Ab initio measurement-understand the common concepts of statistics

Case: every individual|record

Variables: attributes

Error : random error (cannot find the reason) systematic error (regular)

Reliability: the same method repeated measurement of the same object result consistency

Validity: similarity to real results.

difference

• The research subjects are different.
  Reliability: Respondent Validity: Composer

• Different research perspectives

  Reliability: the quality of the measurement validity: the quality of the questionnaire

• Different values

  • Questionnaire validity <questionnaire reliability
  • Maximum validity ≤ square root of reliability
  • High validity means high reliability; high reliability means not necessarily high validity

Normal distribution

• M± 1SD: 68%
• M ± 1.96SD: 95%
• M± 2.58SD: 99%

Skewness: The skewness of the data (the picture below is the right deviation)

Kurtosis: how high

Degree of freedom: unknown number that can be changed freely, X+Y+Z=0, degree of freedom is 2, two numbers are determined, and the third unknown number is automatically determined

For data with a sample size of N, its degree of freedom is naturally N-1. Because it has a mean value, this is the condition that limits it.
Degrees of freedom = number of variables (sample size) N-restricted conditions

hypothetical test

Judgment criteria: significance level-α-commonly used criteria 5%, 1% and 0.1%
p-value: that is, the null hypothesis actually holds, but the result we calculated incorrectly judges that the null hypothesis does not hold.
Use the p value to compare the probability of α to judge the result.

Deep understanding of p-value

This thing has bothered me for a long time, I can only compare but don't understand the meaning.
The p-value represents the contingency of a small probability event in the real sample data. When the contingency is not large, the null hypothesis can be considered wrong. For example, a pork farm claims that its pork is 5kg, and you buy 100 pieces of pork and find that the average is not 5kg, but 4kg, the original hypothesis is that the pork is 5kg, and the backup hypothesis is that the pork is not 5kg. The p-value is the chance that pork does not appear at 5kg. Now you fix the significance level $\alpha$ is 5%, that is, as long as the contingency is less than 5%, the null hypothesis can be rejected, because the lower the contingency, the more common that pork is not 5kg. What is the meaning of the confidence interval below, or pork, if the average of the 100 pieces of pork you buy is 4kg and the standard error is 1kg, then your confidence interval is (4±1)*95% probability quantile. Still pork, if the average of the 100 pieces of pork you buy is 4kg and the standard error is 1kg, then your confidence interval is (4±1)*95% probability quantile.