As previously described, Daraja would like to conduct a survey of users of the Mustard Seed food bank from the past three months, in order to understand what foods these users are interested in accessing at the food bank. If Daraja is interested in understanding the country of origin of each student (to understand their food preferences) as well as their frequency of food bank use (to determine regular versus occasional users), Daraja could select a stratified random sample. The country of origin and frequency of food bank use are the strata in this scenario.

Daraja would then:

1. Determine sample size: Decide on the desired sample size from each stratum. It should be proportionate to the size of each group within the population. For instance, if there are more international students than local students, the sample size for international students should reflect that proportion.
2. Ensure representativeness: Ensure that the selected samples from each stratum represent the characteristics and diversity of the entire population. This means the chosen samples should accurately reflect the distribution and variety of preferences among students using the food bank.
3. Random selection: Randomly select individuals from each stratum. For example:
   • For nationality-based strata: Randomly select students from each country group that represents the diversity of the student population.
   • For frequency-based strata: Randomly select students from the regular and occasional user groups

Then Daraja would have a stratified random sample for the survey. What are some of the challenges for Daraja with this approach?

Daraja is interested in understanding the needs of the users of the Mustard Seed food bank, located on the university campus. If, for example, Daraja was interested in categorizing the population based on the student residences on campus, she may want to select a cluster sample. In order to do this, Daraja would:

1. Randomly select clusters: Randomly choose a few clusters several student residences.
2. Survey all individuals in selected clusters: Unlike in stratified sampling where individuals are selected from each stratum, in cluster sampling, all individuals within the chosen clusters are surveyed. Daraja would survey all students residing in the selected dormitories.
3. Ensure representativeness: Ensure that the selected clusters are diverse and representative of the entire population. This means that the chosen clusters should collectively reflect the diversity and characteristics of the entire student population using the food bank.

Cluster sampling can be more practical and cost-effective than other methods, especially when the population is large and dispersed, as it allows for sampling based on naturally occurring groups such as students living in residence.

Daraja is interested in surveying all of the students who used the Mustard Seed Food Bank over the past few months. If Daraja wanted to have a true random sample from this group, she could use systematic random sampling. She would:

1. Determine sample size: Decide on the desired sample size. For instance, if the total number of students who used the food bank is 300 and the desired sample size is 50, then every 6th student (300 divided by 50) from the list will be selected.
2. Random start: Choose a random starting point from the list of students who used the food bank. This can be done by selecting a random number between 1 and the sampling interval (in this case, 6).
3. Select sample: Begin at the random starting point and select every nth individual according to the sampling interval. For example:
   • If the random start is student #3 on the list, Daraja would then select students #3, #9, #15, #21, and so on, until she reaches the desired sample size.

This approach would offer a balance between randomness and ease of implementation. It allows for a representative sample to be drawn without the complexities involved in other methods, ensuring an unbiased selection from the population of students utilizing the food bank.