TODO: the supplementary sheet is needed to identify the analysis actually conducted. A two-factor factorial design is described, but that alone does not distinguish an independent-groups two-way analysis of variance, a repeated-measures analysis of variance, a mixed design, or a mixed-effects model. The model call, error structure, participant allocation and output headings would establish which analysis was used. In particular, the prose does not establish that every participant experienced every condition.
The two independent variables are social-cue congruence, with congruent and incongruent levels, and cue-to-response delay, with short ( ms) and long ( ms) levels. The response variable is reproduction reaction time, measured in seconds. Thus the known treatment structure is a factorial design, potentially estimating two main effects and their interaction.
TODO: identify the allocation from the missing supplementary sheet or protocol. The eighty recruited participants do not establish whether either factor is within-subjects or between-subjects, whether all observations were retained, or how trials were summarized. The design cannot responsibly be called fully repeated-measures, fully independent-groups or mixed without that information.
TODO: the effect-specific values are unavailable without the supplementary output. Retrieve the rows for congruence, delay and congruence-by-delay interaction, if those terms were fitted. In an appropriate analysis of variance, each F-test compares a term's mean square in ANOVA with its designated error mean square in ANOVA; repeated observations can require different error terms. Neither the factor labels nor the recruited sample size determines those ratios.
TODO: neither the significant effects nor their numerical effect sizes can be determined. Inspect the output's significance results and the definition of its reported effect size. If it supplies partial eta squared, that quantity is ; it is not automatically ordinary eta squared or a fraction of all observed variation. Repeated-measures conventions and the selected error term matter. Report the actual metric and preferably an uncertainty interval; do not manufacture an effect size from the number of participants.
TODO: retrieve both numerator and denominator statistical degrees of freedom for each significant effect from the missing output. The table is also needed to establish which effects, if any, meet the analysis's significance criterion. Participant allocation, exclusions, aggregation and fitted error structure determine the applicable statistical degrees of freedom; the recruitment count is not enough to reconstruct them. No numerical statistical degrees of freedom are asserted here.
TODO: an empirical Results section cannot be completed without the analysis and descriptive output. It must identify the actual factorial design, outcome scale and fitted model; summarize the four condition means with appropriately labeled standard deviations or standard errors; and report the congruence, delay and interaction tests with their actual F-test statistics, statistical degrees of freedom, p-values, effect sizes and relevant confidence intervals.
Interpret an interaction as evidence that the cue-congruence difference varies with delay, not merely as evidence that one separate test was significant and another was not. Any simple-effects analysis must identify its contrasts and multiple testing treatment. If the analysis used transformed reaction times, distinguish the model's scale from raw-second summaries. A nonsignificant result does not establish equality or absence of a theoretically meaningful effect. These are reporting requirements, not placeholders for invented results.
TODO: whether additional analyses are needed depends on the unavailable results and prespecified questions. An estimated congruence-by-delay interaction can be clarified by the cue-congruence contrast at each delay, with confidence intervals and justified multiple testing control. A direct interaction test addresses whether those contrasts differ; comparing their separate significance labels does not.
Even without a significant interaction, an adequately powered, prespecified contrast may address a distinct scientific question; indiscriminate testing until something is significant is not justified. Inspect regression diagnostics and the treatment of dependent trials where appropriate. Without the output, one cannot decide that any particular follow-up is required or conclude that none is necessary.
TODO: the missing condition means and inferential output prevent a conclusion about whether congruent gaze changed reaction time or whether that change depended on delay. The direction, magnitude and uncertainty of those two comparisons are needed before drawing conclusions about attentional guidance in this task.
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