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Statistical hypothesis test

1. What is the statistical hypothesis test?

The "statistical hypothesis test" is to verify whether a hypothesis is statistically correct for the group (called the maternal group). Generally, the population is huge (for example, a Japanese adult, a Shiba Inu kept in Tokyo, a cup of rice from a certain set meal restaurant, etc.), so it is difficult to investigate all the samples in the survey. Pick up the sample (called a specimen) so that it is not biased to what you want to check, and estimate the maternal group from the specimen.

The test is performed by the following procedure.

1. What is the statistical hypothesis test?

The "statistical hypothesis test" is to verify whether a hypothesis is statistically correct for the group (called the maternal group). Generally, the population is huge (for example, a Japanese adult, a Shiba Inu kept in Tokyo, a cup of rice from a certain set meal restaurant, etc.), so it is difficult to investigate all the samples in the survey. Pick up the sample (called a specimen) so that it is not biased to what you want to check, and estimate the maternal group from the specimen.

The test is performed by the following procedure.

① Hypothesis setting

In the statistical hypothesis test, a test is conducted on whether or not the hypothesis that you want to prove will not be established. When statistically rejected (proven that it is incorrect), it is proven that the opposite of the hypothesis, that is, the "conflict hypothesis" indicating that the hypotheses you want to prove are established.

② Setting of the rejection area (danger range)

If the returnless hypothesis is correct, set the boundary of how likely you are to reject the returnless hypothesis. For example, dice A shakes the dice A 10 times under the hypothesis that all eyes come out with the same probability, and have one or two eyes in 10 times. If the return hypothesis is correct, the probability of getting one or two eyes in both 10 times is about 0.001%. It is more natural to think that a 0.001%chance of 0.001%is happening, but that dice A is more likely to have 1 or 2 eyes, that is, the returnless hypothesis is wrong. The criteria for judging that the returnless hypothesis is wrong (rejected) is called a significant level or danger rate, and the area that does not regard the right hypothesis is called a dismissal or dangerous area. 。 The significance level is the probability that the returnless hypothesis is really correct and the accidental hypothesis will be rejected (judged to be correct).

③ Calculation of test statistics and P value

At the time of the test, it is not known what probability the value obtained from the specimen is the value, so it is converted to a test statistics (value for use for the test). Test statistics are a probability distribution that indicates how likely each value can be obtained, and is generally used in mountain -like graphs as shown in the figure below. The lower the height of the mountain, the lower the probability of obtaining the test statistics, and the entire area of the mountain is all possible, 1 (100%). (2), the area where the area to be dismissed when the area of the outside of this mountain is entered is determined as a dismissal area.

Here, we calculate the area outside the mountains, that is, the probability that the value of the mountain, that is, the most extreme result, from the actual test statistics calculated. This probability is called P value.

In the statistical hypothesis test, a test is conducted on whether or not the hypothesis that you want to prove will not be established. When statistically rejected (proven that it is incorrect), it is proven that the opposite of the hypothesis, that is, the "conflict hypothesis" indicating that the hypotheses you want to prove are established.

② Setting of the rejection area (danger range)

If the returnless hypothesis is correct, set the boundary of how likely you are to reject the returnless hypothesis. For example, dice A shakes the dice A 10 times under the hypothesis that all eyes come out with the same probability, and have one or two eyes in 10 times. If the return hypothesis is correct, the probability of getting one or two eyes in both 10 times is about 0.001%. It is more natural to think that a 0.001%chance of 0.001%is happening, but that dice A is more likely to have 1 or 2 eyes, that is, the returnless hypothesis is wrong. The criteria for judging that the returnless hypothesis is wrong (rejected) is called a significant level or danger rate, and the area that does not regard the right hypothesis is called a dismissal or dangerous area. 。 The significance level is the probability that the returnless hypothesis is really correct and the accidental hypothesis will be rejected (judged to be correct).

③ Calculation of test statistics and P value

At the time of the test, it is not known what probability the value obtained from the specimen is the value, so it is converted to a test statistics (value for use for the test). Test statistics are a probability distribution that indicates how likely each value can be obtained, and is generally used in mountain -like graphs as shown in the figure below. The lower the height of the mountain, the lower the probability of obtaining the test statistics, and the entire area of the mountain is all possible, 1 (100%). (2), the area where the area to be dismissed when the area of the outside of this mountain is entered is determined as a dismissal area.

Here, we calculate the area outside the mountains, that is, the probability that the value of the mountain, that is, the most extreme result, from the actual test statistics calculated. This probability is called P value.

④ judgment

Finally, compare which of the significant level specified in ② or the P value obtained in ③ is larger. This is synonymous with whether or not the test statistics are in the dismissal area. P -value

2. Specific examples of statistical hypothesis tests

As introduced on the product page, Study 1 has been confirmed by a statistical hypothesis that the "correct answer rate of how much conversation was heard" was significantly higher than other companies' music earphones. Therefore, as a specific example of the statistical hypothesis test, I will introduce examples of Study1.

In this experiment, 20 college students listen to conversational audio and write out, and as a result, Study 1 has a significant high answer rate of how much conversation has been heard correctly than other companies' earphones. , The statistical hypothesis test was confirmed. That is,

(1) A return hypothesis is made that "Study 1 and other companies 'earphones A, Study 1 and other companies' earphones B are not different in the correct answer rate."

② The significance level is determined to 5%,

(3) Calculate the test statistics and P value based on the hearing and correct answer rate obtained from the 20 people.

④ From the result of P <0.05 (5%), it concludes that "Study 1 has a significantly high answer rate compared to other companies' products A and B."

Finally, compare which of the significant level specified in ② or the P value obtained in ③ is larger. This is synonymous with whether or not the test statistics are in the dismissal area. P -value

2. Specific examples of statistical hypothesis tests

As introduced on the product page, Study 1 has been confirmed by a statistical hypothesis that the "correct answer rate of how much conversation was heard" was significantly higher than other companies' music earphones. Therefore, as a specific example of the statistical hypothesis test, I will introduce examples of Study1.

In this experiment, 20 college students listen to conversational audio and write out, and as a result, Study 1 has a significant high answer rate of how much conversation has been heard correctly than other companies' earphones. , The statistical hypothesis test was confirmed. That is,

(1) A return hypothesis is made that "Study 1 and other companies 'earphones A, Study 1 and other companies' earphones B are not different in the correct answer rate."

② The significance level is determined to 5%,

(3) Calculate the test statistics and P value based on the hearing and correct answer rate obtained from the 20 people.

④ From the result of P <0.05 (5%), it concludes that "Study 1 has a significantly high answer rate compared to other companies' products A and B."

The bar graph shows the average value of the data obtained from the specimen, and the line at the center of the bar graph indicates standard errors. If the population is large, it is necessary to guess the population from the data obtained from the specimen. When performing the same experiment to all the prostitutes in the population, the standard error shows how much the average value of the obtained data may fluctuate.
The total number of data

*n*, Data values*x*, The average data_{i}*x*Then, infinite dispersion*s*Is represented by equation (1), and the standard error SE is represented by (2) using unbiased variance.^{2}

As described above, the statistical hypothesis tests have obtained a significant result in Study 1 that has a significant high answer rate compared to other products A and B, and shows the results in this graph.

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