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8.7: Correlated Pairs
https://stats.libretexts.org/Courses/Luther_College/Psyc_350%3ABehavioral_Statistics_(Toussaint)/08%3A_Tests_of_Means/8.07%3A_Correlated_Pairs
The result is that the standard error of the difference between means is smaller in the correlated $t$ test and, since this term is in the denominator of the formula for $t$ , results in a larger \...The result is that the standard error of the difference between means is smaller in the correlated $t$ test and, since this term is in the denominator of the formula for $t$ , results in a larger $t$ . Therefore, the variance of difference scores is the variance in the first condition ( $X$ ) plus the variance in the second condition ( $Y$ ) minus twice the product of
10.1: Introduction
https://stats.libretexts.org/Courses/Fresno_City_College/Introduction_to_Business_Statistics_-_OER_-_Spring_2023/10%3A_Hypothesis_Testing_with_Two_Samples/10.01%3A_Introduction
Figure $\PageIndex{1}$ If you want to test a claim that involves two groups (the types of breakfasts eaten east and west of the Mississippi River) you can use a slightly different technique when con...Figure $\PageIndex{1}$ If you want to test a claim that involves two groups (the types of breakfasts eaten east and west of the Mississippi River) you can use a slightly different technique when conducting a hypothesis test. (credit: Chloe Lim) Studies often compare two groups. Independent groups consist of two samples that are independent, that is, sample values selected from one population are not related in any way to sample values selected from the other population.
12.7: Correlated Pairs
https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Lane)/12%3A_Tests_of_Means/12.07%3A_Correlated_Pairs
The result is that the standard error of the difference between means is smaller in the correlated $t$ test and, since this term is in the denominator of the formula for $t$ , results in a larger \...The result is that the standard error of the difference between means is smaller in the correlated $t$ test and, since this term is in the denominator of the formula for $t$ , results in a larger $t$ . Therefore, the variance of difference scores is the variance in the first condition ( $X$ ) plus the variance in the second condition ( $Y$ ) minus twice the product of
7.6: Introduction to Two-Sample Tests
https://stats.libretexts.org/Courses/Saint_Mary's_College_Notre_Dame/BFE_1201_Statistical_Methods_for_Finance_(Kuter)/07%3A_Hypothesis_Testing/7.06%3A_Introduction_to_Two-Sample_Tests
Figure $\PageIndex{1}$ If you want to test a claim that involves two groups (the types of breakfasts eaten east and west of the Mississippi River) you can use a slightly different technique when con...Figure $\PageIndex{1}$ If you want to test a claim that involves two groups (the types of breakfasts eaten east and west of the Mississippi River) you can use a slightly different technique when conducting a hypothesis test. (credit: Chloe Lim) Independent groups consist of two samples that are independent, that is, sample values selected from one population are not related in any way to sample values selected from the other population.
10.0: Introduction
https://stats.libretexts.org/Courses/Fresno_City_College/Book%3A_Business_Statistics_Customized_(OpenStax)/10%3A_Hypothesis_Testing_with_Two_Samples/10.01%3A_Introduction
Figure $\PageIndex{1}$ If you want to test a claim that involves two groups (the types of breakfasts eaten east and west of the Mississippi River) you can use a slightly different technique when con...Figure $\PageIndex{1}$ If you want to test a claim that involves two groups (the types of breakfasts eaten east and west of the Mississippi River) you can use a slightly different technique when conducting a hypothesis test. (credit: Chloe Lim) Studies often compare two groups. Independent groups consist of two samples that are independent, that is, sample values selected from one population are not related in any way to sample values selected from the other population.
10.0: Introduction to Two-Sample Tests
https://stats.libretexts.org/Bookshelves/Applied_Statistics/Business_Statistics_(OpenStax)/10%3A_Hypothesis_Testing_with_Two_Samples/10.00%3A_Introduction_to_Two-Sample_Tests
This page explains hypothesis testing in comparing two groups, like in health or education studies. It distinguishes between independent groups (unrelated samples) and matched pairs (dependent samples...This page explains hypothesis testing in comparing two groups, like in health or education studies. It distinguishes between independent groups (unrelated samples) and matched pairs (dependent samples), noting that matched pairs assess population means while independent groups can evaluate means or proportions. The methodology is applicable across diverse fields such as health, politics, and business.

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