[amp_mcq option1=”$$\\frac{{\\left( {1 – {r^2}} \\right)}}{{\\sqrt n }}$$” option2=”$$\\sqrt {\\frac{{\\left( {1 – {r^2}} \\right)}}{{\\left( {n – 2} \\right)}}} $$” option3=”$$0.6745\\left( {\\frac{{1 – {r^2}}}{{\\sqrt n }}} \\right)$$” option4=”$$\\sqrt {\\frac{{\\left( {n – 2} \\right)}}{{\\left( {1 – {r^2}} \\right)}}} $$” correct=”option2″]<\/p>\n
The correct answer is: B. $\\sqrt {\\frac{{\\left( {1 – {r^2}} \\right)}}{{\\left( {n – 2} \\right)}}}$<\/strong><\/p>\n The standard error of the correlation coefficient is a measure of how much the correlation coefficient is likely to vary from sample to sample. It is calculated as follows:<\/p>\n $$\\text{SE}(r) = \\sqrt {\\frac{{\\left( {1 – {r^2}} \\right)}}{{\\left( {n – 2} \\right)}}}$$<\/p>\n where $n$ is the number of pairs of observations.<\/p>\n In this case, there are 25 paired observations, so $n = 25$. Substituting this into the formula, we get:<\/p>\n $$\\text{SE}(r) = \\sqrt {\\frac{{\\left( {1 – {r^2}} \\right)}}{{\\left( {25 – 2} \\right)}}} = \\sqrt {\\frac{{\\left( {1 – {r^2}} \\right)}}{{23}}}$$<\/p>\n The other options are incorrect because they do not include the factor of $\\frac{1}{n-2}$ in the denominator.<\/p>\n","protected":false},"excerpt":{"rendered":" [amp_mcq option1=”$$\\frac{{\\left( {1 – {r^2}} \\right)}}{{\\sqrt n }}$$” option2=”$$\\sqrt {\\frac{{\\left( {1 – {r^2}} \\right)}}{{\\left( {n – 2} \\right)}}} $$” option3=”$$0.6745\\left( {\\frac{{1 – {r^2}}}{{\\sqrt n }}} \\right)$$” option4=”$$\\sqrt {\\frac{{\\left( {n – 2} \\right)}}{{\\left( {1 – {r^2}} \\right)}}} $$” correct=”option2″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[701],"tags":[],"class_list":["post-33770","post","type-post","status-publish","format-standard","hentry","category-business-statistics-and-research-methods","no-featured-image-padding"],"yoast_head":"\n