{"id":210511,"date":"2025-04-30T11:30:56","date_gmt":"2025-04-30T11:30:56","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=210511"},"modified":"2025-04-30T11:30:58","modified_gmt":"2025-04-30T11:30:58","slug":"you-are-designing-a-2x3-factorial-design-and-need-20-participants-in-each-of-6-conditions","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/04\/30\/you-are-designing-a-2x3-factorial-design-and-need-20-participants-in-each-of-6-conditions\/","title":{"rendered":"You are designing a 2×3 factorial design and need 20 participants in each of 6 conditions"},"content":{"rendered":"\n

You are designing a 2×3 factorial design and need 20 participants in each of 6 conditions.<\/p>\n\n\n\n

1 How many participants in total would be needed for a 2×3 independent groups (between-subjects) design?
2 How many participants in total would be needed for a 2×3 repeated-measure groups (within-subjects) design?
3 How many participants in total would be needed for a 2×3 mixed factorial design?<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

1. Independent Groups (Between-Subjects) Design:<\/strong><\/h3>\n\n\n\n

In an independent groups design, each participant is assigned to only one of the six conditions. Since you need 20 participants in each condition, and there are 6 conditions in total (2 levels of factor 1 \u00d7 3 levels of factor 2), the total number of participants can be calculated as:<\/p>\n\n\n\n

[
\\text{Total participants} = 20 \\times 6 = 120
]<\/p>\n\n\n\n

So, 120 participants<\/strong> would be needed for the 2×3 independent groups design.<\/p>\n\n\n\n

2. Repeated-Measures (Within-Subjects) Design:<\/strong><\/h3>\n\n\n\n

In a repeated-measures design, each participant is exposed to all conditions. This means that you don’t need separate participants for each condition. Since you need 20 participants for each of the 6 conditions, the total number of participants required will still be 20 (because each participant will experience every condition).<\/p>\n\n\n\n

Thus, the total number of participants needed in a repeated-measures design is:<\/p>\n\n\n\n

[
\\text{Total participants} = 20
]<\/p>\n\n\n\n

So, 20 participants<\/strong> would be needed for the 2×3 repeated-measures design.<\/p>\n\n\n\n

3. Mixed Factorial Design:<\/strong><\/h3>\n\n\n\n

A mixed factorial design involves a combination of both independent and repeated-measures designs. In this case, one factor is manipulated between-subjects, and the other factor is manipulated within-subjects.<\/p>\n\n\n\n

For this design:<\/p>\n\n\n\n

    \n
  • The between-subjects factor<\/strong> requires 20 participants in each of the 2 levels (this means 20 participants for each level of the between-subjects factor).<\/li>\n\n\n\n
  • The within-subjects factor<\/strong> will involve all 20 participants experiencing the 3 conditions of the within-subjects factor.<\/li>\n<\/ul>\n\n\n\n

    Therefore, for the between-subjects factor (2 levels), the number of participants is:<\/p>\n\n\n\n

    [
    \\text{Participants for between-subjects factor} = 20 \\times 2 = 40
    ]<\/p>\n\n\n\n

    Since the within-subjects factor involves the same 20 participants, no additional participants are needed for that factor.<\/p>\n\n\n\n

    Thus, for the mixed factorial design, the total number of participants required is:<\/p>\n\n\n\n

    [
    \\text{Total participants} = 40
    ]<\/p>\n\n\n\n

    So, 40 participants<\/strong> would be needed for the 2×3 mixed factorial design.<\/p>\n\n\n\n

    Explanation:<\/h3>\n\n\n\n
      \n
    • Independent Groups Design<\/strong>: Each condition requires a unique set of participants, meaning you need as many participants as the total number of conditions.<\/li>\n\n\n\n
    • Repeated-Measures Design<\/strong>: Each participant is exposed to all conditions, so only one set of participants is required to experience all conditions.<\/li>\n\n\n\n
    • Mixed Factorial Design<\/strong>: The total number of participants needed is a combination of the between-subjects and within-subjects requirements, where participants for the within-subjects factor are the same across conditions, and only the between-subjects factor requires additional participants.<\/li>\n<\/ul>\n\n\n\n

      Summary:<\/h3>\n\n\n\n
        \n
      • Independent Groups Design<\/strong>: 120 participants<\/li>\n\n\n\n
      • Repeated-Measures Design<\/strong>: 20 participants<\/li>\n\n\n\n
      • Mixed Factorial Design<\/strong>: 40 participants<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

        You are designing a 2×3 factorial design and need 20 participants in each of 6 conditions. 1 How many participants in total would be needed for a 2×3 independent groups (between-subjects) design?2 How many participants in total would be needed for a 2×3 repeated-measure groups (within-subjects) design?3 How many participants in total would be needed […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-210511","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/210511","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=210511"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/210511\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=210511"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=210511"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=210511"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}