{"id":5378,"date":"2022-08-20T20:04:33","date_gmt":"2022-08-20T20:04:33","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5378"},"modified":"2022-08-20T20:04:33","modified_gmt":"2022-08-20T20:04:33","slug":"11e-preview","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/11e-preview\/","title":{"raw":"11E Preview","rendered":"11E Preview"},"content":{"raw":"In the next in-class activity, you will need to be able to identify statistical significance and practical significance and describe the factors that affect the size of the P-value.\r\n\r\nAs you have seen in previous activities, a one-sample test of proportions tests a claim about a single population proportion, and we have learned to use P-values as evidence to support a claim. This preview assignment will discuss the limitations of the P-value and lead to a discussion of hypothesis test errors in the next activity.\r\n
\r\n

Question 1<\/h3>\r\nSuppose you are studying the proportion of people with lower back pain. In a certain\u00a0 population, 25% of people experience lower back pain. A researcher wants to see if\u00a0 teaching patients how to stretch and exercise will lower incidences of lower back\u00a0 pain.\r\n\r\nShe randomly selects 100,000 people from this population to participate in a study.\u00a0 She teaches the study participants how to stretch and exercise. After two months,\u00a0 she evaluates the participants and finds that 24.75% of the participants experience\u00a0 lower back pain.\r\n
    \r\n \t
  1. Use the DCMP Inference for a Population Proportion tool at\u00a0 https:\/\/dcmathpathways.shinyapps.io\/Inference_prop\/ to calculate the P value for the test.<\/li>\r\n \t
  2. At the 5% significance level, do you reject the null hypothesis? Explain.<\/li>\r\n \t
  3. What is the conclusion, in context?<\/li>\r\n<\/ol>\r\n<\/div>\r\nIf a hypothesis test results in rejecting the null hypothesis because the P-value is less\u00a0 than the significance level, we say we have statistical significance. This means there\u00a0 is enough evidence against the null hypothesis to convince us to reject the null\u00a0 hypothesis.\r\n
    \r\n

    Question 2<\/h3>\r\nIn Question 1, did you show \u201cstatistical significance?\u201d Explain.\r\n\r\n<\/div>\r\nStatistical significance does not necessarily mean the result is interesting or important. If the results are meaningful, we say that the results have practical significance. Having practical significance usually means the results show a significant improvement!\r\n
    \r\n

    Question 3<\/h3>\r\nIn Question 1, did you think you showed \u201cpractical significance?\u201d Explain.\r\n\r\n<\/div>\r\n
    \r\n

    Question 4<\/h3>\r\nSuppose another researcher simultaneously conducted a study, but their study only\u00a0 included 1,200 participants (still a really large study). Similarly, they found that\u00a0 24.75% of participants experienced back pain.\r\n
      \r\n \t
    1. Use the DCMP Inference for a Population Proportion tool at\u00a0 https:\/\/dcmathpathways.shinyapps.io\/Inference_prop\/ to calculate the P value for the test.<\/li>\r\n \t
    2. At the 5% significance level, do you reject the null hypothesis? Explain.<\/li>\r\n \t
    3. What is the conclusion, in context?<\/li>\r\n \t
    4. In this study, did you show \u201cstatistical significance?\u201d Explain.<\/li>\r\n<\/ol>\r\n \r\n\r\n<\/div>\r\n
      \r\n

      Question 5<\/h3>\r\nSummarize the values from the study in Questions 1 and 4 in the following table:\r\n
      \r\n\r\n\r\n\r\n\r\n\r\n
      <\/td>\r\nSample Size<\/td>\r\nSample Proportion<\/td>\r\nP-value<\/td>\r\n<\/tr>\r\n
      Question 1<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
      Question 4<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n
      \r\n

      Question 6<\/h3>\r\nThe sample proportions from both studies are exactly the same, but you came to a\u00a0 different conclusion. What factors contribute to the discrepancy?\r\n\r\n<\/div>\r\n ","rendered":"

      In the next in-class activity, you will need to be able to identify statistical significance and practical significance and describe the factors that affect the size of the P-value.<\/p>\n

      As you have seen in previous activities, a one-sample test of proportions tests a claim about a single population proportion, and we have learned to use P-values as evidence to support a claim. This preview assignment will discuss the limitations of the P-value and lead to a discussion of hypothesis test errors in the next activity.<\/p>\n

      \n

      Question 1<\/h3>\n

      Suppose you are studying the proportion of people with lower back pain. In a certain\u00a0 population, 25% of people experience lower back pain. A researcher wants to see if\u00a0 teaching patients how to stretch and exercise will lower incidences of lower back\u00a0 pain.<\/p>\n

      She randomly selects 100,000 people from this population to participate in a study.\u00a0 She teaches the study participants how to stretch and exercise. After two months,\u00a0 she evaluates the participants and finds that 24.75% of the participants experience\u00a0 lower back pain.<\/p>\n

        \n
      1. Use the DCMP Inference for a Population Proportion tool at\u00a0 https:\/\/dcmathpathways.shinyapps.io\/Inference_prop\/ to calculate the P value for the test.<\/li>\n
      2. At the 5% significance level, do you reject the null hypothesis? Explain.<\/li>\n
      3. What is the conclusion, in context?<\/li>\n<\/ol>\n<\/div>\n

        If a hypothesis test results in rejecting the null hypothesis because the P-value is less\u00a0 than the significance level, we say we have statistical significance. This means there\u00a0 is enough evidence against the null hypothesis to convince us to reject the null\u00a0 hypothesis.<\/p>\n

        \n

        Question 2<\/h3>\n

        In Question 1, did you show \u201cstatistical significance?\u201d Explain.<\/p>\n<\/div>\n

        Statistical significance does not necessarily mean the result is interesting or important. If the results are meaningful, we say that the results have practical significance. Having practical significance usually means the results show a significant improvement!<\/p>\n

        \n

        Question 3<\/h3>\n

        In Question 1, did you think you showed \u201cpractical significance?\u201d Explain.<\/p>\n<\/div>\n

        \n

        Question 4<\/h3>\n

        Suppose another researcher simultaneously conducted a study, but their study only\u00a0 included 1,200 participants (still a really large study). Similarly, they found that\u00a0 24.75% of participants experienced back pain.<\/p>\n

          \n
        1. Use the DCMP Inference for a Population Proportion tool at\u00a0 https:\/\/dcmathpathways.shinyapps.io\/Inference_prop\/ to calculate the P value for the test.<\/li>\n
        2. At the 5% significance level, do you reject the null hypothesis? Explain.<\/li>\n
        3. What is the conclusion, in context?<\/li>\n
        4. In this study, did you show \u201cstatistical significance?\u201d Explain.<\/li>\n<\/ol>\n

           <\/p>\n<\/div>\n

          \n

          Question 5<\/h3>\n

          Summarize the values from the study in Questions 1 and 4 in the following table:<\/p>\n

          \n\n\n\n\n\n
          <\/td>\nSample Size<\/td>\nSample Proportion<\/td>\nP-value<\/td>\n<\/tr>\n
          Question 1<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
          Question 4<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
          \n

          Question 6<\/h3>\n

          The sample proportions from both studies are exactly the same, but you came to a\u00a0 different conclusion. What factors contribute to the discrepancy?<\/p>\n<\/div>\n

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