。考慮到所有因素，采樣速度為每分鐘63個單詞將接近拒絕他的案件。此外，選擇將是他提出了虛假主張。

In any case, if the selection representative stretches out his acceptance region to positive/negative 7 words that are 63 to 77 words, he would be tolerating his case. In this way, to finish up, Hypothesis Testing is a procedure to test claims about the population dependent on the sample. It is a fascinating reasonable subject with a quite statistical jargon. You have to dive more to get familiar with the details.

無論如何，如果the選代表將他的接受范圍擴展到63到77個單詞的正/負7個單詞，那么他將容忍自己的情況。通過這種方式，最后，假設(shè)檢驗是一種測試關(guān)于依賴樣本的總體的聲明的過程。這是一個引人入勝的合理主題，而且具有相當?shù)慕y(tǒng)計術(shù)語。您必須花更多精力去熟悉細節(jié)。

假設(shè)的顯著性水平和排斥區(qū)域 (Significance Level and Rejection Region for Hypothesis)

Type I error probability is normally indicated by α and generally set to 0.05. The value of α is recognized as the significance level.

I型錯誤概率通常由α表示，通常設(shè)置為0.05。 α的值被認為是顯著性水平 。

The rejection region is the set of sample data that prompts the rejection of the null hypothesis. The significance level, α, decides the size of the rejection region. Sample results in the rejection region are labelled statistically significant at the level of α.

拒絕區(qū)域是一組樣本數(shù)據(jù)，提示拒絕原假設(shè)。顯著性水平α決定了拒絕區(qū)域的大小。 剔除區(qū)域的樣品結(jié)果在α水平上被標記為具有統(tǒng)計學(xué)意義。

The impact of differing α is that If α is small, for example, 0.01, the likelihood of a type I error is little, and a ton of sample evidence for the alternative hypothesis is needed before the null hypothesis can be dismissed. Though, when α is bigger, for example, 0.10, the rejection region is bigger, and it is simpler to dismiss the null hypothesis.

不同的α的影響在于，如果α小(例如0.01)，則I型錯誤的可能性很小，并且在可以駁回原假設(shè)之前，需要大量的替代假設(shè)樣本證據(jù)。但是，當α較大(例如0.10)時，拒絕區(qū)域較大，并且更容易消除原假設(shè)。

p值的意義 (Significance from p-values)

A subsequent methodology is to evade the utilization of a significance level and rather just report how significant the sample evidence is. This methodology is as of now more widespread. It is accomplished by the method of a P-value. P-value is a gauge of power of the evidence against the null hypothesis. It is the likelihood of getting the observed value of test statistic, or value with significantly more prominent proof against the null hypothesis (Ho) if the null hypothesis of an investigation question is true. The less significant the P-value, the more proof there is supportive of the alternative hypothesis. Sample evidence is measurably noteworthy at the α level just if the P-value is less than α. They have an association for two-tail tests. When utilizing a confidence interval to playout a two-tailed hypothesis test, reject the null hypothesis if and just if the hypothesized value doesn’t lie inside a confidence interval for the parameter.

隨后的方法是逃避對顯著性水平的利用，而只是報告樣本證據(jù)的顯著性。截止到現(xiàn)在，這種方法更加廣泛。它是通過P值的方法完成的。 P值是針對原假設(shè)的證據(jù)效力的量度。如果調(diào)查問題的原假設(shè)是真實的，則有可能獲得檢驗統(tǒng)計量的觀察值，或獲得對原假設(shè)(Ho)具有明顯更顯著證明的值。 P值的意義越小，證明替代假設(shè)的證據(jù)越多。即使P值小于α，樣本證據(jù)在α水平上也相當可觀。他們有兩個尾巴測試的關(guān)聯(lián)。當使用置信區(qū)間播放二尾假設(shè)檢驗時，如果且僅當假設(shè)值不在參數(shù)的置信區(qū)間內(nèi)時，拒絕原假設(shè)。

假設(shè)檢驗和置信區(qū)間 (Hypothesis Tests and Confidence Intervals)

Hypothesis tests and confidence intervals are cut out of the same cloth. An event whose 95% confidence interval reject the hypothesis is an event for which p<0.05 under the relating hypothesis test, and the other way around. A P-value is letting you know the greatest confidence interval that despite everything prohibits the hypothesis. As such, if p<0.03 against the null hypothesis, that implies that a 97% confidence interval does exclude the null hypothesis.

假設(shè)檢驗和置信區(qū)間是從同一塊布上剪下來的。 95％置信區(qū)間拒絕該假設(shè)的事件是在相關(guān)假設(shè)檢驗下p <0.05的事件，反之亦然。 P值讓您知道最大的置信區(qū)間，盡管所有情況都阻止了該假設(shè)。這樣，如果針對原假設(shè)的p <0.03，則意味著97％的置信區(qū)間確實排除了原假設(shè)。

總體均值的假設(shè)檢驗 (Hypothesis Tests for a Population Mean)

We do a T-test on the ground that the population mean is unknown. The general purpose is to contrast sample mean with some hypothetical population mean, to assess whether the watched the truth is such a great amount of unique in relation to the hypothesis that we can say with assurance that the hypothetical population mean isn’t, indeed, the real population mean.

我們以總體均值未知為由進行T檢驗。一般目的是將樣本均值與某些假設(shè)總體均值進行對比，以評估觀察到的真相與假設(shè)是否有如此多的獨特性，我們可以肯定地說，假設(shè)總體均值并不是，實際人口平均數(shù)。

人口比例假設(shè)檢驗 (Hypothesis Tests for a Population Proportion)

At the point when you have two unique populations Z test facilitates you to choose if the proportion of certain features is the equivalent or not in the two populations. For instance, if the male proportion is equivalent between the two nations.

當您有兩個唯一的總體時， Z檢驗可幫助您選擇某些特征的比例在兩個總體中是否相等。例如，如果兩國之間的男性比例相等。

均等人口方差假設(shè)檢驗 (Hypothesis Test for Equal Population Variances)

F Test depends on F distribution and is utilized to think about the variance of the two impartial samples. This is additionally utilized with regards to the investigation of variance for making a decision about the significance of more than two samples.

F檢驗取決于F分布，并用于考慮兩個公正樣本的方差。關(guān)于方差研究，還可以利用它來決定兩個以上樣本的重要性。

T檢驗，F檢驗和Z檢驗 (T-test, F-test and Z-test)

T-test and F test are totally two unique things. The T-test is utilized to evaluate the population parameter, for example, the population mean, and is likewise utilized for hypothesis testing for a population mean. However, it must be utilized when we don’t know about the population standard deviation. On the off chance that we know the population standard deviation, we will utilize the Z test. We can likewise utilize T statistic to approximate population mean. T statistic is likewise utilised for discovering the distinction in two population means with the assistance of sample means.

T檢驗和F檢驗完全是兩件事。 T檢驗用于評估總體參數(shù)，例如總體平均值，并且同樣用于總體平均值的假設(shè)檢驗。但是，當我們不了解總體標準偏差時，必須使用它。如果我們知道總體標準偏差，我們將使用Z檢驗。我們同樣可以利用T統(tǒng)計量來近似總體均值。同樣，在樣本均值的幫助下，利用T統(tǒng)計量來發(fā)現(xiàn)兩個總體均值之間的區(qū)別。

Z statistic or T statistic is utilized to assess population parameters such as population mean and population proportion. It is likewise used for testing hypothesis for population mean and population proportion. In contrast to Z statistic or T statistic, where we manage mean and proportion, Chi-Square or F test is utilized for seeing if there is any variance inside the samples. F test is the proportion of fluctuation of two samples.

Z統(tǒng)計量或T統(tǒng)計量用于評估總體參數(shù)，例如總體平均值和總體比例。它同樣用于檢驗人口均值和人口比例的假設(shè)。與我們管理均值和比例的Z統(tǒng)計量或T統(tǒng)計量相比，卡方檢驗或F檢驗用于查看樣本內(nèi)部是否存在任何方差。 F檢驗是兩個樣本的波動比例。

結(jié)論 (Conclusion)

Hypothesis encourages us to make coherent determinations, the connection among variables and gives the course to additionally investigate. Hypothesis, for the most part, results from speculation concerning studied behaviour, natural phenomenon, or proven theory. An honest hypothesis ought to be clear, detailed, and reliable with the data. In the wake of building up the hypothesis, the following stage is validating or testing the hypothesis. Testing of hypothesis includes the process that empowers to concur or differ with the expressed hypothesis.

假設(shè)鼓勵我們做出連貫的決定，確定變量之間的聯(lián)系，并提供進一步研究的過程。大多數(shù)情況下，假設(shè)是由對所研究的行為，自然現(xiàn)象或經(jīng)驗證的理論的推測得出的。誠實的假設(shè)應(yīng)該對數(shù)據(jù)清楚，詳細和可靠。在建立假設(shè)之后，接下來的階段是驗證或檢驗假設(shè)。假設(shè)檢驗包括授權(quán)與所表達的假設(shè)一致或不同的過程。

Written by:

撰寫人：

Saurav Singla

紹拉夫·辛格拉

翻譯自: https://medium.com/swlh/hypothesis-test-for-real-problems-64aafe17c1ad