组间和组内比较结果的英文注释

组间和组内比较结果的英文注释
Between-Group and Within-Group Comparisons.
In an analysis of variance (ANOVA), the researcher partitions the variability of a quantitative dependent variable into two sources: between-group and within-group variability.
Between-Group Variability.
Between-group variability refers to the variability in the dependent variable that is due to differences between the groups being compared. This variability is captured by the sum of squares between groups (SSbetween), which is calculated by subtracting the sum of squares within groups (SSwithin) from the total sum of squares (SStotal).
The between-group variability can be further broken down into the variability due to the main effects of each independent variable and the variability due to the
interaction effects between the independent variables.
Within-Group Variability.
Within-group variability refers to the variability in
the dependent variable that is within each group being compared. This variability is captured by the sum of
squares within groups (SSwithin), which is calculated by subtracting the sum of squares between groups (SSbetween) from the total sum of squares (SStotal).
The within-group variability can be further broken down into the variability due to random error and the
variability due to individual differences within each group.
Comparing Between-Group and Within-Group Variability.
The ratio of between-group variability to within-group variability is known as the F-ratio. The F-ratio is used to test the statistical significance of the differences between the groups being compared.
If the F-ratio is statistically significant, then it can be concluded that there is a significant difference in the dependent variable between the groups being compared.
Post-Hoc Tests.
If the overall ANOVA is statistically significant, then post-hoc tests can be used to determine which specific groups are different from each other. Post-hoc tests are multiple comparison procedures that control for the increased risk of Type I error that is associated with making multiple comparisons.
Some of the most common post-hoc tests include:
Tukey's HSD test.
Scheffé's test.
Bonferroni correction.
Assumptions of ANOVA.
The following assumptions must be met in order for ANOVA to be valid:
The dependent variable is normally distributed.
The variances of the dependent variable are equal across all groups.
The groups are independent of each other.
If these assumptions are not met, then the results of the ANOVA may be biased.
Example.
Suppose a researcher wants to compare the mean test scores of three different groups of students. The three groups are:
Group A: Students who studied for the test for 1 hour.
Group B: Students who studied for the test for 2 hours.
Group C: Students who did not study for the test.
The researcher conducts an ANOVA and finds that the F-ratio is statistically significant. This means that there
is a significant difference in the mean test scores of the three groups.
The researcher then conducts post-hoc tests to
determine which specific groups are different from each other. The post-hoc tests show that Group A and Group B
have significantly higher mean test scores than Group C. There is no significant difference in the mean test scores
of Group A and Group B.
Conclusion.
ANOVA is a powerful statistical technique that can be used to compare the means of two or more groups. By understanding the concepts of between-group and within-
group variability, researchers can use ANOVA to gain
insights into the relationships between different variables.。