scholarly journals The Crit coefficient in Mokken scale analysis: a simulation study and an application in quality-of-life research

2021 ◽  
Author(s):  
Daniela R. Crișan ◽  
Jorge N. Tendeiro ◽  
Rob R. Meijer
Keyword(s):  
Sample Size ◽  
False Positive ◽  
General Health Questionnaire ◽  
Small Samples ◽  
Scale Analysis ◽  
Mokken Scale Analysis ◽  
Large Samples ◽  
Quality Of Life Research ◽  
Mokken Scaling ◽  
Assumption Violations

Abstract Purpose In Mokken scaling, the Crit index was proposed and is sometimes used as evidence (or lack thereof) of violations of some common model assumptions. The main goal of our study was twofold: To make the formulation of the Crit index explicit and accessible, and to investigate its distribution under various measurement conditions. Methods We conducted two simulation studies in the context of dichotomously scored item responses. We manipulated the type of assumption violation, the proportion of violating items, sample size, and quality. False positive rates and power to detect assumption violations were our main outcome variables. Furthermore, we used the Crit coefficient in a Mokken scale analysis to a set of responses to the General Health Questionnaire (GHQ-12), a self-administered questionnaire for assessing current mental health. Results We found that the false positive rates of Crit were close to the nominal rate in most conditions, and that power to detect misfit depended on the sample size, type of violation, and number of assumption-violating items. Overall, in small samples Crit lacked the power to detect misfit, and in larger samples power differed considerably depending on the type of violation and proportion of misfitting items. Furthermore, we also found in our empirical example that even in large samples the Crit index may fail to detect assumption violations. Discussion Even in large samples, the Crit coefficient showed limited usefulness for detecting moderate and severe violations of monotonicity. Our findings are relevant to researchers and practitioners who use Mokken scaling for scale and questionnaire construction and revision.

scholarly journals The Crit Value as an Effect Size Measure for Violations of Model Assumptions in Mokken Scale Analysis for Binary Data

2019 ◽  
Author(s):  
Daniela Ramona Crișan ◽  
Jorge Tendeiro ◽  
Rob Meijer
Keyword(s):  
False Positive ◽  
Binary Data ◽  
Simulation Studies ◽  
Mokken Scaling ◽  
Assumption Violations ◽  
Size Measure ◽  
Item Responses ◽  
Size Type ◽  
Nominal Rate ◽  
Questionnaire Construction

In empirical use of Mokken scaling, the Crit index is used as evidence (or lack thereof) of violations of some common model assumptions. The main goal of our study was two-fold: To make the formulation of the Crit index explicit and accessible, and to investigate its distribution under various measurement conditions. We conducted two simulation studies in the context of dichotomously-scored item responses. False positive rates and power to detect assumption violations were considered. We found that the false positive rates of Crit were close to the nominal rate in most conditions, and that power to detect misfit depended on the sample size, type of violation, and number of assumption-violating items. Our findings are relevant to all practitioners who use Mokken scaling for scale and questionnaire construction and revision.

Identifying Problematic Item Characteristics With Small Samples Using Mokken Scale Analysis

2021 ◽  
pp. 001316442110453
Author(s):  
Stefanie A. Wind
Keyword(s):  
Latent Variable ◽  
Item Analysis ◽  
Small Samples ◽  
Scale Analysis ◽  
Mokken Scale Analysis ◽  
Nonparametric Approach ◽  
Level Measurement ◽  
Item Level ◽  
Item Quality ◽  
Item Characteristics

Researchers frequently use Mokken scale analysis (MSA), which is a nonparametric approach to item response theory, when they have relatively small samples of examinees. Researchers have provided some guidance regarding the minimum sample size for applications of MSA under various conditions. However, these studies have not focused on item-level measurement problems, such as violations of monotonicity or invariant item ordering (IIO). Moreover, these studies have focused on problems that occur for a complete sample of examinees. The current study uses a simulation study to consider the sensitivity of MSA item analysis procedures to problematic item characteristics that occur within limited ranges of the latent variable. Results generally support the use of MSA with small samples ( N around 100 examinees) as long as multiple indicators of item quality are considered.

Minimum Sample Size Requirements for Mokken Scale Analysis

2014 ◽  
Vol 74 (5) ◽  
pp. 809-822 ◽  
Author(s):  
J. Hendrik Straat ◽  
L. Andries van der Ark ◽  
Klaas Sijtsma
Keyword(s):  
Sample Size ◽  
Minimum Sample Size ◽  
Scale Analysis ◽  
Mokken Scale Analysis ◽  
Minimum Sample

Growth in Self-Actualization (Personal Orientation Inventory) in Adult Encounter Groups

1981 ◽  
Vol 1 (1) ◽  
pp. 5-8
Author(s):  
Les Beach
Keyword(s):  
Sample Size ◽  
Personal Growth ◽  
Total Sample ◽  
Small Samples ◽  
Total Sample Size ◽  
Personal Orientation Inventory ◽  
Self Actualization ◽  
Personal Orientation

To test the efficacy of the Personal Orientation Inventory in assessing growth in self-actualization in relation to encounter groups and to provide a more powerful measure of such changes, pre- and posttest data from 3 highly comparable encounter groups (N = 43) were combined for analysis. Results indicated that the Personal Orientation Inventory is a sensitive instrument for assessing personal growth in encounter groups and that a larger total sample size provides more significant results than those reported for small samples (e. g., fewer than 15 participants).

The Techniques for Overcoming Depression Questionnaire: Mokken Scale Analysis, Reliability, and Concurrent Validity

2016 ◽  
Vol 85 ◽  
pp. 65 ◽  
Author(s):  
K.E. Freedland ◽  
M. Lemos ◽  
F. Doyle ◽  
B.C. Steinmeyer ◽  
I. Csik ◽  
...  
Keyword(s):  
Concurrent Validity ◽  
Scale Analysis ◽  
Mokken Scale Analysis

scholarly journals W.S. Gosset and Some Neglected Concepts in Experimental Statistics: Guinnessometrics II

2011 ◽  
Vol 6 (2) ◽  
pp. 252-277 ◽  
Author(s):  
Stephen T. Ziliak
Keyword(s):  
Experimental Design ◽  
Sample Size ◽  
Large Scale ◽  
Statistical Significance ◽  
Small Sample ◽  
Small Samples ◽  
Significant Advance ◽  
Economic Approach ◽  
Barley Malt ◽  
Level Of Significance

AbstractStudent's exacting theory of errors, both random and real, marked a significant advance over ambiguous reports of plant life and fermentation asserted by chemists from Priestley and Lavoisier down to Pasteur and Johannsen, working at the Carlsberg Laboratory. One reason seems to be that William Sealy Gosset (1876–1937) aka “Student” – he of Student'st-table and test of statistical significance – rejected artificial rules about sample size, experimental design, and the level of significance, and took instead an economic approach to the logic of decisions made under uncertainty. In his job as Apprentice Brewer, Head Experimental Brewer, and finally Head Brewer of Guinness, Student produced small samples of experimental barley, malt, and hops, seeking guidance for industrial quality control and maximum expected profit at the large scale brewery. In the process Student invented or inspired half of modern statistics. This article draws on original archival evidence, shedding light on several core yet neglected aspects of Student's methods, that is, Guinnessometrics, not discussed by Ronald A. Fisher (1890–1962). The focus is on Student's small sample, economic approach to real error minimization, particularly in field and laboratory experiments he conducted on barley and malt, 1904 to 1937. Balanced designs of experiments, he found, are more efficient than random and have higher power to detect large and real treatment differences in a series of repeated and independent experiments. Student's world-class achievement poses a challenge to every science. Should statistical methods – such as the choice of sample size, experimental design, and level of significance – follow the purpose of the experiment, rather than the other way around? (JEL classification codes: C10, C90, C93, L66)

SMALL SAMPLE SIZE SCIENTIST

PEDIATRICS ◽  
1989 ◽  
Vol 83 (3) ◽  
pp. A72-A72
Author(s):  
Student
Keyword(s):  
Sample Size ◽  
Confidence Intervals ◽  
Causal Explanation ◽  
Small Sample Size ◽  
Small Sample ◽  
Small Samples ◽  
High Expectations ◽  
Sampling Variation ◽  
The Law ◽  
The Stability

The believer in the law of small numbers practices science as follows: 1. He gambles his research hypotheses on small samples without realizing that the odds against him are unreasonably high. He overestimates power. 2. He has undue confidence in early trends (e.g., the data of the first few subjects) and in the stability of observed patterns (e.g., the number and identity of significant results). He overestimates significance. 3. In evaluating replications, his or others', he has unreasonably high expectations about the replicability of significant results. He underestimates the breadth of confidence intervals. 4. He rarely attributes a deviation of results from expectations to sampling variability, because he finds a causal "explanation" for any discrepancy. Thus, he has little opportunity to recognize sampling variation in action. His belief in the law of small numbers, therefore, will forever remain intact.

Sign in / Sign up

Export Citation Format

Share Document