How to use the Dawson sheet to plot and test simple slopes?

Dawson’s sheet online (http://www.jeremydawson.co.uk/slopes.htm) can help you to plot and test simple slope figures for multiple regression in a nice way. However, people could get confused about what values to put in the sheet, so I will explain this sheet in more details.

A general idea of materials, tools and products

You could imagine this sheet as a tool. After entering the values (materials) correctly, you don’t need to do anything, the final “product” will pop out automatically because the plugged-in formula will do all the calculation for you. However, to use any tool correctly, it’s helpful to know the following things:

1) why it requires you to provide certain values (materials);

2) how it will use these values to do the work (tools);

3) what work do you want to get done by using it (products).

Apply this general idea here, for the simple slope business, you want 2 final products: 

Product 1: a figure that plot the relations between x (focal predictor/IV) and y (DV) at 2 values of Z (moderator); Product 2: the p values of testing the significance of these 2 simple slopes. Below is a description of how these 2 products are produced.

Product 1: the simple slope figure

The sheet will plot 2 simple slopes of Y regressed on X according to this formula Y = b0 + b1X + b2Z + b3XZ = (b0 + b2Z) + (b1+b3Z)X. Accordingly, the simple slopes would be different when Z have different values.

You need to set the Z values. Z= the ideal Z/moderator values you want to plot. It’s arbitrary. If you have certain values in mind, you could input them in Cell B25 and B26. It’s more certain when Z only have 2 values in reality, such as gender (usually coded as 0 and 1). If you don’t have any value in mind and you leave Cell B25, B26 empty, it will give you Z’s mean plus and minus 1SD of Z for the 2 values of Z. In addition, you need the value range of X (put them in Cell B23, B24), usually it’s the minimum and maximum value of X in your sample. Sometimes, people use the mean plus and minus 1SD for those 2 X values. If you leave B23 and B24 empty, it will set the 2 X values using mean plus and minus 1SD of X.

A few words about setting the values for X and Z in Cell B23-26 if you are uncertain:

1.     Since the final Y value is based on this b0 + b1X + b2Z + b3XZ, it’s better when you center X and Z to compute the interaction term, you also center X and Z when enter them as separate predictors. This consistency will help you get a more accurate intercept b0. Dawson recommend centering other control variables as well. It may not be necessary, but theoretically it leads to a better intercept value to plot these 2 simple slopes.

2.     B17 to B20 is for you to enter the mean and SD of X and Z. It’s useful when you leave B23 to 26 empty, the sheet can still use the mean and SD to set the conditional values for plotting the simple slope. The mean and SD should be based on the values of the form of X and Z you put into the final model. If you put a centered X and Z into the model, then the mean would be 0 for both. In addition, if you center X, the minimum and maximum value for X should also be based on the centered X.

Product 2: p value corresponding to the simple slope test

This sheet will produce 2 semi-finished products for your final product: 1) the regression coefficient for the simple slope, which people may call it “gradient” and 2) SE of that gradient. Gradient/its SE=t value, which is important to get the p value for the significant test.

Gradient can be computed by b₁+ b₃Z (the formula in G36 is doing the work). Why b1+b3Z? As mentioned above, Y = b0 + b1X + b2Z + b3XZ can be transformed into (b0 + b2Z) + (b1+b3Z)X. Therefore, b1+b3Z is the slope gradient.

b₁ = the unstandardized regression coefficient for focal predictor= B10

b₃ = the unstandardized regression coefficient for interaction term = B12

SE_S = SQRT of (s₁₁ + Z²*s₃₃ + 2*Z*s₁₃) according to Equation 3 in Dawson 2014.

s₁₁ = variance of coefficient of IV b₁ = B37

s₃₃ = variance of coefficient of interaction b₃ = B38

s₁₃ = covariance of coefficients of IV and interaction= B39

This is a place where you could get the wrong value, leading the sheet not function. Check the coefficient variance and covariance matrix carefully.

After you have all the correct values filled into cells, t value for Z’s low value condition will be get in G37 by this formula. It’s corresponding to the equation and value explained above.

=G36/SQRT(B37+(IF(B25="",B19-B20,B25))*(IF(B25="",B19-B20,B25))*B38+2*(IF(B25="",B19-B20,B25))*B39)

Note: t value for Z’s high value condition is computed using the same equation b1+b3Z/ SQRT of (s₁₁ + Z²*s₃₃ + 2*Z*s₁₃), but the values will be different because the Z value will be different, which I will just skip writing the excel formula.

The p value of the significance test will be get in G38 by this formula:

G38=2*TDIST(ABS(G37),(B41-B42-4),1).

Ø  This formula contains this function TDIST(x,deg_freedom,tails) which returns the p value for the Student t-distribution where a numeric value (x) is a calculated value of t (=abs(G37) here).

Ø  2 in the formula means 2-tails, the formula could also be written as TDIST(ABS(G37),(B41-B42-4),2). Why 2 tails? Because you are testing whether the slope is significantly different from 0, it could be both positively or negatively different from 0. With 2 possible directions, you have to use 2 tails.

Ø  Degree of freedom = n - k – 1, where n is the sample size =B41, k is the number of predictors in the mode. If you only have 3 key predictors (X/IV/focal predictor, Z/the moderator, and the interaction term XZ), then k=3, and DF= n-4 =B41 -4.  If you have more predictors in addition to those 3 key predictors, k=3+ B42 (the number of control variables without counting the 3 key predictors), DF = n-k-1=B41-(B42+3)-1= B41-B42-4. If you are still confused about what to put in B42, just count the predictors in the final model, and then minus 3.