15.7 Output group-level stats from dispersion (or variability) weighting

In PRIMER 8, you can now output more detailed statistical information from either dispersion-weighting or variability weighting to a worksheet. You can see this additional option in the comparison of the 'Dispersion Weighting' dialog in PRIMER 8, compared to that in PRIMER 7 (Fig. 15.7).

Fig. 15.7 Comparison of the Pre-treatment > Dispersion Weighting... dialog window in PRIMER 7 (at left) vs PRIMER 8 (at right).

In essence, whenever we calculate the average index of dispersion ($\bar{D}$) for the dispersion weighting pre-treatment, it is drawn from individual indices of dispersion (variance-to-mean ratios, $D_i$) for each of several ($i = 1, \ldots, g$) groups (identified by a factor). It would be helpful, in some situations, to be able to see those original individual indices of dispersion across all of the groups for each variable. The extra tickbox ('$\checkmark$Output group-level worksheet') available in the PRIMER 8 dispersion weighting dialog allows you to produce and examine this underlying statistical information in a worksheet directly.

For example, we can re-visit the data we saw in section 10.4 above, located in the file 'NE_NZ_fish_counts.pri', found in the 'Example_P8' > 'NE_NZ_fish' folder. We can begin by following steps 1, 2 and 3 from section 10.4 on these data; i.e., get the data into PRIMER 8, then:

• Obtain a subset of the data based on the factor of 'Year', from 2010-2015 inclusive (Select > Samples...), with the resulting subset being called 'Data1'.
• Create a combined factor consisting of all combinations of the factors: 'Loc', 'Hab' and 'Year' (Edit > Factors... > Combine...)

Next, we can apply the dispersion weighting pre-treatment on the basis of this combined factor by clicking Pre-treatment > Dispersion Weighting... and in the resulting dialog, choose Factor: Loc-Hab-Year. This time, however, we shall also choose to get ($\checkmark$Stats to worksheet) & ($\checkmark$Output group-level worksheet), then click 'OK'.

This will produce the following three worksheets (assuming 'Data1' contains the subset-selected data):

• 'Data2' contains the dispersion-weighted data.
• 'Data3' contains the statistics associated with the average index of dispersion ($\bar{D}$) for each variable.
• 'Data4' contains the individual indices of dispersion ($D_i$) for each group (columns) and for each variable (rows).

These three data sheets are shown below for the present example.

Note in the above sheet ('Data4', containing individual indices, $D_i$) that there are many missing values. This is simply a consequence of there being zero fish of that species in that particular group of samples; hence, the mean and the variance will both be equal to zero, so no value of $D_i$ can be calculated for that particular cell (or group). Average $\bar{D}$ values for each species are naturally calculated only from those cells (groups of samples) where at least some individuals of that species were recorded (i.e., the non-missing entries).

Finally, note that this '$\checkmark$Output group-level worksheet' option is also available for Pre-treatment > Variability Weighting..., viz.: