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Significance Test--Study Notes

2022-08-09 02:03:00 【Wsyoneself】

  1. Significance testing as a method to determine whether there is a difference between two or even multiple datasets
  2. Significance testing is a type of statistical hypothesis testing
  3. Used to detect whether there is a difference between the experimental group and the control group in a scientific experiment and whether the difference is significant
  4. No hypothesis, no test
  5. First make a hypothesis on the scientific research data, and then use the test to check whether the hypothesis is correct. Generally, the hypothesis to be tested is called the null hypothesis (H0), and the opposite hypothesis is the alternative hypothesis (H1)
    1. If the null hypothesis is true, but the test conclusion is to abandon the null hypothesis, it is a type 1 error, and the probability of occurrence is recorded as α
    2. If the null hypothesis is false, but the test conclusion is to accept the null hypothesis, it is a type II error, and the probability of occurrence is recorded as β
    3. Usually only the maximum probability α of the first type of error is considered, and β is not considered. Such a hypothesis test is a significance test, and α is called the significance level (generally = 0.05, 0.025, 0.01).To represent a significance test, the conclusion error rate must be less than 5% or 2.5% or 1%.(In statistics, events with a probability of less than 5% are often referred to as "impossible events")
    4. If the p value is greater than α, the null hypothesis is accepted, and if it is less than α, the null hypothesis is rejected
  6. The reason for the significance test: to judge whether the difference between the sample and the hypothesis we make about the population is purely chance variation (that is, when the sample data increases, the hypothesis is met), or whether the hypothesis is inconsistent with the overall reality..
  7. Significance test is divided into parametric test and nonparametric test
    1. Parameter test:
      1. Premise: The samples are from normal populations, and these normal populations have the same variance
      2. Test whether the population means are equal
      3. Common method: ANOVA
      4. Element: the number of unknown variables, which can be understood as the number of features
      5. Factor: The behavior (event) that affects the unknown variable, which can be understood as the number of tags
      6. F value (F statistic) = the ratio of between-group mean squares and within-group mean squares, reflecting the magnitude of the effect of random errors
        1. Relationship between p value and F value: F actual value>F lookup table value, then p<=0.05, otherwise p>0.5
  8. Non-parametric test:
    1. Since the parametric test needs to be based on the assumption of normality and homogeneity of variance, it is impossible to always meet the required statistical data in practical work. If the parametric test is forced to be used, it will cause errors.
    2. Nonparametric test based on rank sum
    3. Categories:  
      1. Kruskal-wallis test:
        1. One-way nonparametric analysis of variance
        2. The null hypothesis of this test is: k independent samples come from the same normal population
      2. Friedman test:
        1. Two-way rank analysis of variance
        2. The data to be tested needs to be balanced
        3. Only pay attention to one of the two factors to be used to test the data, and the other factor is used to partition the group
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