Significant factor become non-significant after removing non-significant ones

[#1]

Hey Jmp users, 

When fitting model, after removing non-significant factors, one factor which was significant with a Pvalue 0.048 becomes non-significant. 

I wanted to ask what to do in that case? should we remove it ? 

Thanks!

I 

[#2]

You didn't state what the source of your data is?  Is it from an experiment or from observational data?

A couple of points to keep in mind when developing models to explain the variation in responses:

1. Each coefficient for each term in the model is conditional. Its magnitude, and sometimes the sign, can change.  They depend upon the other variables in the model (and noise).
2. When you remove terms from a model, their cumulative mean squares are pooled in the error term (along with DF's).  This changes the estimate of the mean square error which is the basis for the F-test and subsequent p-values.

Simplifying models requires use of multiple sources of information:

1. Practical significance.  Graphing the results and understanding how much practical significance each factor contributes is ALWAYS more important than statistical significance (which YOU control in how your designed study provide insight into the random variation).  Always ask if the results make sense from a scientific or engineering perspective.

2. R-square, R-square adjusted and most importantly the delta between those.

3. p-values

4. other statistics depending on the source of the data (e.g., for observational data you may want to look for multicollinearity)

[#3]

Completely agree with @statman. Don't rely just on p-values. Combine it with the other information.

[#4]

To reinforce @Dan_Obermiller and @statman 's advice...avoid viewing statistical significance as a binary cliff,,,,either it is or is not significant. Suppose you had a critical p value of 0.05 as so many adopt. Are you willing to say that an effect's p value of 0.051 is NOT significant, and willing adopt significance if it's 0.048? One or two decimal places off in a response could easily make something like this happen.

And what does your graphical analysis of the data suggest? Please tell me you plotted the data six ways from Sunday BEFORE you did any modeling.