{"id":20604,"date":"2025-06-14T14:58:50","date_gmt":"2025-06-14T14:58:50","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=20604"},"modified":"2025-06-14T14:58:54","modified_gmt":"2025-06-14T14:58:54","slug":"suppose-that-you-conduct-three-different-t-tests-to-analyze-the-results-of-an-experiment-with-three-independent-samples-each-individual-t-test","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/suppose-that-you-conduct-three-different-t-tests-to-analyze-the-results-of-an-experiment-with-three-independent-samples-each-individual-t-test\/","title":{"rendered":"suppose that you conduct three different t tests to analyze the results of an experiment with three independent samples each individual t test"},"content":{"rendered":"\n

suppose that you conduct three different t tests to analyze the results of an experiment with three independent samples each individual t test<\/p>\n\n\n\n

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

Correct Answer:<\/strong>
Conducting three individual t-tests<\/em> on three independent samples increases the risk of Type I error<\/strong>, and is not appropriate<\/strong> if you want to compare all three groups together. Instead, one-way ANOVA<\/strong> should be used.<\/p>\n\n\n\n

\n\n\n\n

Explanation (\u2248300 words):<\/strong><\/h3>\n\n\n\n

When analyzing results from an experiment involving three independent samples<\/strong>, it might seem logical to conduct three separate t-tests<\/strong> \u2014 for example, comparing:<\/p>\n\n\n\n

    \n
  1. Group A vs. Group B<\/li>\n\n\n\n
  2. Group A vs. Group C<\/li>\n\n\n\n
  3. Group B vs. Group C<\/li>\n<\/ol>\n\n\n\n

    While each t-test<\/em> is valid for comparing two means<\/strong>, conducting multiple t-tests<\/em> on the same dataset increases the probability of making a Type I error<\/strong> \u2014 falsely rejecting a true null hypothesis.<\/p>\n\n\n\n

    Each individual t-test<\/em> typically has a 5% risk (\u03b1 = 0.05) of Type I error. When you conduct three tests<\/strong>, the family-wise error rate<\/strong> (FWER) increases. The FWER is calculated using:<\/p>\n\n\n\n

    $$
    \\text{FWER} = 1 – (1 – \\alpha)^k
    $$<\/p>\n\n\n\n

    Where:<\/p>\n\n\n\n

      \n
    • $\\alpha = 0.05$<\/li>\n\n\n\n
    • $k = 3$ (number of comparisons)<\/li>\n<\/ul>\n\n\n\n

      So,<\/p>\n\n\n\n

      $$
      \\text{FWER} = 1 – (1 – 0.05)^3 = 1 – 0.95^3 \u2248 0.1426
      $$<\/p>\n\n\n\n

      This means there\u2019s a 14.26% chance<\/strong> of incorrectly finding a statistically significant result just by chance \u2014 much higher than the intended 5%.<\/p>\n\n\n\n

      To appropriately analyze differences among three or more independent groups<\/strong>, you should use a one-way ANOVA (Analysis of Variance)<\/strong>. ANOVA tests whether there is a statistically significant difference among the means<\/strong> of all three groups simultaneously<\/strong>, while maintaining the overall Type I error at 5%.<\/p>\n\n\n\n

      If ANOVA reveals a significant result, post hoc tests<\/strong> (like Tukey’s HSD) can then determine which specific groups differ<\/strong>, while still controlling for multiple comparisons.<\/p>\n\n\n\n

      In conclusion<\/strong>, using multiple t-tests for more than two groups is statistically flawed. ANOVA is the correct approach<\/strong> for comparing three independent samples in a single experiment.<\/p>\n","protected":false},"excerpt":{"rendered":"

      suppose that you conduct three different t tests to analyze the results of an experiment with three independent samples each individual t test The correct answer and explanation is: Correct Answer:Conducting three individual t-tests on three independent samples increases the risk of Type I error, and is not appropriate if you want to compare all […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-20604","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/20604","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=20604"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/20604\/revisions"}],"predecessor-version":[{"id":20605,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/20604\/revisions\/20605"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=20604"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=20604"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=20604"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}