Comparing two slopes

I have a dataset structured as follows:

Variable1  Variable2  Variable3  Variable4  Variable5  Variable6  Variable7  Variable8
60         70         75          73        57         69         85         90
55         66         47          79        63         76         82         97


etc.

Each variable represents the detection performance for a certain position and condition. Variables 1 to 4 are meant to represent condition 1, Variables 5 to 8 are meant to represent condition 2. Detection performance for the same locations (but different conditions) are represented by variables 1 & 5, variables 2 & 6, variables 3 & 7, variables 4 & 8.

I now have plotted the detection performance for both conditions as a line chart. What I want to do, is to compare the slope of both curves using SPSS. What would be the best way to accomplish this? I would like to test if one slope is steeper than the other.

Both curves are representing the detection performance of a target at different locations. I have the directional hypothesis, that the slope of the one curve would be flatter than the other. I am aware that there are different slopes within the curve, so what I am looking for is the "overall slope" for each curve. I suppose this could be accomplished by calculating a regression line. However I am not aware about how to do this with my dataset. Usually predictor and predicted variable are positioned in two fields of your SPSS file. But now they are in the same field: the location of the target should predict the detection performance. And variable 1 to x represents the detection performance on location x.

Do I have to split those two pieces of information detection performance and location, or can this problem be solved with the existing structure of my dataset?

This is how the plot looks like:

And I want to test if the curve of one condition is steeper / flatter than the curve of the other condition.

Detection performance for condition 1 (4 possible target locations) is represented by variables 1 to 4. Detection performance for condition 2 (4 possible target locations) is represented by variables 5 to 8.

The explanatory variables would be the position of the target, the response variable would be the detection performance. Both pieces of information are represented by the same field: Variable1 stands for detection performance on position a, Variable2 stands for detection performance on position b, and so on.

My study design is a within subjects design, each participant was tested on both conditions. In the sample data I provided, each row stands for one participant. Each number stands for the average detection performance of the respective participant for the respective condition (condition 1: variable 1 - 4; condition 2: variable 5 - 8) and the respective location (the same location is represented in Variable 1 & 5, Variable 2 & 6, Variable 3 & 7, Variable 4 & 8).

• When you say 'curve' and 'slope', note that curves tend to have more than one slope. Can you be more specific about your model and what you want to test, please? Commented Jun 23, 2013 at 6:35
• I have edited the question. Please see the last paragraph. An no, this is no homework nor assignment.
– Nico
Commented Jun 23, 2013 at 7:34
• So what are you plotting exactly and what are you trying to achieve? For example, what are your explanatory and response variables? Are you trying to understand some treatment effect and if so have treatments been allocated randomly or is this some form of observational study? As it is currently presented, I think it's going to be difficult for others to respond to your questions with useful guidance. Also, apologies, this should have been a comment rather than an answer. Commented Jun 23, 2013 at 8:43
– Nico
Commented Jun 23, 2013 at 9:34
• Your question is still ambiguous on what is explanatory. See your wording: "result in" conditions 1, 2. It sounds as conditions 1, 2 are pre-existing conditions and so which condition you have is explanatory. If that's true, you need to restructure your data so that you have fields for explanatory variables, but I don't use SPSS and have no idea how you would do that. Commented Jun 23, 2013 at 9:46

It isn't clear to me whether my last post was converted into a comment as such I am re-posting as another answer and will follow up when I am back on line. Answer follows:

Am I correct in responding by saying you are interested in determining whether position and condition affects detection performance? If so, I think that considering the slopes is not the correct approach, although I do think it is possible that a linear model may be suitable. While I am still struggling to understand exactly what you are trying to do, I think a MANOVA (multivariate ANOVA) approach may be applicable.

To give you a bit more context, a MANOVA approach would be useful if you were interested in determining if party affiliation (Democrat, Republic etc) and gender have any effect on voters views on issues such as taxes, gun control etc.

• Thanks for your advise. This is what I already have done. I have computed an ANOVA with condition and position as within-subjects factors. This worked quite well, and answered my question if condition and target position influence detection performance. So this did confirm my first hypothesis. But the cause why I am asking here for help, is the verification of my second hypothesis. The second hypothesis assumes that the overall slope of condition 2 would be flatter than the slope of condition 1.
– Nico
Commented Jun 23, 2013 at 12:27
• Is the position of the target a continuous variable or a categorical variable? I am thinking you could regress detection performance on position, condition (as an indicator/dummy variable) and an interaction term. If the interaction term is significant then the slopes are different. Commented Jun 23, 2013 at 12:50
• The position of the target is continuous. Thanks for the advice. I will have a look at it! :-)
– Nico
Commented Jun 23, 2013 at 12:57