Worksheet 8: Nested ANOVA and REPEATED MEASURES ANOVA 2016 page 2

Worksheet 8: a brief exercise on Nested ANOVA Variance component approach) and Repeated Measures ANOVA. Note that these data are more like real data and may be messy and interpretations may be difficult).

1)  Nested (Variance components modeling) (see map and file ‘Nested – Variance component’)

We are interested in determining the characteristic spatial scale(s) of variance for oak seedling density. This should help identify the processes that are likely to be important to seedling density and identifying the variance associated with different spatial scales should aid in this identification. For example if most of the variance was at the largest spatial scale, there would be a strong indication that regional processes (eg temperature, sunlight, rainfall) were key factors. To do this assessment we set up a nest and spatially scaling design. From largest to smallest the scales are: Region, Location, Site, Transect, Plot. Hence plots are nested in transects, transects in sites, sites in locations and locations in Regions. This design has three replicates within each nest (eg 3 transects in each site). This makes the model more robust (within a variance component model). WE ARE NOT INTERESTED IN P-VALUES. Instead we want simply to determine the spatial scale or scales that contribute most to the variability in the density of seedlings. This is the realm of Nested models.

a)  First check for normality. You know how! I think you will find that the data are distributed as a power function (square root). I have made a variable named Sqr root Seedlings in case you want to use it.

b)  Go to FIT MODEL and enter the terms such that it looks just like the picture below. Start with the most nested term and work your way down. Fr example

  1. Add Transect to the CONSTRUCT MODEL window. Make sure it is highlighted, then click on Site then on NEST. You should have a term that looks like Transect[Site]. Keep adding terms until you get Transect[,Site,Location,Region].
  2. Do the same for Site (shown below) and then Location and Region, which is not nested.
  3. Note that there is no term for Plot, that is because the lowest level of replication (here plot) is always modeled as residual variation.

c)  Now highlight all model terms then click ATTRIBUTES and RANDOM EFFECT.

  1. Why are these random effects???

d)  Run the model and look for the REML VARIANCE COMPONENT ESTIMATES

e)  Now interpret the table – don’t forget the Plot effects – which term models this. Also make a graph to depict this result.

i.  To do this right click in the middle of the REML VARIANCE COMPONENT ESTIMATES table and then on MAKE INTO DATA TABLE. To get the ordering right for the X variables go to the new data table and click Random Effect, COLUMN PROPERTIES,VALUE ORDERING. Now order in a reasonable way.

f)  Come up with some possible mechanisms for variability in seedling density that are consistent with the scales of variation found in the model.

2)  Repeated Measures

a)  (use Repeated measures seedling growth as a function of competition and watering) : In this experiment a researcher was interested in determining the effects of watering and competition on the establishment of oak seedlings. 12 plots were established. Three plots were used as replicates for each of the following treatment combinations: (1) no additional watering, with ambient competition, (2) additional watering, with ambient competition, (3) no additional water, no competition, (4) additional watering, no competition. Measurements were taken 4 times (equal spacing among times). We want to know what the effects are of competition and watering and the degree to which there is a time effect on the results.

  1. Using GLM run a repeated measures analysis (see figure below)
  2. Make sure the data meet the assumptions of the analysis
  3. be careful here, you have 4 dependent variables as the data set is set up. Make sure the PERSON ALITY is MANOVA. You cross COMP$ and WATER$ by putting both in the model effects window. Highlight one of the terms then also highlight the other in the select columns window then push the CROSS button

  1. Hit the RUN button then the CHOOSE REPSONSE button (REPEATED MEASUES) then leave TIME in the Y NAME window and check UNIVARIATE also

  1. You will get two levels of output (BETWEEN SUBJECTS and WITHIN SUBJECTS). Briefly summarize the results. Remember that for the WITHIN SUBJECTS models you only want to look at the F TEST values (these are the multivariate Pillai Trace Values) and the UNIVAR GG EPSILON values (these are the univariate corrected (for Sphericity) values
  2. Now graph the results for the interaction between COMP$ and WATER$. This is a between subject effect so you need to use the average value for the seedlings over time as the dependent variable

  1. Now I would like you to graph the interaction between TIME and COMP$. You need to restructure the dataset to do this. Go to TABLES, STACK and stack the TIME columns so that growth is its own variable and the Time is now a labeling variable.


  1. Now using the new dataset create the graph of interest