If there's no difference between group means at population level, you'd expect the F-statistic in your sample to be about

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In an analysis of variance (ANOVA), the F-statistic compares the variance between group means to the variance within groups. If there is no difference between population means (the null hypothesis is true), the expected value of the F-statistic is approximately 1 because the between-group variance and the within-group variance are on average the same scale.
Option -1: This is implausible for an F-statistic, since F is defined as a ratio of variances and variances cannot be negative. A negative value would violate the fundamental properties of the statistic.
Option 0: While a value of 0 would indicate no between-group variance, in practice the F-statistic is a ratio and cannot be exactly zero unless the between-group variance is exactly zero, which is extremely unlikely with real data. Moreover, F is nonnegative, but under random sampling and finite sample sizes, the distribution centers around 1 under H0 rather than exactly 0.
Option 1: This aligns with the theoretical expectation under the null hypothesis: the F-statistic should be around 1 when there is no real difference among population means. It reflects equal variance components in the numerator and denominator on average.
Option 2: A value of 2 would suggest more between-group variance relative to within-group variance than expected under the null, indicating possible differences among group means. This would be unlikely if, in reality, there is no population difference.
Thus, considering the properties of the F-statistic under the null hypothesis and its interpretation in ANOVA, the value around which you'd expect the sample F-statistic to center is 1.

PSYC20007_2025_SM2 ANOVA, II

If there's no difference between group means at population level, you'd expect the F-statistic in your sample to be about

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