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168 Journal of Child and Family Studies (2024) 33:166-178
interval-level scales such as blood pressure or height
(Hobart & Cano, 2009; Rasch, 1960; Tennant & Conaghan,
2007; Wilson, 2004; Wright & Stone, 1979). Additionally,
an item-person threshold distribution plotted from the Rasch
analysis is another useful tool. This graph is useful to detect
possible significant ceiling or floor effects (Medvedev &
Krageloh, 2022). Thus, Rasch analysis can be considered
the most advanced statistical methodology to precisely
evaluate the reliability and validity of an ordinal measure, as
well as enhance its precision to approximate an interval-
level scale.
Our Study
Our study used Rasch methodology to evaluate the psy-
chometric properties of the structure and attunement scales
of the BCQ and enhance their precision in assessing par-
enting beliefs about infant care. Our study also generated
conversion tables to transform ordinal structure and attu-
nement scores to approximate interval-level scales.
Table 1 Demographic details of participants for Rasch sample and the
UK and NZ random subsamples including their statistical comparisons
using Chi-square (p-values) for categorical variables and t-tests
(p-values) for continuous variables
Demographic Rasch UK random NZ random pa
details sample sample sample
(n =450) (n =225) (n =225)
Mother age
Mean (SD) 31.11 (5.19) 30.89 (5.45) 31.33 (4.92) 0.37
Child order
First child 284 155 130 0.01
Not first child 164 69 95
Child age
Under 6 182 108 74 <0.01
months old
7 to 12 101 27 74
months old
Over 12 154 77 77
months old
Child gender
Boy 231 119 112 0.51
Girl 215 104 111
aStatistical comparison tests conducted between UK and NZ random
Method subsamples only
Participants
The optimal sample size for Rasch analysis using
RUMM2030 software is between 250 and 500 cases to
minimise both Type I and Type II errors (Hagell & Wes-
tergren, 2016). Hagell and Westergren (2016) suggested if
the sample size is larger than 500 cases, it has been shown
to inflate chi-square statistics leading to Type I error.
Conversely, Type II error is likely if the samples are below
250 cases due to limited information for item calibration.
These mean that sample sizes around n = 250 to n = 500
are effective in balancing the statistical interpretation of
RUMM fit statistics, particularly for minimising Type I and
Type II errors under the assumption of Rasch model fit.
To achieve an optimal sample size for Rasch analyses in
order to investigate scale invariance between countries, we
randomly selected 225 participants from each sample. Our
study, with a sample size of 450 for Rasch analysis, aligns
with this recommendation and is therefore well-positioned
to provide reliable Rasch analysis results using the
RUMM2030 software. Our sample size estimates, while
based on dichotomous scales investigated by Hagell and
Westergren (2016), are applicable to polytomous scales as
the core principles of Rasch analysis and the Chi-square
statistics used in RUMM2030 for assessing model fit are
fundamentally similar across both scale types, focusing on
the relationship between item difficulty and respondent
ability irrespective of the number of response options.
The demographic details of the participants in Rasch
sample and subsamples of each country, and the results of
chi-square and statistical tests comparing differences in
these demographics between subsamples are presented in
Table 1. Some demographics were missing in the Rasch
sample, but they were negligible. These included two
mothers who did not report their child's birth order, 13 who
did not report their child's age, and 4 who did not report
their child's gender. Statistical comparison tests indicated
that there were no significant differences for mother's age or
child gender ratio between the randomly selected UK and
NZ subsamples. However, in the UK subsample, there were
more first-time parents and more parents of younger infants
compared to the NZ subsample.
Figure 1 presents the CONSORT diagram of how par-
ticipants were selected for Rasch analyses from two studies:
one conducted in the United Kingdom (UK) and another in
New Zealand (NZ). A CONSORT diagram was used as a
standardised visual representation that can display the flow
of participants through different samples. It provides a
comprehensive overview of participant enrolment, alloca-
tion, follow-up, and analysis. The UK sample consisted of
656 mothers who were recruited through advertisements on
parenting websites and social media including BabyCentre,
Facebook, and Twitter. UK participants completed a
Qualtrics survey that included brief demographics and the
Baby Care Questionnaire, and they were rewarded with a
_L Springer
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Journal of Child and Family Studies (2024) 33:166-178
