Final answer:
In conducting a one-way ANOVA to compare SAT scores across study strategies, equal standard deviations among groups are required. The information suggests there are different standard deviations for the samples, hence, before proceeding, further testing for equal variance must be carried out to ensure the validity of the ANOVA.
Step-by-step explanation:
In the context of conducting an ANOVA test to compare SAT scores amongst different study strategies, it's crucial that the assumption of equal population standard deviations is met. When we say that there are equal standard deviations, we mean that the variability in SAT scores should be roughly the same across all groups being compared. This requirement is necessary because the one-way ANOVA relies on the assumption that the variances within each group are a fair representation of the variances across all groups (homoscedasticity).
From the information provided, it seems that there is an indication of different standard deviations for the samples, which implies that the populations may have differing variances. This would indeed violate the assumption necessary for a one-way ANOVA, which seeks to assess whether any observed differences among group means are greater than would be expected by chance if all group means were actually the same. Therefore, before proceeding with the ANOVA, it is advisable to perform an equal variance test (such as Levene's test or Bartlett's test) to verify whether the variances are statistically similar. If this assumption is not met, the results of the ANOVA might not be valid, and other statistical methods could be considered.