Based on the figure above, what would you expect your statistical test to reveal?

Question

BlackTom AI · Accepted Answer

Crossing lines in a two-way design indicate an interaction: the effect of one factor changes depending on the level of the other factor, even if marginal means are equal.

1) Relevant knowledge points and concepts
- In a two-factor (2x2) ANOVA, a main effect for a factor exists when the marginal means across levels of that factor differ.
- An interaction exists when the difference between levels of one factor depends on the level of the other factor (graphically, nonparallel lines; maximally, lines that cross).
- It is possible to have a strong interaction while the marginal means (and thus main effects) are zero or nonsignificant.

2) Step-by-step reasoning (with explicit numbers)
To make the reasoning concrete, assign plausible cell means that match a crossing-lines figure:
- Therapist A, Diagnosis 1: 8
- Therapist A, Diagnosis 2: 4
- Therapist B, Diagnosis 1: 4
- Therapist B, Diagnosis 2: 8

Compute marginal means:
- Therapist A mean = (8 + 4) / 2 = 6
- Therapist B mean = (4 + 8) / 2 = 6
=> No main effect of therapist (both marginals equal).

- Diagnosis 1 mean = (8 + 4) / 2 = 6
- Diagnosis 2 mean = (4 + 8) / 2 = 6
=> No main effect of diagnosis (marginals equal).

Compute simple effects (differences within levels):
- For Therapist A: Diagnosis1 − Diagnosis2 = 8 − 4 = +4
- For Therapist B: Diagnosis1 − Diagnosis2 = 4 − 8 = −4
These differences differ in sign and magnitude, indicating a clear interaction.

3) Intermediate steps shown above: cell means → marginal means → simple effects → conclusion about interaction.

4) Why the correct answer is correct
The plotted crossing lines imply that the diagnosis effect reverses depending on therapist (simple effects differ), producing a significant interaction term in the ANOVA. Because the positive and negative simple effects cancel when averaged, the marginal means are equal and main effects are absent.

5) Why other options are incorrect
- "No significant main effects or interactions": contradicts the crossing pattern that signals interaction.
- "Main effect of therapist only" / "main effect of diagnosis only" / "main effects of both but no interaction": any of these would show parallel shifts (noncrossing) and unequal marginal means, which is inconsistent with the depicted crossing lines and balanced marginals.

Conclusion: The pattern implies a significant interaction with no main effects; therefore the correct answer is: A significant interaction but no main effects. This matches the provided answer.

Based on the figure above, what would you expect your statistical test to reveal?单项选择题

类似问题

Assuming all relevant assumptions are met, what statistical test would you run to evaluate the extent to which location and person predict the amount of sleep?

Assuming all relevant assumptions are met, what statistical test would you run to evaluate the extent to which diagnosis and therapist predict the amount of improvement?

There is a statistically significant interaction between the cooking time and the presence of oats on the biscuit stability after dunking.

Which ONE of the following thalamic nuclei is targeted by the trigeminothalamic tract?

Which ONE of the following is disinhibited in the direct pathway of the basal ganglia motor loop

30. What is the main purpose of the lecture?

Section FChoose a, b or c as the best answer.29. Which statement is the speaker most likely to agree with?

28. 15-minute neighbourhoods provide residents with inexpensive ____ .

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单