Three of the 37 documents report the experimental results of both theoretical and practical. For these studies, two independent effect values can be obtained. Therefore, 40 effect values were finally obtained for analysis. Table 2 shows each sample’s effect value.

According to the statistical principle of meta-analysis, only data with good homogeneity can be merged. Therefore, the heterogeneity test needs to be conducted on the results of multiple studies in order to select the appropriate effect model according to the heterogeneity analysis results. When the research heterogeneity is large, the random effect model is used for analysis; when the research heterogeneity is small, the fixed effect model is used for analysis.

The commonly used methods of heterogeneity test are Q test and I2 test. The test level of the Q test is usually set to 0.10, and when p<0.10, there is heterogeneity between studies. The calculation formula of Q statistic is as follows:

In equation (6), i is the effect value of the i-th study (the value of g in this study), I is the average effect value of all studies, and sei is the standard error of the i-th study.

The I2 statistic reflects the proportion of heterogeneity in the total variation of the effect value. The value of I2 is between 0 and 100. The greater the value of I2, the greater the heterogeneity. When 0

In equation (7), Q is the chi-square value of the heterogeneity test, and K is the number of studies included in the meta-analysis14.

Table 3 shows the combined effect values of 37 studies. The sample heterogeneity test results show that Q=162.382, P=0.000<0.10, I2=75.983, indicating that there is a large heterogeneity between samples, so the random effect model should be used For analysis.

From the random effect model in Table 3, it can be seen that the combined effect value of the flipped classroom is 0.373, and it reaches a statistically significant level (P<0.001), which shows that the flipped classroom has a positive positive effect on the learning effect of students. According to the effect size standard proposed by Cohen, when the effect value ES<0.2, it is a small effect; when 0.20.8, it is a large effect18, which can be seen, flipped classroom has a moderate positive impact on improving students’ learning effectiveness.

In order to further explore the impact of flipped classrooms on the learning effect of students in different school stages, we divided the included literature into three groups: university, middle school, and elementary school according to the school stage. The combination and effect value of each class are shown in Table 4. The combined effect value of universities is 0.351, 0.471 for secondary schools and 0.294 for primary schools, and the combined effect values of the three have reached statistically significant levels, of which universities and secondary schools are significant at 0.001 level (P<0.001), and primary schools are at 0.01 level (P<0.01), indicating that the flipped classroom has a moderately positive effect on the learning effect of the students in the three stages, and the effect on the learning effect of the primary school students is slightly weaker. The reason may be that the autonomous learning ability of primary school students is still relatively weak. In the absence of teacher supervision, the consciousness is poor, and the pre-class knowledge cannot be learned well, resulting in less effective internalization of knowledge in the class. From the perspective of the effect between groups, QBET=1.880, p=0.391>0.05, indicating that there is no significant difference in the effect of flipping the classroom on the learning effect of students of different school levels.

Different disciplines have their own disciplinary characteristics. For example, the knowledge points of science courses are clear. Teachers often only need to make clear the use of formulas, the derivation of calculation processes or the experimental procedures and principles. The liberal arts courses involve a wide range of relevant knowledge and often require Teachers use various means to mobilize students’ emotions and cause students to think. Other courses like web design require students to have good aesthetic abilities and innovative abilities to make good works. So is the flipped classroom suitable for all disciplines? Does it have the same impact on different disciplines? In order to solve this problem, this study divides the included literature into science, liberal arts and other three categories. The analysis results are shown in Table 5. The combined effect of science is 0.390, the liberal arts is 0.278, and the other is 0.417. The combined effect of the three reaches statistical significance level, of which the science is significant at 0.001 level (P<0.001), and the liberal arts is at 0.05 level (P< 0.05), others are significant at the 0.01 level (P<0.01), indicating that flipped classroom has a moderate positive impact on different disciplines. QBET=0.694, P=0.707>0.05, indicating that there is no significant difference in the effect of flipped classroom on the learning effect of different subjects. In other words, although different disciplines have their own disciplinary characteristics, the effect of flipped classrooms is similar.

This study also explored the impact of flipped classrooms on the learning effect of different types of knowledge. The analysis results are shown in Table 6. The combined effect value of theoretical knowledge is 0.274, practical knowledge is 0.618, and both theoretical and practical knowledge are significant at the 0.001 level (P<0.001). From the perspective of the effect between groups, QBET=4.821, p=0.028<0.05, indicating that there is a significant difference in the effect of flipped classroom on the learning effect of different types of knowledge. Specifically, flipped classroom has a greater impact on the learning effect of practical operation courses, but has a smaller effect on theoretical courses. Further analysis of the literature reveals that most of the practical courses are works design or experimental exploration. For this kind of relatively operable courses, more time is required to practice the knowledge learned. Traditional teaching methods spend a lot of time on explaining the theory or operation steps of the classroom, leaving students little time for actual operation, resulting in students having no time to practice and obtain feedback, and flipped classroom to put theoretical knowledge and operation steps Before the class, the task-driven teaching model is adopted, and the time in the class is used more for students to practice, solve problems, cooperate and communicate, group mutual evaluation, teacher evaluation, etc. These activities in the class can better help students recognize your own shortcomings, so as to improve in time to improve the learning effect. The theoretical courses involve the explanation of some basic concepts and principles. This knowledge is the basis for learning the follow-up courses. The flipped classroom has little effect on improving the learning effect of the theoretical courses. The reason may be that students do not change their knowledge before class. The basic concepts and principles are well understood, and even deviations occur.

Bias, also known as systematic error, refers to the deviation between the result of research or the inferred value and the true value. In the field of social science research, there is widespread reporting bias. Only when the degree of reporting bias is properly evaluated can its impact on the meta-analysis results be minimized as much as possible. Therefore, evaluating reporting bias is indispensable. Due to the small sample size in this study, a qualitative funnel chart and a quantitative Begg’s test were used to detect publication bias.

The characteristic of the funnel chart is more intuitive. Researchers can judge whether the research results are biased by visual inspection, but there may be differences based on the visual inspection of the researcher alone. The Begg rank correlation method is a method of quantitatively identifying bias using the rank correlation test (Begg’s test for short). The test is also suitable for small sample studies. If Z>1.96, P<0.05, there is bias, if Z<1.96, P> 0.05, there is no bias14.

As can be seen from Figure 1, the points on the funnel chart are basically symmetrically scattered around the combined effect value of 0.373, which initially shows that there is no publication bias. Begg’s test results showed that Z=1.212<1.96, P=0.226>0.05, indicating that there is no publication bias, so the combined effect value obtained in this study is relatively stable.