Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2011 Dec;20(4):235-49.
doi: 10.1002/mpr.352. Epub 2011 Oct 24.

Sample size requirements for the internal validation of psychiatric scales

Alexandra Rouquette  1 , Bruno Falissard
Affiliations

Sample size requirements for the internal validation of psychiatric scales

Alexandra Rouquette et al. Int J Methods Psychiatr Res. 2011 Dec.

Abstract

The ratio of subjects to variables (N/p), as a rule to calculate the sample size required in internal validity studies on measurement scales, has been recommended without any strict theoretical or empirical basis being provided. The purpose of the present study was to develop a tool to determine sample size for these studies in the field of psychiatry. First, a literature review was carried out to identify the distinctive features of psychiatric scales. Then, two simulation methods were developed to generate data according to: (1) the model for factor structure derived from the literature review and (2) a real dataset. This enabled the study of the quality of solutions obtained from principal component analysis or Exploratory Factor Analysis (EFA) on various sample sizes. Lastly, the influence of sample size on the precision of Cronbach's alpha coefficient was examined. The N/p ratio rule is not upheld by this study: short scales do not allow smaller sample size. As a rule of thumb, if one's aim is to reveal the factor structure, a minimum of 300 subjects is generally acceptable but should be increased when the number of factors within the scale is large, when EFA is used and when the number of items is small.

PubMed Disclaimer

Figures

Figure 1
Figure 1
Box‐plot of the percentage of variance accounted for by each factor, according to the factor rank in the scale, in all the references.
Figure 2
Figure 2
Path diagram for the three‐factor simulation model with 10 items.
Figure 3
Figure 3
Mean of the values of the salient loadings after rotation on the 10,000 simulations in relation to sample size. Example of a three‐factor scale.
Figure 4
Figure 4
Mean of the standard deviations of the loadings over the 10,000 samples in relation to sample size in the case of Principal Component Analysis (PCA) or Exploratory Factor Analysis (EFA) followed by a promax rotation for the Beck Depression Inventory (BDI) and the Hamilton Depression Rating Scale (HAMD).
Figure 5
Figure 5
Half‐width of the 95% confidence interval of Cronbach's alpha coefficient for three expected values (α) in relation to the sample size and the number of items.
See this image and copyright information in PMC

References

    1. Adachi N., Onuma T., Nishiwaki S., Murauchi S., Akanuma N., Ishida S., Takei N. (2000) Inter‐ictal and post‐ictal psychoses in frontal lobe epilepsy: A retrospective comparison with psychoses in temporal lobe epilepsy. Seizure, 9 (5), 328–335, DOI: 10.1053/seiz.2000.0413S1059-1311(00)90413-8 [pii] - DOI - PubMed
    1. Aleamoni L.M. (1973) Effects of size of sample on eigenvalues, observed communalities, and factor loadings. Journal of Applied Psychology, 58 (2), 266–269, DOI: 10.1037/h0035429 - DOI
    1. Basker M., Moses P.D., Russell S., Russell P.S. (2007) The psychometric properties of Beck Depression Inventory for adolescent depression in a primary‐care paediatric setting in India. Child and Adolescent Psychiatry and Mental Health, 1 (1), 8–14, DOI: 1753‐2000‐1‐8 [pii]10.1186/1753‐2000‐1‐8 - PMC - PubMed
    1. Beck A.T. (1991) Relationship between the Beck Anxiety Inventory and the Hamilton Anxiety Rating Scale with anxious outpatients. Journal of Anxiety Disorders, 5 (3), 213–223, DOI: 10.1016/0887-6185(91)90002-B - DOI
    1. Beck A.T., Ward C.H., Mendelson M., Mock J., Erbaugh J. (1961) An inventory for measuring depression. Archives of General Psychiatry, 4 (6), 561–571. - PubMed