# Should i use ancova or anova? One continuous variable and one categorical variable.

#### kelvarnsen

##### New Member
I have one dependent variable that is continuous. It is the score on a particular achievement test. I have two independent variables. One categorical (three levels of ability) and one continuous variable (motivation) that is based on 6 likert items (ranges from 0 to 42).

I want to find out more about both how each of the independent variables is related to the dependent variable, but also how the two independent variables interact. If for instance motivation is more of a factor in one ability group than the others.
Should I do a ancova analysis with the continuous variable as a covariate or rather a two-way anova and group the continuous variable into categories (highly motivated, average motivated etc)?

What are the advantages of ancova vs anova and vice versa in this case?

#### noetsi

##### Fortran must die
Re: Should i use ancova or anova? One continuous variable and one categorical variabl

Generally you never want to make a continuous variable a categorical one unless you have to. Continuous and categorical IV together are done all the time.

You need to specify interaction terms between your categorical and continuous IV. You apparently want to know this anyhow, but in any case an assumption of ANCOVA is there is no interaction (although a broadly similar method called ATI can be used if there is interaction).

#### kelvarnsen

##### New Member
Re: Should i use ancova or anova? One continuous variable and one categorical variabl

Ok, so I'll just stick with one continuous and one categorical IV.

But what should i do then? With one categorical IV and one continuous IV and i want to know both how each of the IV's are related to the DV AND how the two IV's interact (because i suspect they do). If I had two categorical IV's i could use anova and plot the interaction. What do i do with one categorical IV and one continuous IV?

What do you mean by "specify interaction terms between your..."?

#### Dason

Re: Should i use ancova or anova? One continuous variable and one categorical variabl

What software are you doing? It's easy enough to fit interactions between continuous and categorical variables in most software.

#### kelvarnsen

##### New Member
Re: Should i use ancova or anova? One continuous variable and one categorical variabl

I'm using spss.

#### noetsi

##### Fortran must die
Re: Should i use ancova or anova? One continuous variable and one categorical variabl

You specify an interaction term by multiplying the categorical variable level by the level of the continuous IV. I have forgotten whether ANCOVA creates dummy variables (sometimes called design variables) but I will assume they do as regression does. Then you will have two dummy variables for ability (the third level will reflected in the intercept). So you would have dummy1 (for one level of ability)*continuous var as one interaction term and dummy2*continousvar as a second interaction term.

If ANOVA allows (I forget) you to just use the categorical variable itself without creating dummies you would just have categoricalvariable*continous variable as a single interaction variable. The * means times. That is you create each interaction term by multiplying one of the categorical variables times the continuous variable.

If the results of the interaction term are signficant then you have interaction. You should plot the relationship of the continuous variable at different levels of the categorical variable to see what form this takes (SPSS will do this in ANOVA if you tell it do in the plots).

#### kelvarnsen

##### New Member
Re: Should i use ancova or anova? One continuous variable and one categorical variabl

If ANOVA allows (I forget) you to just use the categorical variable itself without creating dummies you would just have categoricalvariable*continous variable as a single interaction variable. The * means times. That is you create each interaction term by multiplying one of the categorical variables times the continuous variable.

If the results of the interaction term are signficant then you have interaction. You should plot the relationship of the continuous variable at different levels of the categorical variable to see what form this takes (SPSS will do this in ANOVA if you tell it do in the plots).
think you can just use the categorical variable directly and not dummy variables.

but how do i plot the continuous variable for the different levels of the categorical variable? spss does this if both IV are categorical, but not sure how to do it if one is continuous.

#### noetsi

##### Fortran must die
Re: Should i use ancova or anova? One continuous variable and one categorical variabl

I have never actually seen that done in honesty. I am not sure you can plot it although of course the interaction would exist. As the level changed of the categorical var the slope of the continuous IV would change as well. That is what inteaction is after all the relationship of one IV to the DV changing at different levels of the other IV. But again I am not sure if you can actually plot this.

I would try it in SPSS and see what results.

#### Dason

Re: Should i use ancova or anova? One continuous variable and one categorical variabl

But again I am not sure if you can actually plot this.
Why not? The interaction basically just means that instead of just having different intercepts we also have different slopes for each group. So you could easily plot X vs Y and then just draw the estimated regression lines for each of the groups.

#### noetsi

##### Fortran must die
Re: Should i use ancova or anova? One continuous variable and one categorical variabl

I meant that I was not sure that the SPSS plot in ANOVA would do this.

Wouldn't you plot the continuous IV slope and then see if it changed at different levels of the other categorical var? I guess it would depend on whether you were interested on the interaction effect on the continuous var or on the categorical var.

#### kelvarnsen

##### New Member
Re: Should i use ancova or anova? One continuous variable and one categorical variabl

I meant that I was not sure that the SPSS plot in ANOVA would do this.

Wouldn't you plot the continuous IV slope and then see if it changed at different levels of the other categorical var? I guess it would depend on whether you were interested on the interaction effect on the continuous var or on the categorical var.
i don't think spss does it.

i am primarily interested in seeing the interaction effect on the categorical var.

#### noetsi

##### Fortran must die
Re: Should i use ancova or anova? One continuous variable and one categorical variabl

I think you would plot the mean DV on each level of the categorical variable at different ranges of the continuous variable. Then you would look to see if the distance between the levels of the categorical variable (i.e. the distance between the mean of the DV on each categorical level) changed at different ranges of the continuous variable (ordinal interaction). Or if one level of the categorical variable was higher on the DV than another level of the categorical variable at some ranges of the continuous IV, but lower on others (disordinal). The later is a lot more serious for analysis.

In practice it would be a lot easier to do this with a continuous IV if you had a sense of at what level of the continous variable such changes would occur.

#### kelvarnsen

##### New Member
Re: Should i use ancova or anova? One continuous variable and one categorical variabl

I think you would plot the mean DV on each level of the categorical variable at different ranges of the continuous variable. Then you would look to see if the distance between the levels of the categorical variable (i.e. the distance between the mean of the DV on each categorical level) changed at different ranges of the continuous variable (ordinal interaction). Or if one level of the categorical variable was higher on the DV than another level of the categorical variable at some ranges of the continuous IV, but lower on others (disordinal). The later is a lot more serious for analysis.

In practice it would be a lot easier to do this with a continuous IV if you had a sense of at what level of the continous variable such changes would occur.
i think i get it, but how do i do this in spss?

#### kelvarnsen

##### New Member
Re: Should i use ancova or anova? One continuous variable and one categorical variabl

i guess what i really want to find out, is what effect does the covariate (motivation) have on the relationship between ability (categorical IV) and achievement (continuous DV). I guess ancova is the right answer then?