# Statistical methods

## Sampling

A snowball samplingtechnique was used, based on recruiting the people living in Saudi Arabia duringthe coronavirus early stages of the outbreak. Snowball sampling is generally used in circumstances where participants are hard to find. Because of its nature, it is a non-probability sampling method, and the odds of any particular participant being chosen may not be the same, and hence it could be biased, and it is impossible to determine sampling errors. A power analysis was conducted to calculate at the minimum required sample size to arrive at a statistically significant solution. The power measures the probability of rejecting the null hypothesis when we should thereby reduce the Type-II error (i.e., finding a difference between two groups when there is actually none). For a power of 0.95 (i.e.,α-error- 0.05) and a medium effect size range of 0.5, a minimum of 700 samples is required. The effect size is used to measure if the observed difference (if at all) is meaningful and important even though they are significant.

Data Collection and Survey Aninternal consistency

technique was used to validate the Societal Anxiety Questionnairefor Adults (SAQ-A30) sent for survey using parameters such as todevelop validity, cut-off scores, invariability, and factor structure. The internal consistency test measures the reliability with which the survey is actually measuring what we intended it to measure. The technique involves including at least two questions that measure the same thing and checking if the respondents are answering the same level for all these related questions. A higher internal consistency would mean that the questions are properly worded and clearly articulated to the participants. The questionnaire used had a good internal consistency of 0.91 (Cronbach's α).

Data Analysis

Anindependent t-testwas used to examine the differences found in the mean score of SAQ-A30 between the male and female genderand between the married and unmarried. A t-test was used to compare the mean value of the parameter under consideration from two different samples and test whether the samples are from populations from two different mean values. It is likely that two samples from the same population might have a difference in mean values by chance. The t-test helps in differentiating such differences in mean values due to chance from the actual difference in mean values. Here, between the two groups (male vs. female and married vs. unmarried),the difference in mean anxiety level on either side for any group over the other is to be measured, and hence a two-tailed t-test is used. The significance level in the t-test gives the probability with which the difference found in the mean values could be due to the change in sampling.

Aone-way variance Analysis (ANOVA)look at byScheffe'sposthoc test was also used to examine differences found in the mean score of SAQ-A30 betweendifferent age groups.One-way ANOVA is similar to the t-test but can be used to compare the difference in mean values of a particular variable of interest of more than two groups and is used to determine if the difference in mean of any one group from the others is due to chance or if there is an actual difference. The significance level (F-statistic) gives the probability that the difference could be due to chance. Scheffe'sposthoc test is done after the ANOVA analysis to find out which pairs of means are significant if the ANOVA analysis found a significant F-statistic.

Pearson's correlation coefficient (R) was applied to examine the relationshipbetween anxiety levels of respondents and their age in years. The R-value measures how strong the linear relationship is between two variables, and the sign of the value gives the direction of the relationship. The value ranges from -1 to 1. An R-value close to zero suggests a weak relationship while close to the other extremes of -1 and 1 suggests a strong relationship. The positive value would mean a positive relationship while a negative value means a negative relationship