The aim of this study is to investigate the levels of parental stress 3 months after (T2) the strict physical distancing government initiated physical distancing protocols related to the COVID-19 pandemic (T1). The study also aims to investigate how predictors measured during the COVID-19 pandemic are associated with parental stress 3 months after when the majority of the protocols are lifted.

Hypothesis/Research Questions H1: There will be a significant decrease in parental stress from T1 to T2. Exploratory: Investigate the difference in level of parental stress across different demographic subgroups.

H2: Higher level in angry at child, relationship quality and anxiety/depression and less reduction from T1 to T2 in angry at child and anxiety/depression will be associated with less reduction in parental stress from T1 to T2, above and beyond gender, age and number of children in household.

This study is part of a 'The Norwegian COVID-19, Mental Health and Adherence project".

Statistical analysis:

Repeated surveys like the present one typically have a lot of drop out and missing data. Therefore, we will use mixed models instead of paired t-tests, repeated measures ANOVAs, and ordinary linear regression to analyze the data. Mixed models use maximum likelihood estimation, which is the state of the art approach to handle missing data (Schafer & Graham, 2002). Especially if data are missing at random, which is likely in our survey, mixed models give more unbiased results than the other analytic methods (O'Connel et al., 2017).

In preliminary analyses, and for the dependent variables (parental stress) the combination of random effects and covariance structure of residuals that gives the best fit for the "empty" model (the model without fixed predictors except the intercept) will be chosen. Akaike's Information Criterion (AIC) will used to compare the fit of different models. Models that give a reduction in AIC greater than 2 will be considered better (Burnham & Anderson, 2004). The program SPSS 25.0 will be used (IBM Corp, 2018).

First, H1 about decrease in parental stress will be tested by using parental stress as dependent variable in a model using time (T1 period = 0, T2 period = 1) as a predictor. Second, demographic group variables will be added as predictors. Third, the initial (T1) levels of angry at child and anxiety/depression will be added, together with the interactions of these constant covariates with time. Relationship quality during the whole pandemic period, measured at T2, is considered a constant and is thus included as predictor. These interactions represent tests of H2 about the covariates predicting change in parental stress. Finally, the T2 angry at child and anxiety/depression as constant covariates will be added, together with the interactions of these constant covariates with time. These interactions represent tests of H2 about the change in the covariates from T1 to T2 predicting change in parental stress from T1 to T2s.

Relationship quality were assessed with three items: 1) From the beginning of the pandemic have you been more or less satisfied with your relationship? 2) I have had several problems in the relationship with my spouse, 3) I have developed a closer relationships to my spouse.

The Patient Health Questionnaire (PHQ-9)3. This measure is routinely used to assess symptoms of depression in accordance with the diagnostic criteria for major depression disorder and consists of nine items where each is scored on a four-point Likert scale.

The Generalized Anxiety Disorder 7 (GAD-7) was used to obtain symptoms of anxiety and worry, encompassing seven items scored on a four-point Likert scale.

Angry at child was measured with a single item Demographics include gender, age, psychiatric diagnosis and number of children in household.

Possible transformations:

All variables will be assessed in their original and validated format as is recommended practice, as long as this is possible with regards to statistical assumptions underlying the pre-defined analyses (i.e., multiple regression). However, if this is not possible with regards to the statistical assumptions behind the analyses, transformation (e.g., square root or log-transformations) may be needed to apply interval-based methods, alternatively the use of non-parametric tests.

Inference criteria Given the large sample size in this study, the investigators pre-define their significance level: p < 0.01 to determine significance.

Sample size:

The sample size at T1 included 2880 participants. For the present study at T2, all participants will be invited to participate in accordance with the study plan. The data collection period will continue for up to three weeks until as many of the participants at baseline have responded.

Missing data:

Maximum likelihood

Exploratory:

Questions addressed in the future paper which is not pre-specified will be defined as exploratory.

Inclusion Criteria:

• Eligible participants are all adults with at least one child, including those of 18 years and above
• Who are currently living in Norway and thus experiencing identical NPIs, and
• Who had provided digital consent to partake in the study.

Exclusion Criteria:

• Children and adolescents (individuals below 18) Adults not residing in Norway during the measurement period

The participants are parents in the general population.