ANCOVA (Analysis of Covariance) can be used to analyze the data by incorporating the pretest scores as a covariate in an experimental research design with a one-group pretest-posttest design. ANCOVA allows for controlling the influence of the pretest scores on the posttest outcome variable, thus providing a more precise estimation of the treatment effect.
Here's how you can use ANCOVA in this context:
Collect data: Obtain pretest and posttest scores from a single group of participants who have undergone an intervention or treatment.
Assess assumptions: Check if the assumptions of ANCOVA are met, including normality of the outcome variable, linearity of the relationship between the covariate (pretest) and the outcome (posttest), homogeneity of regression slopes, and independence of observations.
Conduct ANCOVA: Perform the ANCOVA analysis with the pretest scores as the covariate and the posttest scores as the dependent variable. The treatment or intervention is considered the independent variable.
Interpret results: Examine the significance of the treatment effect (independent variable) after controlling for the pretest scores (covariate). The adjusted posttest means or estimated marginal means can be used to compare the treatment effect.
Report findings: Present the results, including the significance of the treatment effect, adjusted means, standard errors, confidence intervals, and any other relevant statistical information.
ANCOVA helps to account for the pre-existing differences among participants by statistically adjusting for the influence of the pretest scores. This improves the accuracy of estimating the treatment effect and reduces potential confounding factors. However, it's important to note that ANCOVA relies on the assumption of no interaction between the covariate and the treatment and that the relationship between the covariate and the outcome is linear.
As always, consulting with a statistician or utilizing statistical software can help ensure the appropriate application of ANCOVA and accurate interpretation of the results in your specific research context.
For a one-group design, ancova doesn't have much utility. You can, of course, partial out the effect of some third variable (extraneous) from scores of both the pre- and post-test, if doing so is important to addressing the specific research question/s you wish to explore.
My guess is that you'd likely be better off to consider methods such as: (a) dependent t-test or simple repeated measures anova; (b) wilcoxon signed-ranks sum test, depending on what sorts of assumptions you're willing to make about the nature of the scores with which you're working.
You say you have one independent and two dependent variables. Are the dependent variables the pre and the post tests? And what is you independent variable (e.g., randomly allocating people into two conditions, or some naturally occurring variable, like left and right handers). If I am understanding this correctly, then there are several analysis choices including an ANCOVA and a t-tests on the gain scores. The choice of these depends on what the independent variable is (or more specifically, the relation between it and the pre scores). So, more details are necessary to answer this.
You are looking for a repeated measures ANCOVA (a variation on rmANOVA). Completely possible, but there are assumptions and requirements which can sometimes be difficult to meet. You might consider generalized linear models (glm).