c) There is a correlation between students’ levels of anxiety and the number of days they are absent from school (r = 0.53, p = 0.31). Interpret if this result was statistically significant and explain why or why not.
My answer is this: The analysis gives us a correlation result, r = 0.53, with a p value, p = 0.31.
r = 0.53, p = 0.31, provides correlation between “students’ levels of anxiety” and the “number of days they are absent from school.” Using the p value, p = 0.31 to make the determination if this correlation is statistically significant or not, results in that, here p = 0.31, which is greater than p < 0.05, and therefore, we can conclude that r = 0.53 is not statistically significant at p < 0.05.
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Agree.
To interpret whether the correlation result is statistically significant or not, we need to compare the p-value with a predetermined threshold, typically set at 0.05. The p-value represents the probability of obtaining a correlation as extreme as the one observed in the sample, assuming there is no underlying population correlation.
In this case, the p-value is given as 0.31. Since the p-value (0.31) is greater than the threshold (0.05), we can conclude that the correlation between students' levels of anxiety and the number of days they are absent from school (r = 0.53) is not statistically significant at the conventional significance level of p < 0.05.
In other words, the observed correlation of 0.53 could have occurred by chance alone, and there is not enough evidence to confidently conclude that there is a true correlation between anxiety levels and school absenteeism in the population. However, it is important to note that statistical significance does not imply practical or meaningful significance.