Fundamentals of Mathematics in Medical Research: Theory and Cases

Estimation and Decision Theory

Author(s): Carlos Polanco * .

Pp: 30-44 (15)

DOI: 10.2174/9789815223132124010008

* (Excluding Mailing and Handling)

Abstract

 This chapter covers the basic concepts of inferential statistics and hypothesis testing. The section commences with an explanation of the confidence intervals for the population mean and population standard deviation. Also discussed are the concepts of cut-off, Type I and Type II errors, false positives, and false negatives. We investigate performance metrics including sensitivity, specificity, true positive rate, and true negative rate. In addition, receiver operating characteristic (ROC) curves are introduced and their usefulness in assessing test performance is emphasized. In addition, binomial and normal distribution tests are discussed. This chapter provides a solid foundation for comprehending the principles and practical applications of inferential statistics in decision-making and the interpretation of scientific results. 

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      • 15. middleware::check_user_access:114
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      • 18. vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:183
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      • 16. app/Models/Subject.php:238
      • 17. app/Http/Controllers/ChapterController.php:1434
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      • 14. app/Models/Subject.php:238
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      • 16. app/Models/Subject.php:255
      • 17. app/Http/Controllers/ChapterController.php:1435
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      • 11. app/Models/ContentAccess.php:647
      • 12. app/Http/Controllers/ChapterController.php:1465
      • 13. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 14. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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      400μsalphaeurekaselec_live_10_06_2022ContentAccess.php#647
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      • 11. app/Models/ContentAccess.php:647
      • 12. app/Http/Controllers/ChapterController.php:1478
      • 13. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 14. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1518
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
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      860μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
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      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 3741 and `b`.`banner_from_date` <= 1740514717 and `b`.`banner_to_date` >= 1740514717 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.46msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 3741
      • 3: 1740514717
      • 4: 1740514717
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='28e411db6cdad7ed0b149f10444706ed'
      270μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
        JetFfe8IUa4uEtbkfqRbtPCalmIYUVgcqAi6g9Er
        uc_cart_id
        28e411db6cdad7ed0b149f10444706ed
        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/22837" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /chapter/22837
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:16 [ "x-https" => array:1 [ 0 => "1" ] "host" => array:1 [ 0 => "alpha.eurekaselect.com" ] "priority" => array:1 [ 0 => "u=0, i" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] ]
        request_cookies
        []
        
        response_headers
        0 of 0
        array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Tue, 25 Feb 2025 20:18:37 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6InJuZUFHZVo5cjlqdDJDREpHQTZtOXc9PSIsInZhbHVlIjoiN0tRMVY2Rk1NVzFxS2g3dGhUcWxqVEU2MElXK2VlR2VQeHZDR29ELzI0WHdSRVRTd09VV3JlMFBpRm1wNTUwNEhYRlM0Y0hrcE1ZdHhZY05IVGdQWjI0bU1tK0wwb25uVk1Mak80VVI3Z2txVE93YlNuQVNETHE0NGRvZk1waDUiLCJtYWMiOiIwMGY1ZmU3ZTM5NzdiYzVkNTdmZjI4MjI1OTAwOGQzMDE1ZmJlZGNmNzMxZDkxOGU4MTBkMjM1NjZlMjczMzZjIiwidGFnIjoiIn0%3D; expires=Fri, 28 Feb 2025 08:18:37 GMT; Max-Age=216000; path=/; secure; samesite=laxXSRF-TOKEN=eyJpdiI6InJuZUFHZVo5cjlqdDJDREpHQTZtOXc9PSIsInZhbHVlIjoiN0tRMVY2Rk1NVzFxS2g3dGhUcWxqVEU2MElXK2VlR2VQeHZDR29ELzI0WHdSRVRTd09VV3JlMFBpRm1wNTUwNEhYRlM0Y" 1 => "alphaeurekaselectnet_session=eyJpdiI6IjZDVmltVUJRemxpczlWZUl1clgwOFE9PSIsInZhbHVlIjoiNHVpTTczMXhRRGJFa0lpaHFJcU0wa3lrb2xaYVV6eE5Gc0RleEplOXpkOGFhc1JTSUFaV2h6VjdmWE9GN3Iwa0xHUHRaUmFWYWVsWHdLTzlpOHlaSHEvbWkxazBiNDZzMkFrTWd3U3NyRUV6Z0JOdlQ0UjByNkNIVDRSUUpScjQiLCJtYWMiOiI4ODg5NTU0NDA0Njg5NWZjNGE0YmU3ZDEzYmI0MTFiM2QxMDBiNmY1MWVmNWUwMTFlNWQ2NDNhODYyYmYyOWVjIiwidGFnIjoiIn0%3D; path=/; secure; httponly; samesite=laxalphaeurekaselectnet_session=eyJpdiI6IjZDVmltVUJRemxpczlWZUl1clgwOFE9PSIsInZhbHVlIjoiNHVpTTczMXhRRGJFa0lpaHFJcU0wa3lrb2xaYVV6eE5Gc0RleEplOXpkOGFhc1JTSUFaV2h6Vjd" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6InJuZUFHZVo5cjlqdDJDREpHQTZtOXc9PSIsInZhbHVlIjoiN0tRMVY2Rk1NVzFxS2g3dGhUcWxqVEU2MElXK2VlR2VQeHZDR29ELzI0WHdSRVRTd09VV3JlMFBpRm1wNTUwNEhYRlM0Y0hrcE1ZdHhZY05IVGdQWjI0bU1tK0wwb25uVk1Mak80VVI3Z2txVE93YlNuQVNETHE0NGRvZk1waDUiLCJtYWMiOiIwMGY1ZmU3ZTM5NzdiYzVkNTdmZjI4MjI1OTAwOGQzMDE1ZmJlZGNmNzMxZDkxOGU4MTBkMjM1NjZlMjczMzZjIiwidGFnIjoiIn0%3D; expires=Fri, 28-Feb-2025 08:18:37 GMT; path=/; secureXSRF-TOKEN=eyJpdiI6InJuZUFHZVo5cjlqdDJDREpHQTZtOXc9PSIsInZhbHVlIjoiN0tRMVY2Rk1NVzFxS2g3dGhUcWxqVEU2MElXK2VlR2VQeHZDR29ELzI0WHdSRVRTd09VV3JlMFBpRm1wNTUwNEhYRlM0Y" 1 => "alphaeurekaselectnet_session=eyJpdiI6IjZDVmltVUJRemxpczlWZUl1clgwOFE9PSIsInZhbHVlIjoiNHVpTTczMXhRRGJFa0lpaHFJcU0wa3lrb2xaYVV6eE5Gc0RleEplOXpkOGFhc1JTSUFaV2h6VjdmWE9GN3Iwa0xHUHRaUmFWYWVsWHdLTzlpOHlaSHEvbWkxazBiNDZzMkFrTWd3U3NyRUV6Z0JOdlQ0UjByNkNIVDRSUUpScjQiLCJtYWMiOiI4ODg5NTU0NDA0Njg5NWZjNGE0YmU3ZDEzYmI0MTFiM2QxMDBiNmY1MWVmNWUwMTFlNWQ2NDNhODYyYmYyOWVjIiwidGFnIjoiIn0%3D; path=/; secure; httponlyalphaeurekaselectnet_session=eyJpdiI6IjZDVmltVUJRemxpczlWZUl1clgwOFE9PSIsInZhbHVlIjoiNHVpTTczMXhRRGJFa0lpaHFJcU0wa3lrb2xaYVV6eE5Gc0RleEplOXpkOGFhc1JTSUFaV2h6Vjd" ] ]
        session_attributes
        0 of 0
        array:5 [ "_token" => "JetFfe8IUa4uEtbkfqRbtPCalmIYUVgcqAi6g9Er" "uc_cart_id" => "28e411db6cdad7ed0b149f10444706ed" "_previous" => array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/22837" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]
        ClearShow all
        Date ↕MethodURLData
        #12025-02-25 20:18:37GET/chapter/22837112182