数据统计 - One Way ANCOVA

• One-way ANCOVA: analysis of covariance
• can be thought of as an extension of the one-way ANOVA to incorporate a covariate.
• used to determine whether there are any significant differences between two or more independent (unrelated) groups on a dependent variable.
• whereas the ANOVA looks for differences in the group means, the ANCOVA looks for differences in adjusted means (i.e., adjusted for the covariate).

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Nine assumptions before one-way ANCOVA

• dependent variable and covariate variable(s) should be measured on a continuous scale (i.e., they are measured at the interval or ratio level)
• independent variable should consist of two or more categorical, independent groups.
• independence of observations, which means that there is no relationship between the observations in each group or between the groups themselves.
• no significant outliers.
• residuals should be approximately normally distributed for each category of the independent variable. You can test for normality using two Shapiro-Wilk tests of normality: one to test the within-group residuals and one to test the overall model fit.
• homogeneity of variances. You can test this assumption in SPSS Statistics using Levene’s test for homogeneity of variances.
• covariate should be linearly related to the dependent variable at each level of the independent variable. You can test this assumption in SPSS Statistics by plotting a grouped scatterplot of the covariate, post-test scores of the dependent variable and independent variable.
• There needs to be homoscedasticity.
• There needs to be homogeneity of regression slopes, which means that there is no interaction between the covariate and the independent variable.

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Test Procedure in SPSS Statistics

• Click Analyze > General Linear Model > Univariate… on the main menu
• Transfer the dependent variable into the Dependent Variable box, the independent variable, into the Fixed Factor(s): box, and the covariate into the Covariate(s): box, by selecting each variable (by clicking on it) and clicking the relevant button.

Reference:
https://statistics.laerd.com/spss-tutorials/ancova-using-spss-statistics.php#procedure