Regression: What Makes You Think You’re So Smart?

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REGRESSION: WHAT MAKES YOU THINK YOU’RE SO SMART?

What Makes You Think You’re So Smart?

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You must read each slide, and complete any questions on the slide, in sequence.

Welcome

What Makes You Think You’re So Smart?

Authors:

Kelly M. Goedert, Seton Hall University

Susan A. Nolan, Seton Hall University

Kaylise D. Algrim, Seton Hall University

Confidence is a funny thing. Some people seem to carry it naturally, whereas others struggle to find it. But where does confidence come from? And is it earned?

Large group of students writing an exam in the classroom. One of them is trying to cheat.

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A study examined whether certain attitudes about intelligence increased the likelihood that people would be overconfident about their abilities (Ehrlinger, Mitchum, & Dweck, 2016). To determine their attitudes about intelligence, participants rated a series of statements on a scale of 1 (strongly disagree) to 6 (strongly agree). The statements included “You have a certain amount of intelligence, and you can’t really do much to change it” and “You can always substantially change how intelligent you are” (p. 95). Participants who tend to endorse statements like the first one are more likely to believe that intelligence is an innate, unchangeable quality. Participants who tend to endorse statements like the second one are more likely to see intelligence as something that can be changed.

Which group do you think has a stronger tendency to be overconfident about their performance compared with others?

Those who believe intelligence is innate and unchangeable are more likely to be overconfident.

Those who believe intelligence can change are more likely to be overconfident.

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Ehrlinger and her colleagues (2016) hypothesized that individuals who believed that intelligence was an innate, unchangeable quality would be more likely to overestimate how well they performed in comparison to others. The researchers also thought that people who viewed intelligence as changeable would evaluate themselves more accurately.

The study had two phases. In the first phase, participants completed a measure of their theories of intelligence (Dweck, 1999)—the scale from which you saw two statements on the previous screen. Lower scores on this scale indicate the participant believes intelligence is highly stable, whereas higher scores indicate the participant believes intelligence is changeable. Several days later, the researchers put the confidence of participants to the test: Participants took a moderately difficult 10-item test on antonyms. Afterward, they indicated how well they thought they did on the antonyms test relative to other test takers by selecting a percentile score between 0 ( which indicated “worse than all other students”) and 99 (which indicated “better than all others”) (Ehrlinger et al., 2016, p. 96).

The researchers hypothesized that people who view intelligence as mostly stable would be more likely to overestimate their performance than those who view intelligence as changeable.

When testing that hypothesis, what is the predictor variable?

The participants’ scores on the antonyms test

The participants’ scores on the measure of their theories of intelligence

The participants’ estimates of their test performance relative to other test takers

The participants’ actual intelligence

Correct! The participants’ score on the theories of intelligence survey is used to predict overconfidence.

Actually, the participants’ score on the theories of intelligence survey is used to predict overconfidence.

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The researchers hypothesized that people who view intelligence as highly stable will be more likely to overestimate their performance than those who view intelligence as changeable.

When testing that hypothesis, what is the outcome variable?

The participants’ scores on the antonyms test

The participants’ scores on the measure of their theories of intelligence

The participants’ estimates of their test performance relative to other test takers

The participants’ predictions of their scores on the antonyms test

Correct! The outcome variable is the participants’ estimates of their performance relative to others.

Actually, the outcome variable is the participants’ estimates of their performance relative to others.

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The experimenters conducted a regression analysis on the results and made the output from the analysis publicly available on Open Science Framework (osf.io/fm5c2). From this output, we can derive the regression equation shown here. The equation predicts participants’ relative performance estimates (from 0% to 99%) from their scores on the measure of their theories of intelligence, while controlling for their actual scores on the antonyms test. Remember: The theories of intelligence survey includes a series of statements that participants rate on a scale of 1 to 6; average scores on the overall measure range from 1, indicating views of intelligence as highly stable, to 6, indicating views of intelligence as highly changeable.

relative performance estimate = –12.10 (theories of intelligence score) + 0.13 (antonyms test score)

Based on this regression equation, what kind of regression analysis did the researchers perform?

Simple linear regression analysis

Multiple regression analysis

Between-groups regression analysis

Partial regression analysis

Correct! The researchers used two predictor variables, so this is a multiple regression analysis.

Actually, the researchers used two predictor variables, so this is a multiple regression analysis.

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relative performance estimate = –12.10 (theories of intelligence score) + 0.13 (antonyms test score)

What does the regression equation tell us about the relation between scores on the theories of intelligence measure and participants’ estimates of their performance relative to others?

For every 1-point increase in the theories of intelligence score, there is a 12.10-point decrease in participants’ relative performance estimates.

For every 1-point decrease in the theories of intelligence score, there is a 12.10-point decrease in participants’ relative performance estimates.

Participants’ theories of intelligence scores are unrelated to their relative performance estimates.

As participants’ theories of intelligence scores increase, so do their relative performance estimates.

Correct! The negative sign for the slope of the theories of intelligence variable indicates that as theories of intelligence scores go up, relative performance scores tend to go down.

Actually, the negative sign for the slope of the theories of intelligence variable indicates that as theories of intelligence scores go up, relative performance scores tend to go down.

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Recall that the researchers hypothesized that people who view intelligence as highly stable will be more likely to overestimate their performance than will those who view intelligence as changeable. Also, recall that lower scores on the theories of intelligence scale indicate that participants think intelligence is highly stable, whereas higher scores on that scale indicate that participants think intelligence is highly changeable.

relative performance estimate = –12.10 (theories of intelligence score) + 0.13 (antonyms test score)

Were the regression results consistent or inconsistent with the researchers’ hypothesis? (Hint: Use the regression equation to help you answer this question.)

The regression equation indicates that higher theories of intelligence scores are associated with higher scores on the antonyms test, which is consistent with the researchers’ hypothesis.

Using the regression equation alone, it is not possible to tell whether the results were consistent or inconsistent with the researchers’ hypothesis.

The regression equation indicates that participants who view intelligence as highly changeable (i.e., higher scores on the theories of intelligence scale) tend to give higher relative performance estimates, which indicates they tend to be overconfident. This result is inconsistent with the researchers’ hypothesis.

The regression equation indicates that participants with more stable views of intelligence (i.e., lower scores on the theories of intelligence scale) tend to give higher relative performance estimates, which indicates they tend to be overconfident. This result is consistent with the researchers’ hypothesis.

Correct! The researchers’ hypothesis was supported. People with more stable views of intelligence tended to be overconfident in their performance.

Actually, the researchers’ hypothesis was supported. People with more stable views of intelligence tended to be overconfident in their performance.

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Previously, we saw that the regression coefficient (or slope) for the predictor, theories of intelligence score, was –12.10. This slope is the unstandardized (or raw) regression coefficient. The standardized version of this regression coefficient is β = –0.51.

What different information do we get from these two versions of the regression coefficient?

The unstandardized regression coefficient represents the expected slope if the results are not statistically significant, whereas the standardized regression coefficient represents the expected slope when the results are statistically significant.

Both of these regression coefficients provide the same information.

The unstandardized regression coefficient allows us to make precise predictions in terms of the values on the scales used in this study, whereas the standardized regression coefficient is more useful for comparing the strengths among different predictors or across different studies.

The standardized regression coefficient allows us to make precise predictions in terms of the values on the scales used in this study, whereas the unstandardized regression coefficient is more useful for comparing the strengths among different predictors or across different studies.

Correct! Unstandardized coefficients are useful for predicting specific scores, whereas standardized coefficients are useful for making comparisons across predictors and studies.

Actually, unstandardized coefficients are useful for predicting specific scores, whereas standardized coefficients are useful for making comparisons across predictors and studies.

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We previously said that the results of the study supported the researchers’ hypothesis that people who view intelligence as highly stable will be more overconfident in their performance on a test than people who view intelligence as highly changeable.

Which of the following are additional conclusions that can be drawn from this study?

Because the analyses controlled for participants’ actual scores on the antonyms test, we can conclude that having a stable view of intelligence causes overconfidence.

Because the analyses controlled for participants’ actual scores on the antonyms test, we can conclude that being overconfident causes a person to have a stable view of intelligence.

Performing well on tests causes overconfidence.

We cannot draw causal conclusions from a regression analysis.

Correct! Just as with correlation, regression analyses do not tell us about causal relations.

Actually, just as with correlation, regression analyses do not tell us about causal relations.

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The bottom line: It’s great to feel confident about your intelligence, but if you’re sure you’re born with it, think again.

Pessimistic Party Pooper

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REFERENCES

Dweck, C. S. (1999). Self-theories: Their role in motivation, personality, and development. New York, NY: Psychology Press.

Ehrlinger, J., Mitchum, A. L., & Dweck, C. S. (2016). Understanding overconfidence: Theories of intelligence, preferential attention, and distorted self-assessment. Journal of Experimental Social Psychology, 63, 94–100. https://doi.org/10.1016/j.jesp.2015.11.001