hello this is dr. Gandhi welcome to my video on conducting a two-way and Cova in spss I have here in the SPSS data editor fictitious data and it's set up so that I can perform an ANOVA I have a referral variable and this has two levels voluntary and involuntary a treatment independent variable and this has three levels cognitive behavior therapy psychodynamic therapy and Gestalt therapy and then I have a pretest and these scores would have been collected before the treatment was administered and before we know the referral status before the referral status is determined so we can assume that we have participants and they would know there's a possibility of coming to this treatment program but they would not know the referral status whether it was voluntary or involuntary when the pretest was administered the pretest is going to be the covariant in this example so it would have to be administered before either of the independent variables and then we have the post-test so we can assume that these scores the pretest and the post-test scores are from a psychometric instrument designed to capture some sort of construct related to mental health like depression or anxiety and that a high score indicates more severe symptoms and a lower score less severe symptoms so before I demonstrate the an Cova first I'm going to run a two way ANOVA so I'll include just referral treatment and post-test I cover the assumptions for ANOVA and for Inc of in other videos so here I'll be focusing really just on the analysis although for the antique OVA for the to weigh in Cove I will be demonstrating the homogeneity of regression assumption because the way to test that is a little different for two-way and Cova as opposed to a one-way in Cova so first the ANOVA so go to analyze general linear model and univariate and here we have the univariate dialog and this dialog this general linear model you're very dialog is the same whether you're conducting an ANOVA or Anik Cova so the configuration for ANOVA I'm going to reuse that Frank Ovid and just add the covariant so first we have the dependent variable that's going to be post-test and then we have the fixed factors or the independent variables so one is referral and the other is treatment under plots I'm going to move referral to the horizontal axis and treatment to the separate lines text box and add that continue under post hoc the referral independent variable only has two levels so there's no need for a post hoc test there it won't it won't run treatment has three levels so I'm gonna move that over I'm going to use a two key post hoc test under equal variances assumed and continue I'm not going to make any changes under save it under options and remove referral treatment and referral times treatment over to display means for compare main effects and for the confidence interval adjustment I move this to a bone Froning adjustment descriptive statistics estimates of effect size and observed power I'll add those as well as homogeneity tests under the display frame here continue and okay so this is an ANOVA this is not an an Kovas this will not have the covariate included and if we take a look at the tests of between-subjects effects we can see that for the independent variable referral we do not have a statistically significant finding point 0 6 2 is greater than point zero 5 for treatment the independent variable treatment we do have a statistically significant finding point 0 1 3 and the interaction effect referral times treatment is also statistically significant point 0 3 7 so we're going to want to see how these significance values change the probability values change when we add the pretest in as a covariant so I move back to the data editor in order to run the and Cova I would just need to go to analyze general linear model univariate an add pretest over to the covariant list box however I want to test the assumption of homage a of regression so I'm going to have to make a change under model to test that and then come back and run the and Cova after that so instead of the full factorial here for specify model I'm going to make this custom and again this is just to test the Homa J of regression assumption so you can see we have the independent variable referral independent variable treatment the covariant pretest all in this factors in covariates list box and we want to leave under build term the type set to interaction and I want to have all three possible two-way interactions over here in this model as well as the three-way interaction so using the control key first I'll select referral and treatment move that over then I'll select referral and pretest that over and then treatment and pretest so all possible all the three possible pairwise comparisons I've moved over and then back in factors in Coverity I'll select all three we have a three-way interaction here so referral times treatment pretest times referral pretest times treatment and pretest times referral times treatment again this is custom up here up top click continue and click OK and I'm only really interested in one table that's the tests between subjects of effects and I'm only interested in the combinations I put in to that custom model so referral times treatment looking at here the p-value 0.5 a2 referral times pretest 0.71 9 treatment times pretest 0.35 one and the three-way interaction referral times treatment times pretest 0.36 so we do not have any statistically significant findings for these interactions so we're going to assume that we have met the assumption of how much a of regression moving back to the data editor so before I continue and complete the Ann Cova I do want to mention of course there are other assumptions and I'm not going to test those here we want to make sure that the dependent variable the post-test is normally distributed for every combination of the levels of the independent variables I'll make sure we have how much day of variance no outliers the relationship between the independent variables the dependent variable must be linear and of course how much today of regression and I tested for that so moving over to general linear model under allies general linear model univariant go back to model and move away from custom over here to full factorial click continue and now I'm ready to conduct the an Cova click OK and we can see here in the descriptive statistics that if we look at these different combinations of the levels of the independent variables the one that really seems to stand out is the voluntary level of the independent variable referral and the CBT level of the independent variable treatment the mean there just under 39 quite a bit lower than the other mean values taking a look here at the Levine's test in this table we have a p-value here of 0.25 4 that is not statistically significant so we would assume that we have satisfied the Holmes a of variance assumption moving down to tests between subjects effects we can see that the pretest we have a statistically significant finding therefore pretest that's the covariant we do not have a main effect for referral that's point 1 3 1 so no statistically significant main effect for referral for treatment however we do have a statistically significant main effect Oh point zero zero two and the interaction effect between referral and treatment that's statistically significant as well moving down the output we have estimates here for the referral variable we have the voluntary and involuntary level and these are adjusted for the covariate pretest and moving down to treatment the same thing for estimates these means are adjusted for the pretest for treatment and then we have the pairwise comparisons here and we can see that we have a statistically significant difference between CBT psychodynamic CBT and Gestalt but not between psychodynamic and Gestalt so CBT psychodynamic point zero zero three CBT Gestalt point zero two but psychodynamic min Gestalt that's point one six one not statistically significant and then under profile plots have referral on the x-axis and we have the estimated marginal means on the y-axis and for the different lines CBT is in blue this academic and green and Gestalt in brown and we can see as we move from voluntary to involuntary the CBT mean increases quite a bit Gestalt is about the same and psychodynamic decreases moving from voluntary to involuntary and again this is with us controlling for the pretest partially out the effect of the pretest by using the an Cova so the an Cova allows us to partial out the effect of a covariant I hope you found this video on conducting a two-way and Cove and SPSS to be useful as always if you have any questions or concerns feel free to contact me I'll be happy to assist you