{"id":154,"date":"2018-03-06T10:48:00","date_gmt":"2018-03-06T09:48:00","guid":{"rendered":"https:\/\/kindsonthegenius.com\/blog\/2018\/03\/06\/welchs-t-test-how-and-when-to-use-it\/"},"modified":"2020-11-05T13:46:51","modified_gmt":"2020-11-05T12:46:51","slug":"welchs-t-test-how-and-when-to-use-it","status":"publish","type":"post","link":"https:\/\/kindsonthegenius.com\/blog\/welchs-t-test-how-and-when-to-use-it\/","title":{"rendered":"Welch&#8217;s t-Test &#8211; How and When to Use it"},"content":{"rendered":"<div style=\"color: #555555; font-size: 18px; line-height: 30px; text-align: justify;\">\n<div style=\"font-family: 'segoe ui';\"><b>Welch&#8217;s t-test<\/b><br \/>The Welch&#8217;s t-test is also called unequal variances t-test that is used to test if the means of two populations are equal. This test is different from the Student&#8217;s t-test and is normally applied when the there is difference in variance between the two population variances. It can also be applied when the sample sizes are unequal.<\/p>\n<p><a href=\"https:\/\/kindsonthegenius.com\/blog\/hypothesis-testing-how-to-perform-paired-sample-t-test\/\" target=\"_blank\" rel=\"noopener noreferrer\"><span style=\"color: black;\">Learn about paird-samples t-test here<\/span><\/a><br \/><span style=\"color: black;\">&nbsp;<\/span><br \/><b>When to use Welch&#8217;s t-test<\/b><br \/>The Welch&#8217;s t-test can be applied in the following scenario <\/p>\n<ul>\n<li>When the distribution is assumed to be normal<\/li>\n<li>When the samples have unequal variances<\/li>\n<li>Sample sizes are unequal<\/li>\n<\/ul>\n<p><a href=\"https:\/\/kindsonthegenius.com\/blog\/kindson-the-genius-blog-posts\/\" target=\"_blank\" rel=\"noopener noreferrer\">See a solved example here<\/a><\/p>\n<p><b>Procedure in Performing Welch&#8217;s t-test<\/b><br \/>Step 1: State your null and alternate hypothesis<\/p>\n<p><b>H<sub>0<\/sub>:<\/b> \u03bc<sub>1<\/sub> = \u03bc<sub>2<\/sub><br \/><b>H<sub>a<\/sub><\/b>: \u03bc<sub>2<\/sub> \u2260 \u03bc<sub>1<\/sub><\/p>\n<p>Here the null hypothesis states that the means of the two populations are the same<br \/>The alternate hypothesis states that the means of the two populations are not the same<br \/>So a test is needed to decided this!<\/p>\n<p><b>Step 2<\/b>: Calculate the means of the two samples<br \/>Take the sum of of each sample and divide by the total number of items <\/p>\n<p><b>Step 3:<\/b> Calculate the standard deviation of the two samples<br \/>Standard deviation can be found using the formular<\/p>\n<div style=\"clear: both; text-align: center;\"><a href=\"https:\/\/3.bp.blogspot.com\/-BHRoNDpZPLU\/Wp5uRYzlbQI\/AAAAAAAABEQ\/psLDNemE2B8vG00oWZnvlOZtRTl_HCcygCLcBGAs\/s1600\/Standard-deviation-formular.jpg\" style=\"margin-left: 1em; margin-right: 1em;\"><img decoding=\"async\" loading=\"lazy\" border=\"0\" data-original-height=\"125\" data-original-width=\"422\" height=\"58\" src=\"https:\/\/3.bp.blogspot.com\/-BHRoNDpZPLU\/Wp5uRYzlbQI\/AAAAAAAABEQ\/psLDNemE2B8vG00oWZnvlOZtRTl_HCcygCLcBGAs\/s200\/Standard-deviation-formular.jpg\" width=\"200\" \/><\/a><\/div>\n<p>&nbsp;Don&#8217;t worry about this formular, it would become clearer when we take an example.<\/p>\n<p><b>Step 4<\/b>: Calculate the t-value using the formula<\/p>\n<div style=\"clear: both; text-align: center;\"><a href=\"https:\/\/1.bp.blogspot.com\/-iNRwGLi10aE\/Wp5ilbUmAwI\/AAAAAAAABDg\/3grcLXg1C7QU4J0gFVZZhyuQSwoczTCJgCLcBGAs\/s1600\/Welch%2Bt-test%2Bformula.jpg\" style=\"margin-left: 1em; margin-right: 1em;\"><img decoding=\"async\" loading=\"lazy\" border=\"0\" data-original-height=\"139\" data-original-width=\"354\" height=\"125\" src=\"https:\/\/1.bp.blogspot.com\/-iNRwGLi10aE\/Wp5ilbUmAwI\/AAAAAAAABDg\/3grcLXg1C7QU4J0gFVZZhyuQSwoczTCJgCLcBGAs\/s320\/Welch%2Bt-test%2Bformula.jpg\" width=\"320\" \/><\/a><\/div>\n<p>&nbsp;where<\/p>\n<ul>\n<li><img decoding=\"async\" border=\"0\" data-original-height=\"23\" data-original-width=\"24\" src=\"https:\/\/3.bp.blogspot.com\/-3acUm7CSIRA\/Wp5lO5PZwXI\/AAAAAAAABEA\/1RQvuSJSmsAulub0eShTmM_IassmVFThACLcBGAs\/s1600\/x1bar2.JPG\" \/>&nbsp; is the mean of the first sample<\/li>\n<li>s<sub>1<\/sub> is the standard deviation of the first sample<\/li>\n<li>N<sub>2<\/sub> is the first sample size<\/li>\n<li>the same is calculated for the second sample <\/li>\n<\/ul>\n<p><b>Step 5:<\/b> Calculate the degrees of freedom<\/p>\n<p>The degrees of freedom given by v is calulated using the formular belows:<\/p>\n<div style=\"clear: both; text-align: center;\"><a href=\"https:\/\/1.bp.blogspot.com\/-rawdGLOVCxo\/Wp5ju1ei5AI\/AAAAAAAABDs\/GzCg-sDvrWoZwObatBKoK8-d8QsjNYISACLcBGAs\/s1600\/Welch-degree%2Bof%2Bfreedom.JPG\" style=\"margin-left: 1em; margin-right: 1em;\"><img decoding=\"async\" loading=\"lazy\" border=\"0\" data-original-height=\"188\" data-original-width=\"431\" height=\"139\" src=\"https:\/\/1.bp.blogspot.com\/-rawdGLOVCxo\/Wp5ju1ei5AI\/AAAAAAAABDs\/GzCg-sDvrWoZwObatBKoK8-d8QsjNYISACLcBGAs\/s320\/Welch-degree%2Bof%2Bfreedom.JPG\" width=\"320\" \/><\/a><\/div>\n<p>where v1 is the degrees of freedom from the first sample and is given by the formula<br \/>v<sub>1<\/sub> = N<sub>1<\/sub> &#8211; 1<\/p>\n<p>and v<sub>2<\/sub> is the degrees of freedom from the second sample and is given by the formula<br \/>and v<sub>2<\/sub> = N<sub>2<\/sub> &#8211; 1<\/p>\n<p><b>Step 6<\/b>: Compare the calculated t with the tabulated t<br \/>Normally, the calulcated value of t (called the test statistic) would either be greater thanor less than the tabulated value of t(called the critical value) <\/p>\n<p><b>Step 7:<\/b> Draw your conclusion<br \/>The conclution would be wether the null hypothesis is accepted or rejected based on the problem being solved.<br \/>If the value of the test statistic is greater than the critical value, then we reject the null hypothesis. Otherwise&nbsp; the null hypothesis is accepted if the test statistic is less than(or within) the critical value.<br \/><a href=\"https:\/\/kindsonthegenius.com\/blog\/kindson-the-genius-blog-posts\/\" target=\"_blank\" rel=\"noopener noreferrer\">Try a sample exercise solved here <\/a><br \/><a href=\"https:\/\/www.youtube.com\/watch?v=s5-5lx6e33k&amp;list=PLMz1vLpcJgGDIBSfqGfEl3bON0M-zAb5B\" target=\"_blank\" rel=\"noopener noreferrer\">Watch the Video Lessons on Youtube <\/a> <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Welch&#8217;s t-testThe Welch&#8217;s t-test is also called unequal variances t-test that is used to test if the means of two populations are equal. This test &hellip; <\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0},"categories":[223],"tags":[544],"_links":{"self":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/154"}],"collection":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/comments?post=154"}],"version-history":[{"count":4,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/154\/revisions"}],"predecessor-version":[{"id":1711,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/154\/revisions\/1711"}],"wp:attachment":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/media?parent=154"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/categories?post=154"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/tags?post=154"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}