What is the difference between linear, quadratic and cubic polynomial contrasts (e.g. for increasing levels of a treatment) ? When it is recommended to use the cubic contrast while I have linear and quadratic contrasts ?
This analysis is used to study the effect of diffrent graded doses that must be increased linearly eg. 0,0.5,1,1.5,2,....on the tested parameter. By this analysis you can make an equation to know the most suitable dose of the tested material ( drug, supplement)
The orthogonal polynomial analysis depending on treatment levels. Calculation by number of levels minus 1 (n-1). For example, you have 3 levels of treatmentservice (0, 100, 200 g) the polynomial analysis will be (3-1=2) which is linear(1) and quadratic(2), whereas when you use 4 treatment levels it will be 4-1= 3 levels of polynomial which is linear (1), quadratic(2) and cubic(3). Here is all I can tell....
Dear Mr A. E. Kholif
Polymonial effect was used to determine the shape of the curve that the tested parameters follow in fuction of increasing levels of a treatment (e.g. drog or addtive doses). But, in animal science cubic and quartic effect were not examined because they could not be interpreted.
If the measured values between first and last are in the form of zigzag, you should use cubic. If they are in the form of curve (protuberance or pit), you should quadratic.
Else, use linear.
When you have equal spaced quantitative levels of treatments you can partition the total sums of squares into number of components equal to df of treatment, So if you have a treatment with 2 levels only, the df=1 then you can look at the linear trend only. If you have df=2 then you can look at linear and quadratic trends. In case of df=3, then you can look to linear, quadratic and cubic trends.
Linear trend means that your response factor (y)=a+bX,
Quadratic trend means that y=a+b1X+b2X2
Cubic trend means that y=a+b1X+b2X2+b3X3
Linear trend indicating that each unit increase in your independent variable (level of treatment) (say dose, vitamin, salt …etc.) will increase/decrease the value of y by constant level.
Quadratic trend means that the rate of gain (increase) or loss ( decrease) in y will be fast at the beginning and then decrease
Cubic trend means that the rate of gain (increase) or loss (decrease) in y will be fast at the beginning, then decrease and increased again (See the following figure)
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Finally, you can calculate each b-value using means of treatments and the polynomial coefficients and use it to predict the value of your response factor.
The aforementioned explanations are true. I agree. In addition, Probably, you should do diff firstly using duncan and or tukey.
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