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My personal experiences have shown me multiple times that by only boosting my confidence in my ability to solve a problem, without gaining any additional knowledge, I was able to solve it!

My question is, has this been studied that to what extent our confidence in our abilities can help us to find a solution for a problem?

If so, can you please provide a link?

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Quick answer:

A brief Google search show cases where this occurred. For example, it seems that a study on medical students showed a significant relationship between confidence and ability after training, although not before training (Clanton et al., 2014). This being said, the Dunning-Kruger effect always comes to mind when such questions come up…

References

Clanton, J., Gardner, A., Cheung, M., Mellert, L., Evancho-Chapman, M., & George, R. L. (2014). The relationship between confidence and competence in the development of surgical skills. Journal of Surgical Education, 71(3), 405–412. http://doi.org/10.1016/j.jsurg.2013.08.009

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I think what you are reffering to is known as self-efficacy.

Perceived self-efficacy is defined as people's beliefs about their capabilities to produce designated levels of performance that exercise influence over events that affect their lives. Self-efficacy beliefs determine how people feel, think, motivate themselves and behave.

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A strong sense of efficacy enhances human accomplishment and personal well-being in many ways. People with high assurance in their capabilities approach difficult tasks as challenges to be mastered rather than as threats to be avoided. Such an efficacious outlook fosters intrinsic interest and deep engrossment in activities. They set themselves challenging goals and maintain strong commitment to them. They heighten and sustain their efforts in the face of failure.

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Most courses of action are initially organized in thought. People's beliefs in their efficacy shape the types of anticipatory scenarios they construct and rehearse. Those who have a high sense of efficacy, visualize success scenarios that provide positive guides and supports for performance. Those who doubt their efficacy, visualize failure scenarios and dwell on the many things that can go wrong. It is difficult to achieve much while fighting self-doubt.

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Perceived self-efficacy to control thought processes is a key factor in regulating thought produced stress and depression. It is not the sheer frequency of disturbing thoughts but the perceived inability to turn them off that is the major source of distress. Both perceived coping self-efficacy and thought control efficacy operate jointly to reduce anxiety and avoidant behavior.

Reference :

Bandura, A. (1994). Self-efficacy. In V. S. Ramachaudran (Ed.), Encyclopedia of human behavior (Vol. 4, pp. 71-81). New York: Academic Press. (Reprinted in H. Friedman [Ed.], Encyclopedia of mental health. San Diego: Academic Press, 1998).

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There are studies that looked explicitly at confidence and performance. There is a well-known relationship between confidence and performance: the less skilled people are, the less calibrated their confidence is (they are less able to estimate whether they are correct or not), and the more overconfident they tend to be. It's sad, it means that the less knowledgeable people don't even realize they are not knowledgeable.

You can also draw conclusions indirectly from the psychosocial literature and for example the well established "stereotype threat" effect. Members of minority groups with a negative stereotype do not perform well when they are explicitly tested on that stereotype (e.g. African Americans on IQ tests, women on math tests, etc). But they perform as well as other groups if they are told the same test is testing something else; and they perform poorly on a tests that actually test something else if they are told it is about their stereotype. You can speculate that negative stereotypes decrease confidence and reduce performance.

There are also more studies you could draw on, for example showing that wrong feedbacks reduce learning rate etc. But at the top of my head, I can't think of a study that tested your precise question (if confidence boosts performance). My understanding of the confidence/decision-making literature is that the answer is no. What matters most is to have a well calibrated confidence (being confident when you are right, and not confident when you are wrong). Being underconfident (e.g. due to a stereotype), harms your performance, but being overconfident too.

Lichtenstein, S., & Fischhoff, B. (1977). Do those who know more also know more about how much they know?. Organizational behavior and human performance, 20(2), 159-183.

Steele, C. M., & Aronson, J. (1995). Stereotype threat and the intellectual test performance of African Americans. Journal of personality and social psychology, 69(5), 797.

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