{"id":1503,"date":"2012-12-28T10:16:06","date_gmt":"2012-12-28T01:16:06","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=1503"},"modified":"2012-12-28T12:57:13","modified_gmt":"2012-12-28T03:57:13","slug":"students-t-test","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=1503","title":{"rendered":"Student’s t-test"},"content":{"rendered":"

When you would like to compare two averages between samples, you could use such formulas of Student’s t-test as following chart according to the number and the variances between dependent or independent samples.<\/p>\n

$\"t-test(EN)\"$ <\/a><\/p>\n

Paired t-test as below;<\/p>\n

$\\displaystyle t = \\frac{\\bar X_D - \\mu_0}{SD\/\\sqrt{n}} \\cdot\\cdot\\cdot(1)$ <\/p>\n

Independent two samples t-test with unequal sample sizes and unequal variances, called as Welch’s t-test, as below;<\/p>\n

$\\displaystyle t = \\frac{\\bar X_1 - \\bar X_2}{SD_p} \\cdot\\cdot\\cdot(2) \\vspace{0.2in}\\\\ SD_p = \\sqrt{\\frac{SD_1^2}{n_1} + \\frac{SD_2^2}{n_2}}$ <\/p>\n

Independent two samples t-test with equal sample sizes and unequal variances as below;<\/p>\n

$\\displaystyle t = \\frac{\\bar X_1 - \\bar X_2}{SD_p \\sqrt{\\frac{2}{n}}} \\cdot\\cdot\\cdot(3) \\vspace{0.2in}\\\\SD_p = \\sqrt{\\frac{SD_1^2 + SD_2^2}{2}}$ <\/p>\n

Independent two samples t-test with unequal sample sizes and equal variances as below;<\/p>\n

$\\displaystyle t = \\frac{\\bar X_1 - \\bar X_2}{SD_p \\sqrt{\\frac{1}{n_1} + \\frac{1}{n_2}}} \\cdot\\cdot\\cdot(4) \\vspace{0.2in}\\\\ SD_p = \\sqrt{\\frac{(n_1 -1)SD_1^2 + (n_2 - 1)SD_2^2}{n_1 + n_2 - 2}}$ <\/p>\n

Reference:Student’s t-test<\/a><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

When you would like to compare two averages between samples, you could use such formulas of Student’s t- … “Student’s t-test” \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[7],"tags":[],"class_list":["post-1503","post","type-post","status-publish","format-standard","hentry","category-statistics"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t