Two out of the several programs funded by Louisiana Balance of State Continuum of Care (Laboscoc) are Partners in Health and Housing for Baton Rouge and Rapid Re-Housing – Baton Rouge (Laboscoc, 2023). Both programs, in part, help homeless individuals and persons at risk of becoming homeless find shelter and necessary community support (Louisiana Housing Corporation, 2024; Startcorp, 2024). Unpublished records indicate that in the past three years, Partners in Health and Housing for Baton Rouge and Rapid Re-Housing – Baton Rouge have provided support to 101 and 123 such individuals, respectively. A descriptive study seeking to capture the views of individuals who have received housing support from the two programs in the past three years may determine the sample size by applying Krejcie and Morgan’s sample size formula (Royse et al., 2016). The sample size formula takes the form:
s = X2NP(1-P) ÷ {d2(N-1) + [X2P(1-P)]}
Where,
s is the sample size
X2 is the chi-square value for 1 degree of freedom (3.841 applied in this case given that 95% confidence level is assumed)
N is the population size
P is the proportion of the population with a characteristic of interest (0.5 assumed in this case)
d is the acceptable margin of error expressed as a proportion (0.05 assumed in this case)
For the hypothesized study, the population size is 224 and hence the sample size may be determined as follows:
s = 3.841 x 224 x 0.5(1-0.5) ÷ {0.052(224-1) + [3.841 x 0.5(1-0.5)]}
s = 3.841 x 224 x 0.5(1-0.5) ÷ {0.052(224-1) + [3.841 x 0.5(1-0.5)]}
s = 3.841 x 224 x 0.5(0.5) ÷ {0.052(223) + [3.841 x 0.5(0.5)]}
s = 3.841 x 224 x 0.5(0.5) ÷ {0.052(223) + [3.841 x 0.5(0.5)]}
s = 215.096 ÷ {0.5575 + [0.96025]}
s = 215.096 ÷ {1.51775} = 141.72
The appropriate sample size for the study would thus be 142. As would be expected, the computed sample size falls between 132 and 152, which are the sample sizes posted by Royse et al. (2016, p. 223) for population sizes of 200 and 250 respectively (holding all other factors constant).
Sample Size Determination Download file
References
Louisiana Balance of State Continuum of Care (2023). Louisiana Balance of State CoC. Squarespace. https://static1.squarespace.com/static/5ad7424f7c9327973957a9dd/t/65b7f550d2495331c59765d5/1706554704354/CoC-2023-LA_Press.pdf?utm_campaign=Public%20Announcements&utm_source=hs_email&utm_medium=email&_hsenc=p2ANqtz-_Vg3uXPSIbRifGzIZJs84u3LcEA7d7mZVRCz5OYTIVGAM-41FDYtCQnmhn00_1hkxqGKCr
Louisiana Housing Corporation (2024). Programs and Outreach: COC rapid re-housing. Louisiana Housing Corporation. https://www.lhc.la.gov/programs-and-outreach
Royse, D., Thyer, B. A., Padgett, D. K., & Logan, T. K. (2016). Program evaluation: An introduction to an evidence-based approach (6th ed.). Cengage Learning.
Startcorp (2024). Baton Rouge Programs. Startcorp. https://www.startcorp.org/baton-rouge