{"id":1033,"date":"2015-08-17T10:25:50","date_gmt":"2015-08-17T09:25:50","guid":{"rendered":"http:\/\/pcool.dyndns.org:8080\/statsbook\/?page_id=1033"},"modified":"2025-06-24T00:09:38","modified_gmt":"2025-06-23T23:09:38","slug":"questions-statistical-tests","status":"publish","type":"page","link":"https:\/\/pcool.dyndns.org\/index.php\/questions-statistical-tests\/","title":{"rendered":"Questions Statistical Tests"},"content":{"rendered":"\n

The data set smokers.rda<\/a> contains the time to fracture healing (in weeks) of patients who presented with a tibial fracture (variable ‘Time’). Smokers and non-smokers are indicated in the variable ‘Group’ (nominal data<\/a>). <\/p>\n\n\n\n

smokers<\/mark><\/em>\n\u00a0<\/em>\u00a0 Patient\u00a0\u00a0\u00a0\u00a0\u00a0 Group Time<\/em>\n1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0 Smoker\u00a0\u00a0 10<\/em>\n2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0 Smoker\u00a0\u00a0 11<\/em>\n3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3\u00a0\u00a0\u00a0\u00a0 Smoker\u00a0\u00a0 11<\/em>\n4\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4\u00a0\u00a0\u00a0\u00a0 Smoker\u00a0\u00a0 12<\/em>\n5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 5\u00a0\u00a0\u00a0\u00a0 Smoker\u00a0\u00a0 15<\/em>\n6\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 6\u00a0\u00a0\u00a0\u00a0 Smoker\u00a0\u00a0 17<\/em>\n7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 7\u00a0\u00a0\u00a0\u00a0 Smoker\u00a0\u00a0 17<\/em>\n8\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0 Smoker\u00a0\u00a0 18<\/em>\n9\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 9\u00a0\u00a0\u00a0\u00a0 Smoker\u00a0\u00a0 18<\/em>\n10\u00a0\u00a0\u00a0\u00a0\u00a0 10\u00a0\u00a0\u00a0\u00a0 Smoker\u00a0\u00a0 19<\/em>\n11\u00a0\u00a0\u00a0\u00a0\u00a0 11\u00a0\u00a0\u00a0\u00a0 Smoker\u00a0\u00a0 22<\/em>\n12\u00a0\u00a0\u00a0\u00a0\u00a0 12\u00a0\u00a0\u00a0\u00a0 Smoker\u00a0\u00a0 24<\/em>\n13\u00a0\u00a0\u00a0\u00a0\u00a0 13 Non Smoker\u00a0\u00a0 10<\/em>\n14\u00a0\u00a0\u00a0\u00a0\u00a0 14 Non Smoker\u00a0\u00a0 10<\/em>\n15\u00a0\u00a0\u00a0\u00a0\u00a0 15 Non Smoker\u00a0\u00a0 11<\/em>\n16\u00a0\u00a0\u00a0\u00a0\u00a0 16 Non Smoker\u00a0\u00a0 12<\/em>\n17\u00a0\u00a0\u00a0\u00a0\u00a0 17 Non Smoker\u00a0\u00a0 15<\/em>\n18\u00a0\u00a0\u00a0\u00a0\u00a0 18 Non Smoker\u00a0\u00a0 15<\/em>\n19\u00a0\u00a0\u00a0\u00a0\u00a0 19 Non Smoker\u00a0\u00a0 16<\/em>\n20\u00a0     20 Non Smoker   17<\/em><\/mark><\/code><\/pre>\n\n\n\n
    \n
  1. Using the sign test and <=16 weeks as \u2018cut off\u2019 point; is fracture healing significantly delayed in patients who smoke (significant when p < 5%)?<\/li>\n\n\n\n
  2. Using the Chi Square test and the same ‘cut off’ point, is there a statistically significant difference? (significant when p < 5%). The Chi Square distribution table is shown below:<\/li>\n<\/ol>\n\n\n\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t
    Degrees 
    \nof 
    \nFreedom<\/th>    		10%<\/th>5%<\/th>1%<\/th>\n<\/tr>\n<\/thead>\n
    1<\/td>2.71<\/td>3.84<\/td>6.63<\/td>\n<\/tr>\n
    2<\/td>4.61<\/td>5.99<\/td>9.21<\/td>\n<\/tr>\n
    3<\/td>6.25<\/td>7.81<\/td>11.34<\/td>\n<\/tr>\n
    4<\/td>7.78<\/td>9.49<\/td>13.28<\/td>\n<\/tr>\n
    5<\/td>9.24<\/td>11.07<\/td>15.09<\/td>\n<\/tr>\n
    10<\/td>15.99<\/td>18.31<\/td>23.21<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n
      \n
    1. Using the Wilcoxon test, is there a significant difference at p=5%?<\/li>\n\n\n\n
    2. Would it be reasonable to use a t-test?<\/li>\n\n\n\n
    3. Consider the above study as a pilot study for a larger study and estimate the sample size required to show a 10% difference. Assume Normality, a significance level of 5% and a power of 80%.<\/li>\n<\/ol>\n\n\n\n
      The value of radioisotope bone scanning in the diagnosis of multiple myeloma is being evaluated. 50 consecutive patients with suspected multiple myeloma and a high erythrocyte sedimentation rate (ESR) were identified. The ESR was consider high if is was more than 10 mm per hour. All 50 patients had a radioisotope bone scan. Ten patients had a positive bone scan, showing one or more areas of increased uptake of radioisotope. In 36 of the 50 patients the diagnosis of multiple myeloma was made following bone marrow aspiration. Six of these patients had a positive bone scan.<\/p>\n\n\n\n
        \n
      1. Calculate the following performance estimators:\n
          \n
        • True Positives<\/li>\n\n\n\n
        • True Negatives<\/li>\n\n\n\n
        • False Positives<\/li>\n\n\n\n
        • False Negatives<\/li>\n\n\n\n
        • Positive Predictive Value<\/li>\n\n\n\n
        • Negative Predictive Vale<\/li>\n\n\n\n
        • Sensitivity<\/li>\n\n\n\n
        • Specificity<\/li>\n\n\n\n
        • Accuracy<\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • On the basis of these performance estimators, is radioisotope bone scanning useful in making the diagnosis in patients with suspected multiple myeloma?<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"
          The data set smokers.rda contains the time to fracture healing (in weeks) of patients who presented with a tibial fracture (variable ‘Time’). Smokers and non-smokers are indicated in the variable ‘Group’ (nominal data). The value of radioisotope bone scanning in the diagnosis of multiple myeloma is being evaluated. 50 consecutive patients with suspected multiple myeloma […]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-1033","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages\/1033","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/comments?post=1033"}],"version-history":[{"count":17,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages\/1033\/revisions"}],"predecessor-version":[{"id":4347,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages\/1033\/revisions\/4347"}],"wp:attachment":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/media?parent=1033"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}