数据统计 - One Way ANCOVA

2021-11-23

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).

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.

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.

【数据统计 - One Way ANCOVA】Reference:
https://statistics.laerd.com/spss-tutorials/ancova-using-spss-statistics.php#procedure

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