{"id":19097,"date":"2016-12-14T17:59:12","date_gmt":"2016-12-14T17:59:12","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=19097"},"modified":"2016-12-14T17:59:12","modified_gmt":"2016-12-14T17:59:12","slug":"statistics-the-matched-pairs-t-test","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/statistics-the-matched-pairs-t-test\/","title":{"rendered":"Statistics: the matched pairs t-test"},"content":{"rendered":"

The tutor shows an example of the matched pairs t-test.<\/h1>\n

In my post from Dec 11<\/a> I began about the matched pairs t-test. It’s used to determine if two samples come from the same population.<\/p>\n

In my previous post<\/a> I mentioned generating two lists of random numbers. The second one, I pointed out, has all its entries increased by 5.<\/p>\n

Here are the two lists:<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
random<\/td>\nrandom + 5<\/td>\ndiff<\/tr>\n
13<\/td>\n95<\/td>\n-82<\/td>\n<\/tr>\n
48<\/td>\n66<\/td>\n-18<\/td>\n<\/tr>\n
7<\/td>\n83<\/td>\n-76<\/td>\n<\/tr>\n
99<\/td>\n7<\/td>\n92<\/td>\n<\/tr>\n
92<\/td>\n57<\/td>\n35<\/td>\n<\/tr>\n
41<\/td>\n64<\/td>\n-23<\/td>\n<\/tr>\n
68<\/td>\n62<\/td>\n6<\/td>\n<\/tr>\n
35<\/td>\n88<\/td>\n-53<\/td>\n<\/tr>\n
21<\/td>\n57<\/td>\n-36<\/td>\n<\/tr>\n
64<\/td>\n34<\/td>\n30<\/td>\n<\/tr>\n
91<\/td>\n28<\/td>\n63<\/td>\n<\/tr>\n
18<\/td>\n96<\/td>\n-78<\/td>\n<\/tr>\n
31<\/td>\n7<\/td>\n24<\/td>\n<\/tr>\n
97<\/td>\n98<\/td>\n-1<\/td>\n<\/tr>\n
73<\/td>\n92<\/td>\n-19<\/td>\n<\/tr>\n<\/table>\n

<\/p>\n

Testing against a supposition that the samples come from the same distribution, the mean difference should be 0. The t-statistic is the observed mean difference, minus 0, all divided by the standard deviation of the observed differences:<\/p>\n

t = (diff<\/span> – 0)\/(\u03a3(diff)2<\/sup>\/(n-1))1\/2<\/sup><\/p>\n

It has n-1 degrees of freedom: 14, in this case.<\/p>\n

Crunching the numbers (this time, with the Casio fx-260Solar<\/a>) gives t=-0.174, which is virtually the middle of the distribution. In this context, the matched pairs t-test cannot distinguish that one list differs from the other. <\/p>\n

HTH:)<\/p>\n

Source:<\/p>\n

Harnett, Donald L. and James L. Murphy. Statistical Analysis for Business and Economics<\/u>. Don Mills: Addison-Wesley, 1993.<\/p>\n

Jack of Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"

The tutor shows an example of the matched pairs t-test. In my post from Dec 11 I began about the matched pairs t-test. It’s used to determine if two samples come from the same population. In my previous post I …<\/p>\n

Statistics: the matched pairs t-test<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[371,90,19],"tags":[2067],"class_list":["post-19097","post","type-post","status-publish","format-standard","hentry","category-business","category-calculator-usage","category-statistics","tag-matched-pairs-t-test"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/19097","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=19097"}],"version-history":[{"count":20,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/19097\/revisions"}],"predecessor-version":[{"id":19117,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/19097\/revisions\/19117"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=19097"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=19097"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=19097"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}