In this paper, the two-factor analysis of variance is improved and verified.

Analysis and Evaluation on the Examination Results of Mathematics Major of Middle School Teachers

Self-study exam ".

Keywords: two-factor analysis of variance; Interactive effect; meaning

1 Introduction

Two-factor analysis of variance is a statistical analysis method, which can be used to analyze the different level pairs of two factors.

Whether the results have a significant impact and whether there is interaction between them. Generally, two-factor analysis of variance is adopted, and two factors are analyzed first.

The design experiment is carried out by the combination of different levels of factors, and the sample content obtained under each combination is required to be the same. ordinary

The calculation formulas of two-factor ANOVA introduced in the textbook (such as [1] and [2]) are all based on the above situation. Actually, it should be.

When used, the sample contents of the experimental data are sometimes inconsistent. In order to ensure the consistency of sample content, it is often necessary to weigh the data.

New screening, so it is possible to lose some information. More importantly, many data are not from pre-designed experiments.

The sample content of each combination may be different, so the traditional data processing method is no longer suitable for retaining more information.

In this paper, the relevant formulas in the two-factor variance analysis method are improved, so that the data from a wider range of sources can be analyzed and processed, and

Using the improved two-factor analysis of variance, this paper analyzes the examination effect of Yangzhou middle school teachers' self-study examination.

double factor variance analysis

The calculation structure of two-factor variance analysis method is complex and the calculation amount is large. The detailed derivation process can be found in [1] or [2], which is directly given in this paper.

The calculation formula is improved.

There are factor A and factor B. Factor A has R-class A 1, A2,? ，Ar； There are s-level factors b, B 1, B2,? Bachelor's degree. Factors

A and B (I = 1, 2,? ，r j = 1，2，？ S) is set to nij, and the sample is yij 1, yij2,? ,

yijnij .

According to the idea of square sum decomposition, the calculation formula of test statistics is as follows. First, the following symbols are introduced: y =

1

n∈

r

i = 1

∑ s

j = 1

∑

nij

k = 1

yijk，

Yi. . = ∑

s

j = 1

∑

nij

k = 1

yijk，i = 1，2，？ , river

y.j . = *

r

i = 1

∑

nij

k = 1

yijk，j = 1，2，？ , S. where: n = ∑.

r

i = 1

∑ s

j = 1

nij。

The sum of squares of total deviation ST, factor A effect SA, factor B effect SB and interaction effect SA ×B are as follows.

And the calculation of the sum of squares of errors SE can be simplified as follows:

ST =√

r

i = 1

∑ s

j = 1

∑

nij

k = 1

y2

ijk - n？ y2。

SA =√

r

i = 1

y2i

. .

nickel

- n？ Y2, where: ni = ∑.

s

j = 1

nij。

SB =√

s

j = 1

y2。

j.

New Jersy

- n？ Y2, where nj = ∑.

r

i = 1

nij。

SA×B =√

r

i = 1

∑ s

j = 1

y2

ij。

nij

- n？ y2 - SA - SB。

SE = ST - SA - SB - SA ×B。

The above results can be summarized as the following ANOVA table:

Table 1 ANOVA table

Variance source square sum degree of freedom mean square and F ratio

Factor A SA r- 1 SA =

Salvation Army (Salvation Army)

r - 1

FA =

Salvation Army (Salvation Army)

southeast

Factor B SB s- 1 SB =

fool

s - 1

FB =

fool

southeast

Interaction sa× b (r-1) (s-1) sa× b =

SA ×B

(r - 1) (s - 1)

FA ×B =

SA ×B

southeast

Error standard error =

southeast

n - rs

Sum ST n- 1

At the significant level α, if FA

E Fα(r- 1, n-rs), think that factor A has a significant impact on the results, otherwise think that factor A.

The influence on the results is not significant; If FB

E Fα( s- 1, n-rs), think that factor B has a significant impact on the results, otherwise think that factor B.

The influence on the results is not significant; If FA ×B

E f α ((r- 1) (s- 1), n-RS), it is considered that the interaction between factor A and factor B is significant.

Otherwise, the interaction between these two factors is not significant.

Three application examples

When evaluating the effect of teachers' self-study examination, besides considering the quality, foundation, effort and other factors of participants, others

An important factor that can't be ignored is the time to take the self-study exam. The open course of teachers' self-study exam is carried out in a rolling cycle.

It breaks the law of gradual progress in regular learning. The learning order of each class in each grade is different, which is very important for learning.

The effect is bound to have a certain impact. This influence should be more significant for candidates majoring in mathematics, because the courses of mathematics major

The logic and cohesion between them are very strong. Considering this reason, this paper uses two-factor variance score to score the test scores of mathematics majors.

Analytical methods are used for evaluation and analysis. However, because the number of people taking the exam in each class is different in each grade, it is suitable for use.

In this paper, an improved two-factor analysis of variance is given.

Self-taught examination for middle school teachers, the first course of Kloc-0/2 in three grades (Grade 94, Grade 96 and Grade 97) of mathematics.

Two-way ANOVA was performed on a test score. Taking grades as factor A and courses as factor B, therefore, factor A has three waters.

Flat, factor B has 12 level. Namely: r = 3, s = 12.

79

In order to save space and omit the original data and complicated calculation process, the following variance analysis table is calculated according to the formula given above:

Table 2 Variance Analysis Table

Significance of mean square deviation and f ratio of square sum of degrees of freedom of variance source

The factor a116221825811093514226 3.

Factor b128631121693174711281533.

Interactive 571151822596117151825433 3

Error 402904 2456 164 105.

Total 600273 12 249 1

At the significance level α= 0. 0 1，FA = 35。 4226 >: F0。 0 1 (2 ,2456) = 4.62, which shows that factor a has a significant influence on the results, that is, it is different.

There are significant differences in test scores among different grades. It can be considered that it broke the normal learning order and had a great influence on the learning effect.

FB = 7 1。 28 15 & gt； F0.0 1 ( 1 1，2456) = 2。 26, which shows that factor B has a more significant impact on the results, that is, the test scores of different courses.

There are significant differences in performance. This is caused by the difficulty of each course, and the influence of the course is greater than that of the grade.

The ring. FA ×B = 15。 8254 > F0.01(22,2456) =1.84, which shows that there is a significant interaction between factor A and factor B, that is, grade and curriculum.

There is a great influence between them.

In fact, among the three grades, only 94 students study in the normal learning order. Are there four basic courses in Grade 96?

Take the self-study exam on the basis of study. Grade 97, on the other hand, began to take the self-study exam from the last class. The following are ten in three grades.

Average score of two courses and total average score of each grade:

Table 3 Average scores of courses in different grades

grade

Course123456789112 total average

Grade 94 75 66 85 765 438+0 68 78 68 76 84 76 64 72 72

Grade 96 64 565 438+0 78 865 438+0 70 78 72 73 85 64 60 60 765 438+0

Grade 97 5140 75 78 62 70 67 68 74 67 43 64 62

Judging from the average test scores and the total average scores of each grade, most courses in grade 94 are the highest scores.

Ok, grade 96 is the second, and grade 97 is the worst; There is no obvious difference between grades 94 and 96, but there are obvious differences between grades 94, 96 and 97.

The above analysis shows that although there are many factors that affect candidates' grades, in the current self-taught examination for middle school teachers, mathematics majors

The order of offering courses breaks the normal learning order and runs counter to the basic law of knowledge renewal, which is an important factor affecting the results of candidates' self-taught exams.

Factors. The current way of offering examination courses has a negative impact on the self-study examination for middle school teachers, which aims at improving the quality of middle school teachers.

Acknowledgement: I am grateful to the Adult Education Office of the Academic Affairs Office of Yangzhou Institute of Education for providing the original data.

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