In a correlational study, what do a scatterplot revealing an indistinct 'cloud' of data points and a calculated Pearson's r of -.02 indicate?

In a correlational study, a scatterplot reveals an indistinct 'cloud' of data points, and the calculated Pearson's $$r$$ is a trivial $$-.02$$. These descriptive statistics alone make it clear that the variables are essentially unrelated, even though inferential statistics are still required for the formal research report.

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Before conducting inferential statistics, researchers must thoroughly understand their data at a descriptive level to clearly see 'what happened' in their study. Even though inferential statistics are required for formal reporting, descriptive statistics alone can provide strong preliminary evidence about whether a treatment worked or if variables are unrelated.

Understanding Descriptive Statistics

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KPU Research Methods in Psychology - 4th American Edition

In a study comparing two groups, the treatment group ($$n = 50$$) has a mean score of $$34.32$$ ($$SD = 10.45$$) and the control group ($$n = 50$$) has a mean score of $$21.45$$ ($$SD = 9.22$$), resulting in an extremely strong Cohen's $$d$$ of $$1.31$$. These descriptive statistics alone clearly indicate that the treatment was effective, although inferential statistics (like a $$t$$-test) are still required for a formal research report.

Example of Descriptive Statistics Showing an Effect

Example of Descriptive Statistics Showing No Effect

Inferential statistics are a set of mathematical techniques used by researchers to determine whether a statistical result or relationship observed in a study's sample reflects something that is genuinely true of the broader population.

Inferential Statistics

Before conducting inferential statistics, researchers must thoroughly understand their data at a ____ level to clearly see 'what happened' in their study.

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