See also the following attachment to understand more about how to interpret your results:

1- You have to see your if your treatments are equally spaced (incremented) or not

2- See my code for generating the polynomial contracts values for the not equally spaced treatments.

3- If you found linear and quadratic effects, so your conclusion should be as follows: the results showed highly significant linear and quadratic effects for the x treatment.

Hello Dr Ahmed,

Did you try to use the following sas code to generate the polynomial contrasts values:

Example:

If you have 4 level of feed additives: 0, 0.5, 0.75 and 1 ml/kg DM

proc iml;

x={0 0.5 0.75 1};

xp=orpol(x,3);

print xp;

run; quit;

The contrast values will be as follow:

-0.760639 -0.084515 0.2535463 0.591608 (Linear) 0.4029115 -0.644658 -0.322329 0.5640761 (Quadratic) -0.095346 0.5720776 -0.76277 0.2860388 (Cubic)

So, try first to see the contrast values that you used in Sas code to make sure that your results are correct.

regards

Basim

I think Basim Refat is right.

See if there is a compelling reason to use a quadratic fit based on arguments from physics or chemistry. If not go with the linear if the R-square value of the fit is high enough. Based on mathematical modeling and perhaps solving a differential equation of the situation if it suggests a quadratic type of behavior then go for it. Otherwise a simpler model (ie linear) is always superior to a higher degree polynomial model.

To my kvowing the higher degree is used

If you obtain linear and quadratic at the same time you have to discuss only the quadratic effect only.

See also the following attachment to understand more about how to interpret your results:

1- You have to see your if your treatments are equally spaced (incremented) or not

2- See my code for generating the polynomial contracts values for the not equally spaced treatments.

3- If you found linear and quadratic effects, so your conclusion should be as follows: the results showed highly significant linear and quadratic effects for the x treatment.

Hello Dr Basim Refat

I’m already use the code you have sent to generate polynomial contrasts value, and obtained significant linear and quadratic effects for the same parameter. Moreover, the statistical analysis was performed by Dr. M.L. Galyean and Dr. U.Y. Anele.

You can have significance with both linear and quadratic effects, especially when using orthogonal pol. The linear means you have a trend, the quadratic that the trend is not at constant "speed" (I mean slope). You should include both in a descriptive model if such model is needed, you should use a combination of both for a test.

When polynomial contrasts i anova suggest nonlinear response it may be more informative to use (grouped) regression and appropriate nonlinear function. Quadratic function tends to be an approximation for a more suitable function (may not behave well at the end points)

All it tells you is that the response is NOT linear. For example in statistical Package GENSTAT nonlinear contrasts are used instead of quadratic. Use grouped regression model with suitable nonlinear function

Following on fram what I said before, fit your chosen function to EACH REPLICATE and then analyse meaningful function parameters and/or any derived functions according to the design of your Experiment.

quadratic and linear is explained by the graphic. Usually linear is a solid increase or decrease (Y) without certain point as the effect of supplementation or condition (by level of X). meanwhile quadratic there is a certain point that the supplementation or condition (X) will affect the parameter at the maximum (Y), then the (X) will have no any effects and/or decrease/increase after the maximum certain point.

When linear and quadratic trends are observed it most often implies that as the graded level of or equally spaced treatment (independent variable) increases, the variable under consideration (dependent variable) either increases or decreases, reaches a peak (maximum or minimum variable response to the treatment) at a particular treatment level and later declines or increases as the treatment level further increases. By this, the best (superior) or worst (inferior) treatment level is when the highest or lowest peak is attained before the decline or increase sets in, depending on the nature of the variable under consideration. In general, linear response implies a steady response or trend while quadratic trend implies an unsteady response as the treatment level increases.

Dear Ahmed;

If a homogeneous material is being worked on, there is no problem. These effects should be considered because there is a transfer of effect when regularly increasing doses are investigated.