Subtopic: Mean, median, mode and standard deviation
Question Statement:
There is a significant difference between scores from two groups if
Options:
(A) the means are large compared to the standard error
(B) the difference between the means is large compared to the standard error
(C) the means are small compared to the standard error
(D) the difference between the standard deviations is large compared to the means
Official Answer Key:
B
Step-by-Step Solution & Explanation
In a two-sample significance test (t-test), the test statistic is t = (x̄₁−x̄₂)/SE(x̄₁−x̄₂). A large |t| — i.e. the difference of means large relative to its standard error — indicates the difference is unlikely to be due to sampling variation alone, so the groups are judged significantly different. The absolute size of the means (A, C) is irrelevant to significance; only their difference relative to its own uncertainty matters.
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