Mostly, without considering the role of other stakeholders/projects/schemes, one project while assessing its impact claims all the changes happened as its impact!
The assessment of impact involves understanding the nature of whatever changes that have been taken place as well as to determine its significance relevance to our life whilst attribution or the contribution is about the impact on their interventions and that directly affects the target group.
It stands to reason that one would want to assess whether, and/or how far, activities have influenced a change (or set of changes): one needs to assess and communicate success but one must also learn to improve in the future. The term "attribution" is used when an outcome can be accurately measured. The formal definition of "attribution" is “the ascription of a causal link between observed (or expected to be observed) changes and a specific intervention” (SIDA 2007). But, the term "contribution" is more loosely defined, and normally refers to "the performance of one of the partners in a collaborative, joint intervention or the contribution to the results of such an intervention that can be attributed to the performance of one or several of the partners individually" (SIDA, 2007).
The design and monitoring (logical) framework for a project (and its theory of change) ought to specify the agents of change. Anyway, several methodologies can be used to assess attribution and contribution to change: they include contribution analysis, participatory learning and action, the most significant change technique, outcome harvesting, process tracing, qualitative comparative analysis, quasi-experimental approaches, and randomized control trials.
Reference
SIDA. (2007). Glossary of key terms in evaluations and results-based management. Published in cooperation with OECD/DAC. Retrieved from https://www.oecd.org/dac/evaluation/dcdndep/39249691.pdf
In the case of project impact assessment, attribution compares with the baseline and also does the statistical analysis whereas a contribution looks after the project contribution (outcomes). In the assessment process, these two go together however, a contribution is a foundation for the attribution.
Impact assessment by comparing the situation with baseline may be a case of overestimation. Off course, contribution is a foundation for the attribution. RCT is the best way to know the pure contribution of project/ technology.