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Suppose we conducted a study and examined the relationship between Number of Years in School and Number of Offenses Committed. We found the correlation value (r) to be .72, but it was not significant. Despite having such a high value, why might this relationship not be statistically significant?

User LJW
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There are a few possible reasons why a high correlation coefficient could be non-significant:

1. Small sample size. Statistical significance depends on having enough data points to rule out the possibility that the observed relationship is due to chance alone. With a small N, even a strong correlation could be non-significant.

2. Lack of variability. If there is little variability or spread in the X (Years in School) and Y (Offenses Committed) values, the correlation will be weakened, making it harder to detect a real relationship. Not enough variance in the data.

3. Outliers or extreme values. A few very high-leverage or outlying points can distort the correlation and its significance. If removed, the correlation may become significant.

4. Distribution characteristics. Non-normality or non-linearity in the relationship can make it harder to detect significance. Transforming or dummy coding variables may help.

5. Sampling error. There was just an unlucky or unrepresentative sample selected, and a different sample might yield a significant result. More data is needed to reach a firm conclusion.

6. Noise. There are other confounding or intervening variables not accounted for, masking the true relationship. The correlation reflects some unwanted variance, not a "real" effect.

In summary, while a high r value suggests an strong relationship, additional considerations are needed to determine if it is statistically significant or meaningful. The r value alone is not enough. Please let me know if you have any other questions!

User AntoineMoPa
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