How to compare significance of different between 2 linear lines

[#1]

Hi. I have 2 linear lines plotted, which is an chemical concentration changes (ideal vs actual case) against work duty cycles, and I found 2 linear did not overlay each other. How to use JMP analysis to show both trends has significant difference or not? Thank you.

[#2 · Accepted solution]

You can use what statisticians call analysis of covariance (ANCOVA). Arrange the data so that you have a column for your X, Y, and grouping variable. Select Analyze > Fit Model. Enter the response data column in the Y role. Select the X and grouping data column, click Macros, and select Full Factorial. Now click Run. Examine the Effect Tests table. If the cross term (interaction effect) is not significant, then the slope is the same for both groups. If the grouping term is not significant, then the intercepts are the same for both groups.

[#3]

Hi Mark,

Thanks for your the help again, very appreciate that :)

I analyzed the data using your method and here's the effect test Prob > F
results. I've put up some questions below which I don't understand.

Work duty (<0.0001*) ~ May I know what does it means for this significant
difference?
Case (0.0067*) ~ May I know what does it means for this significant
difference?
Work duty*Case (0.4079) ~ The interaction effect has no significant
difference

Thank you.

[#4]

I analyzed your data this way, too, and got the same results.

The p-value = 0.4 for work duty * case means that the interaction effect is null, so the slope for both cases is the same. You can now remove this term to produce a new model.

The fact that the case term is significant (p-value = 0.007) means that the two cases have a different y-intercept. So the two cases produce parallel trend lines (common slope) that are offset from each other. You add the estimate of case term to the estimate for the intercept to obtain the intercept for a particular case. The intercept is not significantly different fron 0 (p-value = 0.38) so the case estimate is the intercept for each case. The intercept for the actual case is -0.29 and the ideal case is 0.29.

The significant term for work duty, of course, means that the concentration is linearly related to this factor. It is the slope of the line.