Receiving Helpdesk

should i use equal or unequal variance

by Rosie Paucek Sr. Published 3 years ago Updated 3 years ago

Shall you use the test for equal or unequal variances? If you have equal numbers of data points, or the numbers are nearly the same, then you should be able to safely use the two-sample test for equal variances
test for equal variances
In statistics, an F-test of equality of variances is a test for the null hypothesis that two normal populations have the same variance.
https://en.wikipedia.org › F-test_of_equality_of_variances
.

Should I use equal or unequal variance t-test?

1. Use the Variance Rule of Thumb. As a rule of thumb, if the ratio of the larger variance to the smaller variance is less than 4 then we can assume the variances are approximately equal and use the Student's t-test.

What is the difference between equal and unequal variance?

The Two-Sample assuming Equal Variances test is used when you know (either through the question or you have analyzed the variance in the data) that the variances are the same. The Two-Sample assuming UNequal Variances test is used when either: You know the variances are not the same.

How do you know when to assume equal variances?

If the variances are relatively equal, that is one sample variance is no larger than twice the size of the other, then you can assume equal variances. By looking at the output of the Levene's test you decide which row to use.

Should variance be equal?

If the variances of two random variables are equal, that means on average, the values it can take, are spread out equally from their respective means.

Why is equal variance important?

It is important because it is a formal requirement for statistical analyses such as ANOVA or the Student's t-test. The unequal variance doesn't have much impact on ANOVA if the data sets have equal sample sizes.

What does it mean to have unequal variance?

Your prime goal is not to ask whether two populations differ, but to quantify how far apart the two means are. The unequal variance t test reports a confidence interval for the difference between two means that is usable even if the standard deviations differ.

How do you compare the variance between two groups?

In order to compare multiple groups at once, we can look at the ANOVA, or Analysis of Variance. Unlike the t-test, it compares the variance within each sample relative to the variance between the samples.

Can variance and standard deviation be equal?

Generally, "the variance is equal to the square of the standard deviation" is widely used as the relationship between the variance and the standard deviation for a sample data set.

How to find variance in a sample?

To calculate variance, start by calculating the mean, or average, of your sample. Then, subtract the mean from each data point, and square the differences. Next, add up all of the squared differences. Finally, divide the sum by n minus 1, where n equals the total number of data points in your sample.

What is the null hypothesis for a variance t test?

For the unequal variance t test, the null hypothesis is that the two population means are the same but the two population variances may differ. The unequal variance t test reports a confidence interval for the difference between two means that is usable even if the standard deviations differ.

Should you use equal or unequal variance?

Should I use equal or unequal variance? Here's the short answer: just use the Unequal Variances column. However, if you know that the population variances are equal, you can use df = n1 + n2 − 2. (Note: population variances, not sample variances.) Tha is usually (not always) a bit higher than the degrees of freedom computed by the general formula.

What are the most common statistical tests that make the assumption of equal variance?

The most common statistical tests and procedures that make this assumption of equal variance include: 1. ANOVA.

What is the ratio of the larger variance to the smaller variance?

As a rule of thumb, if the ratio of the larger variance to the smaller variance is less than 4, then we can assume the variances are approximately equal and use the two sample t-test.

How to test if two populations are equal?

A two sample t-test is used to test whether or not the means of two populations are equal. The test makes the assumption that the variances are equal between the two groups. There are two ways to test if this assumption is met: 1. Use the rule of thumb ratio. As a rule of thumb, if the ratio of the larger variance to the smaller variance is less ...

How to test ANOVA?

An ANOVA assumes that each of the groups has equal variance. There are two ways to test if this assumption is met: 1. Create boxplots. Boxplots offer a visual way to check the assumption of equal variances. The variance of weight loss in each group can be seen by the length of each box plot. The longer the box, the higher the variance.

Is an ANOVA robust against equal variance?

In general, ANOVA’s are considered to be fairly robust against violations of the equal variances assumption as long as each group has the same sample size. However, if the sample sizes are not the same and this assumption is severely violated, you could instead run a Kruskal-Wallis Test, which is the non-parametric version of the one-way ANOVA.

Why use a test for equal variance?

Use a test for equal variances to test the equality of variances between populations or factor levels. Many statistical procedures, such as analysis of variance (ANOVA) and regression, assume that although different samples can come from populations with different means, they have the same variance. Because the susceptibility of different ...

What happens if the p-value is greater than adequate choices of alpha?

If the resulting p-value is greater than adequate choices of alpha, you fail to reject the null hypothesis of the variances being equal. You can feel confident that the assumption of equal variances is being met. For tests for equal variances, the hypotheses are: H 0: All variances are equal. H 1: Not all variances are equal.

Why do you use the ANOVA model?

You use the ANOVA general linear model (GLM) because you have unequal sample sizes. Because this unbalanced condition increases the susceptibility to unequal variances, you decide to test the assumption of equal variances.

When to base conclusions on Levene's method?

Under these conditions, if Levene's method gives you a smaller p-value than the multiple comparisons method, then you should base your conclusions on Levene's method. Otherwise, you can base your conclusions on the multiple comparisons method, but remember that your type I error rate is likely to be greater than α.

Which is more powerful, F-test or Bartlett's test?

Any departure from normality can cause these tests to yield inaccurate results. However, if the data conform to the normal distribution, then the F-test and Bartlett's test are typically more powerful than either the multiple comparisons method or Levene's method.

Can ANOVA be affected by inequality of variance?

For example, ANOVA inferences are only slightly affected by inequality of variance if the model contains only fixed factors and has equal or almost equal sample sizes. Alternatively, ANOVA models with random effects and/or unequal sample sizes could be substantially affected.

image
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1 2 3 4 5 6 7 8 9
8.3.21PHP Version869msRequest Duration2MBMemory UsageGET {post}Route
  • warninglog[07:13:28] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
  • warninglog[07:13:28] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
  • warninglog[07:13:28] LOG.warning: Callables of the form ["Swift_SmtpTransport", "Swift_Transport_EsmtpTranspor...
  • warninglog[07:13:28] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
  • warninglog[07:13:28] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
  • warninglog[07:13:28] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[07:13:28] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[07:13:28] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[07:13:28] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[07:13:28] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[07:13:28] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • Booting (14.39ms)
  • Application (854ms)
  • 1 x Application (98.31%)
    854.07ms
    1 x Booting (1.66%)
    14.39ms
    7 templates were rendered
    • themes.DevBlog.content.post (resources/views/themes/DevBlog/content/post.blade.php)34blade
      Params
      0
      post
      1
      postContent
      2
      author
      3
      updated_at
      4
      bing_rich_snippet_text
      5
      bing_rich_snippet_link
      6
      bing_related_keywords
      7
      google_related_keywords
      8
      bing_news_title
      9
      bing_news_description
      10
      bing_videos
      11
      bing_images
      12
      bing_search_result_title
      13
      bing_search_result_description
      14
      bing_search_result_url
      15
      bing_paa_questions
      16
      bing_paa_answers
      17
      bing_slider_faq_questions
      18
      bing_slider_faq_answers
      19
      bing_pop_faq_questions
      20
      bing_pop_faq_answers
      21
      bing_tab_faq_questions
      22
      bing_tab_faq_answers
      23
      google_faq_questions
      24
      google_faq_answers
      25
      google_rich_snippet
      26
      google_search_result
      27
      indexedArray
      28
      total_images
      29
      total_videos
      30
      settings
      31
      url_current
      32
      menus
      33
      sidebar
    • themes.DevBlog.layouts.master (resources/views/themes/DevBlog/layouts/master.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.head (resources/views/themes/DevBlog/panels/head.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.header (resources/views/themes/DevBlog/panels/header.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.navbar (resources/views/themes/DevBlog/panels/navbar.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.footer (resources/views/themes/DevBlog/panels/footer.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.scripts (resources/views/themes/DevBlog/panels/scripts.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    uri
    GET {post}
    middleware
    web, checkdate
    as
    post.show
    controller
    App\Http\Controllers\Frontend\json_data\PostController@show
    namespace
    where
    file
    app/Http/Controllers/Frontend/json_data/PostController.php:18-166
    7 statements were executed827ms
    • select * from `posts` where `published_at` <= '2025-06-20 07:13:28' and `slug` = 'should-i-use-equal-or-unequal-variance' and `posts`.`deleted_at` is null limit 1
      4.54ms/app/Providers/RouteServiceProvider.php:54receivinghelpdeskask
      Metadata
      Bindings
      • 0. 2025-06-20 07:13:28
      • 1. should-i-use-equal-or-unequal-variance
      Backtrace
      • 15. /app/Providers/RouteServiceProvider.php:54
      • 18. /vendor/laravel/framework/src/Illuminate/Routing/Router.php:842
      • 19. Route binding:39
      • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 21. /vendor/laravel/framework/src/Illuminate/Foundation/Http/Middleware/VerifyCsrfToken.php:78
    • select * from `json_post_contents` where `json_post_contents`.`post_id` = 162332 and `json_post_contents`.`post_id` is not null and `rewrite_id` = 0
      10.36msmiddleware::checkdate:30receivinghelpdeskask
      Metadata
      Bindings
      • 0. 162332
      • 1. 0
      Backtrace
      • 19. middleware::checkdate:30
      • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 21. /vendor/laravel/jetstream/src/Http/Middleware/ShareInertiaData.php:61
      • 22. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 23. /vendor/laravel/framework/src/Illuminate/Routing/Middleware/SubstituteBindings.php:50
    • select * from `nova_menu_menus` where `slug` = 'header' limit 1
      730μs/vendor/outl1ne/nova-menu-builder/src/helpers.php:32receivinghelpdeskask
      Metadata
      Bindings
      • 0. header
      Backtrace
      • 15. /vendor/outl1ne/nova-menu-builder/src/helpers.php:32
      • 17. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 18. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
      • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
    • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`menu_id` = 1 and `nova_menu_menu_items`.`menu_id` is not null and `parent_id` is null order by `parent_id` asc, `order` asc, `name` asc
      420μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
      Metadata
      Bindings
      • 0. 1
      Backtrace
      • 19. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
      • 20. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
      • 22. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 23. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
    • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`parent_id` in (1) order by `order` asc
      270μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
      Metadata
      Backtrace
      • 24. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
      • 25. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
      • 27. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 28. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 29. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
    • select `id`, `post_title`, `slug` from `posts` where `status` = 'publish' and `posts`.`deleted_at` is null order by RAND() limit 10
      809ms/app/View/Composers/SidebarView.php:22receivinghelpdeskask
      Metadata
      Bindings
      • 0. publish
      Backtrace
      • 14. /app/View/Composers/SidebarView.php:22
      • 15. /app/View/Composers/SidebarView.php:12
      • 16. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
      • 17. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
      • 20. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
    • select * from `fake_users` where `fake_users`.`id` = 39920 limit 1
      1.94msview::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15receivinghelpdeskask
      Metadata
      Bindings
      • 0. 39920
      Backtrace
      • 21. view::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15
      • 23. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
      • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 25. /vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • 26. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
    App\Models\FakeUser
    1
    Outl1ne\MenuBuilder\Models\MenuItem
    1
    Outl1ne\MenuBuilder\Models\Menu
    1
    App\Models\JsonPostContent
    1
    App\Models\Post
    11
        _token
        HTgDtxnPwofdyU9hRRxlrvaOkyE4x7nwhplNKByn
        _previous
        array:1 [ "url" => "https://receivinghelpdesk.com/ask/should-i-use-equal-or-unequal-variance" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /should-i-use-equal-or-unequal-variance
        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:25 [ "cookie" => array:1 [ 0 => "_pk_id.64.7c30=f1da73957a866ce3.1750383793.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6Ik1mWFFJTDJ2bUZzR3dVc25QNUJZR1E9PSIsInZhbHVlIjoiNjlLNEdMQWxDMVFvaXV2V2pmdXA1dkFNNEdVNnlZSXdnRnM0eTh2alZIU01GYndWSDVYVnF1cWtCZGErSmFCWDFFMVF4MWk1b2gxWXF2eGVNelpvZmEwbFF1ZWxaZFdtVXhSdkpMZmZzR0tzb3puNjV5bEVrNjczb09LVCtpVDEiLCJtYWMiOiIxNzY5NzNmMzkxZjY1OTFjMGExYjgwY2M1NTBlMTcwM2RmMTgxNTA0NTY1MDllYjQ3MzM1OTYyNDg3MmFjNWU5IiwidGFnIjoiIn0%3D; askhelpdesk_session=eyJpdiI6IjZGNCtpRHNHeks4ekFwVDlJbGZoaUE9PSIsInZhbHVlIjoibFlpZmtWZVJVbkZGRklhRHI0WGdWNWxHWWZFVE4zYkRxMzhqTU11dU9UaXYydXN4NHlvZ0NOVUdqa040RXF4THphL0RhWkRjMWVnenBOcFMreE5NLzkxZU02WFpoemJLQ0M5UitQU1hRNHgxYkQ5R0IwRGVZT1J2TDBFcjA5YTQiLCJtYWMiOiIwMWFmMDk1YjZmNzU4ZDg1NDEzNjRhZWZjMzVkNzc1YmMyMmUzNThiNWJiZGM1ZWU2Mzg2MzA2Zjc3NDg3YjU3IiwidGFnIjoiIn0%3D_pk_id.64.7c30=f1da73957a866ce3.1750383793.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6Ik1mWFFJTDJ2bUZzR3dVc25QNUJZR1E9PSIsInZhbHVlIjoiNjlLNEdMQWxDMVFvaXV2V2pmdXA1d" ] "cf-ipcountry" => array:1 [ 0 => "US" ] "cf-connecting-ip" => array:1 [ 0 => "216.73.216.169" ] "cdn-loop" => array:1 [ 0 => "cloudflare; loops=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 => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "accept-encoding" => array:1 [ 0 => "gzip, br" ] "cf-ray" => array:1 [ 0 => "9527934fc92f55fa-ORD" ] "priority" => array:1 [ 0 => "u=0, i" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "cf-visitor" => array:1 [ 0 => "{"scheme":"https"}" ] "connection" => array:1 [ 0 => "close" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "216.73.216.169, 172.69.58.185" ] "x-server-addr" => array:1 [ 0 => "154.12.239.204" ] "host" => array:1 [ 0 => "receivinghelpdesk.com" ] ]
        request_server
        0 of 0
        array:56 [ "USER" => "runcloud" "HOME" => "/home/runcloud" "SCRIPT_NAME" => "/ask/index.php" "REQUEST_URI" => "/ask/should-i-use-equal-or-unequal-variance" "QUERY_STRING" => "" "REQUEST_METHOD" => "GET" "SERVER_PROTOCOL" => "HTTP/1.0" "GATEWAY_INTERFACE" => "CGI/1.1" "REDIRECT_URL" => "/ask/should-i-use-equal-or-unequal-variance" "REMOTE_PORT" => "56456" "SCRIPT_FILENAME" => "/home/runcloud/webapps/ReceivingHelpDesk/ask/index.php" "SERVER_ADMIN" => "you@example.com" "CONTEXT_DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/" "CONTEXT_PREFIX" => "" "REQUEST_SCHEME" => "http" "DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/" "REMOTE_ADDR" => "172.69.58.185" "SERVER_PORT" => "80" "SERVER_ADDR" => "127.0.0.1" "SERVER_NAME" => "receivinghelpdesk.com" "SERVER_SOFTWARE" => "Apache/2.4.63 (Unix) OpenSSL/1.1.1f" "SERVER_SIGNATURE" => "" "LD_LIBRARY_PATH" => "/RunCloud/Packages/apache2-rc/lib" "PATH" => "/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin" "HTTP_COOKIE" => "_pk_id.64.7c30=f1da73957a866ce3.1750383793.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6Ik1mWFFJTDJ2bUZzR3dVc25QNUJZR1E9PSIsInZhbHVlIjoiNjlLNEdMQWxDMVFvaXV2V2pmdXA1dkFNNEdVNnlZSXdnRnM0eTh2alZIU01GYndWSDVYVnF1cWtCZGErSmFCWDFFMVF4MWk1b2gxWXF2eGVNelpvZmEwbFF1ZWxaZFdtVXhSdkpMZmZzR0tzb3puNjV5bEVrNjczb09LVCtpVDEiLCJtYWMiOiIxNzY5NzNmMzkxZjY1OTFjMGExYjgwY2M1NTBlMTcwM2RmMTgxNTA0NTY1MDllYjQ3MzM1OTYyNDg3MmFjNWU5IiwidGFnIjoiIn0%3D; askhelpdesk_session=eyJpdiI6IjZGNCtpRHNHeks4ekFwVDlJbGZoaUE9PSIsInZhbHVlIjoibFlpZmtWZVJVbkZGRklhRHI0WGdWNWxHWWZFVE4zYkRxMzhqTU11dU9UaXYydXN4NHlvZ0NOVUdqa040RXF4THphL0RhWkRjMWVnenBOcFMreE5NLzkxZU02WFpoemJLQ0M5UitQU1hRNHgxYkQ5R0IwRGVZT1J2TDBFcjA5YTQiLCJtYWMiOiIwMWFmMDk1YjZmNzU4ZDg1NDEzNjRhZWZjMzVkNzc1YmMyMmUzNThiNWJiZGM1ZWU2Mzg2MzA2Zjc3NDg3YjU3IiwidGFnIjoiIn0%3D_pk_id.64.7c30=f1da73957a866ce3.1750383793.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6Ik1mWFFJTDJ2bUZzR3dVc25QNUJZR1E9PSIsInZhbHVlIjoiNjlLNEdMQWxDMVFvaXV2V2pmdXA1d" "HTTP_CF_IPCOUNTRY" => "US" "HTTP_CF_CONNECTING_IP" => "216.73.216.169" "HTTP_CDN_LOOP" => "cloudflare; loops=1" "HTTP_SEC_FETCH_MODE" => "navigate" "HTTP_SEC_FETCH_SITE" => "none" "HTTP_ACCEPT" => "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" "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" "HTTP_UPGRADE_INSECURE_REQUESTS" => "1" "HTTP_SEC_CH_UA_PLATFORM" => ""Windows"" "HTTP_SEC_CH_UA_MOBILE" => "?0" "HTTP_SEC_CH_UA" => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" "HTTP_CACHE_CONTROL" => "no-cache" "HTTP_PRAGMA" => "no-cache" "HTTP_ACCEPT_ENCODING" => "gzip, br" "HTTP_CF_RAY" => "9527934fc92f55fa-ORD" "HTTP_PRIORITY" => "u=0, i" "HTTP_SEC_FETCH_DEST" => "document" "HTTP_SEC_FETCH_USER" => "?1" "HTTP_CF_VISITOR" => "{"scheme":"https"}" "HTTP_CONNECTION" => "close" "HTTP_X_FORWARDED_PROTO" => "https" "HTTP_X_FORWARDED_FOR" => "216.73.216.169, 172.69.58.185" "HTTP_X_SERVER_ADDR" => "154.12.239.204" "HTTP_HOST" => "receivinghelpdesk.com" "HTTPS" => "on" "REDIRECT_STATUS" => "200" "REDIRECT_HTTPS" => "on" "FCGI_ROLE" => "RESPONDER" "PHP_SELF" => "/ask/index.php" "REQUEST_TIME_FLOAT" => 1750383807.9855 "REQUEST_TIME" => 1750383807 ]
        request_cookies
        0 of 0
        array:4 [ "_pk_id_64_7c30" => null "_pk_ses_64_7c30" => null "XSRF-TOKEN" => "HTgDtxnPwofdyU9hRRxlrvaOkyE4x7nwhplNKByn" "askhelpdesk_session" => "tBJrelQto219MZqbrg5uYIYMQhlc4ZwupsZYZPlg" ]
        response_headers
        0 of 0
        array:7 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "private, must-revalidate" ] "date" => array:1 [ 0 => "Fri, 20 Jun 2025 01:43:28 GMT" ] "pragma" => array:1 [ 0 => "no-cache" ] "expires" => array:1 [ 0 => -1 ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6InVkNFVabnY0ZHI0Y0daYlN0b1VRVVE9PSIsInZhbHVlIjoiTjlnN0pabGNON2h5TEFnRk5sSDZxUnllejJ2bGI1cVdOaVNUOG1TeGRoYkZiNGNEb3VsR0xteUNvQjRJUWUrbGtYbFpSeXpKWHFYYzRtYmZ6ZG5XVFlORjl0ekxYWHJySlVsNUhvYjJGWGI4ckZnOStrbVhhU2U5SWdIczRRemciLCJtYWMiOiJlMzBiMjFjMDRmY2NlMTk5N2NkMDA0YzBkZmUyZTZjMGE2NThiMzJkMzg5YWNiZDc1MGFhYmY1NTc3ODFhMDIzIiwidGFnIjoiIn0%3D; expires=Fri, 20-Jun-2025 03:43:28 GMT; Max-Age=7200; path=/; samesite=laxXSRF-TOKEN=eyJpdiI6InVkNFVabnY0ZHI0Y0daYlN0b1VRVVE9PSIsInZhbHVlIjoiTjlnN0pabGNON2h5TEFnRk5sSDZxUnllejJ2bGI1cVdOaVNUOG1TeGRoYkZiNGNEb3VsR0xteUNvQjRJUWUrbGtYbFpSe" 1 => "askhelpdesk_session=eyJpdiI6IjIzM0lMY1ROLzhLbzZKSSt3SlprR3c9PSIsInZhbHVlIjoiRFlkOUdlZmhMOERLK0FFTHBPSHBjRzhDR2pLUmFGdGNXQ1VTVHpwWEI2aGdUWUh1aGExSzhwenZwYy91ZHZmM0h6aHpzSlZpckI1L3ovZ0dXdUViNmNqZUlXSGNrMVBHTElXcG1QV3JNSlFEZ0hEQXlNeTBMVy9LT3k2c2dmb0MiLCJtYWMiOiIyNDM2NDdjMjRmNjg3NjA1ZGIwODU0NTgzN2U5NWFiZGY2MTRkZDUzNjQzMDVkMzdmMWQ5ZGZmYzQ5NWQ4NWIwIiwidGFnIjoiIn0%3D; expires=Fri, 20-Jun-2025 03:43:28 GMT; Max-Age=7200; path=/; httponly; samesite=laxaskhelpdesk_session=eyJpdiI6IjIzM0lMY1ROLzhLbzZKSSt3SlprR3c9PSIsInZhbHVlIjoiRFlkOUdlZmhMOERLK0FFTHBPSHBjRzhDR2pLUmFGdGNXQ1VTVHpwWEI2aGdUWUh1aGExSzhwenZwYy91ZHZm" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6InVkNFVabnY0ZHI0Y0daYlN0b1VRVVE9PSIsInZhbHVlIjoiTjlnN0pabGNON2h5TEFnRk5sSDZxUnllejJ2bGI1cVdOaVNUOG1TeGRoYkZiNGNEb3VsR0xteUNvQjRJUWUrbGtYbFpSeXpKWHFYYzRtYmZ6ZG5XVFlORjl0ekxYWHJySlVsNUhvYjJGWGI4ckZnOStrbVhhU2U5SWdIczRRemciLCJtYWMiOiJlMzBiMjFjMDRmY2NlMTk5N2NkMDA0YzBkZmUyZTZjMGE2NThiMzJkMzg5YWNiZDc1MGFhYmY1NTc3ODFhMDIzIiwidGFnIjoiIn0%3D; expires=Fri, 20-Jun-2025 03:43:28 GMT; path=/XSRF-TOKEN=eyJpdiI6InVkNFVabnY0ZHI0Y0daYlN0b1VRVVE9PSIsInZhbHVlIjoiTjlnN0pabGNON2h5TEFnRk5sSDZxUnllejJ2bGI1cVdOaVNUOG1TeGRoYkZiNGNEb3VsR0xteUNvQjRJUWUrbGtYbFpSe" 1 => "askhelpdesk_session=eyJpdiI6IjIzM0lMY1ROLzhLbzZKSSt3SlprR3c9PSIsInZhbHVlIjoiRFlkOUdlZmhMOERLK0FFTHBPSHBjRzhDR2pLUmFGdGNXQ1VTVHpwWEI2aGdUWUh1aGExSzhwenZwYy91ZHZmM0h6aHpzSlZpckI1L3ovZ0dXdUViNmNqZUlXSGNrMVBHTElXcG1QV3JNSlFEZ0hEQXlNeTBMVy9LT3k2c2dmb0MiLCJtYWMiOiIyNDM2NDdjMjRmNjg3NjA1ZGIwODU0NTgzN2U5NWFiZGY2MTRkZDUzNjQzMDVkMzdmMWQ5ZGZmYzQ5NWQ4NWIwIiwidGFnIjoiIn0%3D; expires=Fri, 20-Jun-2025 03:43:28 GMT; path=/; httponlyaskhelpdesk_session=eyJpdiI6IjIzM0lMY1ROLzhLbzZKSSt3SlprR3c9PSIsInZhbHVlIjoiRFlkOUdlZmhMOERLK0FFTHBPSHBjRzhDR2pLUmFGdGNXQ1VTVHpwWEI2aGdUWUh1aGExSzhwenZwYy91ZHZm" ] ]
        session_attributes
        0 of 0
        array:4 [ "_token" => "HTgDtxnPwofdyU9hRRxlrvaOkyE4x7nwhplNKByn" "_previous" => array:1 [ "url" => "https://receivinghelpdesk.com/ask/should-i-use-equal-or-unequal-variance" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]