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Nov 1, 2018 2:30 AM
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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.

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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.

Learn it once, use it forever!

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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.

Learn it once, use it forever!

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Re: How to compare significance of different between 2 linear lines

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.

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.

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Re: How to compare significance of different between 2 linear lines

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.

Learn it once, use it forever!

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