Exam 12: Bivariate Statistics and Statistical Inference

Correct Answer:

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In social work research, as in many other fields, a p-value of 0.05 or lower is typically considered the threshold for statistical significance. This standard is widely adopted, although it is somewhat arbitrary and other thresholds (like 0.01 or 0.10) can be used depending on the context and the level of confidence a researcher wishes to have in their results.

Given the p-values listed: .75, .50, .03, .21, .13, the one that is considered statistically significant according to typical standards is:

.03

This p-value of 0.03 means that there is a 3% probability that the observed data, or something more extreme, could have occurred under the null hypothesis. In other words, if there truly were no effect or no difference (as the null hypothesis states), there would only be a 3% chance of obtaining the observed results or results that are more extreme purely due to random chance.

A statistically significant result suggests that the researcher can reject the null hypothesis with a reasonable level of confidence, typically 95% confidence when using the 0.05 threshold. In this case, with a p-value of 0.03, the researcher can be 97% confident that the results are not due to random chance, and thus, there is likely a real effect or difference present.

It is important to note that statistical significance does not necessarily imply practical significance or importance. A result can be statistically significant but still be of little practical value if the effect size is very small. Additionally, statistical significance does not confirm causation; it merely suggests that there is evidence to reject the null hypothesis of no effect or no difference.