If your curious, here is a quick and simple sample size calculator that allows the user to just plug in there data (you can test various scenarios etc):
Step 1: Calculating the number of samples required
When developing any sampling strategy (be it waste audits, conducting surveys etc.), the number of samples required will be a function of satisfying statistical validity requirements, and budgetary/resource constraints.
With waste audits in particular, the costs are sufficiently prohibitive that a municipality will never be able to collect the number of samples required to gather a representative sample size (which is normally measured at the 95% confidence interval, +/- 5%).
With this in mind, a proposed approach is to “work in reverse”, where in we estimate the total number of audits the budget allows for, and then allocate those samples to specific housing types/geographic regions. The goal is to “place” these samples in areas that serve as a rough approximation for the municipality as a whole.
Step 2: Allocating the Samples
Once we have determined the number of samples that the budget allows for, the next step is to allocate the samples to account for the following factors:
- Different types of households
- Geographic proximity
- “One Offs/Aberrations”
Step 2a) Accounting for different types of households
The breakdown of single family households in Municipality X is as follows:
- Single-Detached Houses: 78,975 (67.81%)
- Semi-Detached Houses: 20,240 (17.38%)
- Row House: 17,215 (14.78%)
- Other Single Attached Homes: 35 (0.03%)
As such, our samples should be allocated to approximate for the relative contribution of each housing type. Assuming that our budget allows for 20 audits, we would want to sample 14 Single-Detached Households, 3 Semi-Detached Households and 3 Row-Houses. Given that the “Other” housing type constitutes such a small percentage of overall households, there is a rational for omitting it from the data set.
Step 2b) Accounting for Geographic Proximity and Demography
Once we have calculated the number of samples we will take from each housing type, the next step is to sample households from different geographic regions within the city.
For the purposes of simplicity, lets assume that Municipality X can largely be divided into four areas (North, South, East and West).
While there is an initial inclination to simply allocate the number of samples to each area evenly (5 from each area), consideration needs to be given to population density. As an example, if we know that East Municipality X is home to 60% of the population, then we would need to weight it accordingly when allocating samples.
As an illustrative example, lets assume that the population breakdown of Municipality X is as follows:
- East Municipality X: 60%
- North Municipality X: 20%
- South Municipality X: 10%
- West Municipality X: 10%
Therefore, of our 20 samples that the budget allows for, 12 should be conducted in North Municipality X, 4 in North Municipality X, 2 in South Municipality X and 2 in West Municipality X.
The next step is to overlay this data with what we have calculated from Step 2a. The number of samples for each housing type, in each region (accounting for population density) is:
Note that we do not have rounded figures for samples – While the above describes a largely quantitative exercise, selecting areas for audits is also a qualitative judgement as well. These are rough guidelines for how to allocate samples – the project manager has a certain amount of latitude in terms of where they want to conduct audits.
Step 2c) Accounting for One Offs
Extending upon my earlier point surrounding qualitative judgement, there are certain areas of the city that we may want to sample because we know that there is something peculiar about it, i.e. Springdale Single Family homes may actually have 3 families living inside, or areas with a high incidence of illegal basement apartments.
I would recommend that 2 samples be used to target these “One off” areas, to get a better understanding of how these a-typical housing arrangements affect household generation and recovery.
Step 3: Comparing Samples from Previous Audits
Whenever you are comparing audits taken at different times (to assess trends in waste composition etc.) we must follow the “like with like” principle.
The following criteria should be used when comparing audits taken at different times:
- Must be the same housing type
- Must be the same geographic region
- Must be the same season
- Only the relative composition of the waste/recycling streams can be compared
The last point may require some elaboration, in that conventional auditing procedures would compare the weights of materials disposed/recovered. However, if the Bin type (or frequency of collection) has changed, then you can no longer conduct comparisons using weight based metrics. Only the relative contribution of the waste stream can be readily compared.
It is also recommended that an analysis of variance test be conducted on all samples to determine the degree of variability among samples taken from different regions, housing types etc.
This is an important test, in that if we observe a low variation in waste/recyclables composition between study sites, then there is no need to stratify the audit samples moving forward. We operate under the assumption that different housing types/areas produce different quantities and types of waste – this assumption may not be valid. Households in Municipality X may actually have homogenous consumption and disposal habits.