Chapter 1: Mean comparison test and variance analysis.
In the research process of economic and social problems, it is often necessary to compare whether there are significant differences in some indicators between phenomena, especially when the sample size n is relatively large. According to the central limit theorem of random variables, the average value of samples is similar to that of normal distribution. Therefore, the comparative test of the average mainly studies whether the hypothesis about the normal population is established.
The main contents of this chapter:
1. single sample t test); The average value of a single population;
2. Independent sample T test of the mean of two independent total samples;
3. Paired sample T test of the mean of two related populations;
4. One-way ANOVA;
5. Two-factor analysis of variance (general linear model → univariate).
Assumption condition: the data studied obey normal distribution or approximately obey normal distribution.
In the analysis menu, the mean comparison test can be obtained from the menu comparison mean and the general linear model.
Section 1 Single Population Mean T Test (Single Sample T Test)
The t-test of a single population is also called the t-test of a single sample, that is, to test whether the mean of a single variable is different from the assumed mean. Compare the sample mean of a single variable with the assumed constant, and draw the conclusion that the previous assumption is correct by testing.
Example 2. 1 According to the wage levels of different industries in China in 2002, it is tested whether the annual average wage income of employees in state-owned enterprises is equal to 10000 yuan, assuming that the data approximately obeys a smooth distribution.
First of all, the hypothesis holds: H0: salary of state-owned enterprises 10000 yuan.
H 1: the salary of state-owned enterprises is not equal to 10000 yuan.
Section 2, Two-sample T-test of two populations.
I. independent samples t test two independent samples.
Independent sample t test is to test whether there is a significant difference between the mean values of two unrelated population samples. Two unrelated overall samples are also called independent samples, such as the comparison of the average value of an index of the same product produced by two unrelated enterprises, and the comparison of the height and weight of children in different regions. Whether there is a significant difference in the mean of the two populations can be tested by sampling. Example 2. 2 A medical research institute investigated whether there is a significant difference in the therapeutic effect of a drug on men and women, and investigated 10 male users and 7 female users, and scored all indicators comprehensively after taking the drug. The better the effect, the higher the score, and the total score obtained by everyone is shown in Table 2-2. According to the table, the math teacher came in with a pile of test papers.
It seems that the PE teacher caught a cold because of the cold weather in winter.
So it became two math classes, and I tried it by the way.
The math teacher's name is Ou Dao, a very mathematical name, with black eyes all the year round.
Documents were distributed one after another.
As a student, Su Mu had no choice but to take out mathematical reference materials and wanted to try his luck to see if he could find the original question.
"ding! I checked the math topic, and the math score is+1, and now the score is1100, and the score is level 1. "
Suddenly, the voice in his head startled him and almost didn't slide down from the stool.
Yan Xiaoke, a deskmate, held back a smile.
Island mercilessly stared Su Mu one eye.
"? …"
Su Mu stare big eyes, some unbelievable.
"What the hell is this? Is this really a system with such a thing as a system? "
Su Mu continue to turn around, the same voice again.
"ding! You checked the math topic, the math integral is+1, the current integral is 2/ 100, and the score is level 1. "
He just looked at it and actually increased his score?
Su Mu felt his mind clear.
These unfamiliar math problems also look familiar.
He became more and more excited.
These are the changes that really appear in front of his eyes!
Su Mu books faster and faster, integral is more and more, until nakajima came and stood in front of him, to react quickly back.
At this time, his integral has reached 81100.
He didn't panic and continued to check the questions on the test paper.
Finally, the system ushered in a new prompt.
"Ding, your math integral is enough, grade: level 2, and now the integral is 0/ 1000!"
At this moment, Su Mu seemed to wake up, and those unfamiliar math problems seemed to have become friends for many years!
How dare he!
Got it!
Got it! !
I can't believe I get it!
Su Mu heart suddenly deeply touched, feel very bitter and sweet.
As if to test his grades, Su Mu's mind was completely lost in the examination paper, which was a kind of students' thirst for knowledge.
Time goes by bit by bit, even Su Mu didn't find it.
Unfortunately, although his mathematics has reached the second level, there are still some problems that cannot be solved.
"Ding ..."
This time it's not a system prompt, but a class bell.
Su Mu really felt that time passed so quickly for the first time.
It was a long two hours, and now he still has some unfinished work.
Is this what it feels like to be a schoolmaster? He thought silently.
In this paper, Su Mu thinks he should get 103.
Because he got rid of all unanswerable questions.
And those simple topics, Su Mu has a kind of confidence.
The answer he got must be the right answer!
……
"I want to study hard."
Fighting back the inner excitement, Su Mu straightened up.