{"id":100294,"date":"2025-02-20T22:42:55","date_gmt":"2025-02-20T22:42:55","guid":{"rendered":"https:\/\/peraltafinancing.com\/agriculture\/paired-t-test-with-solved-example\/"},"modified":"2025-02-20T22:42:55","modified_gmt":"2025-02-20T22:42:55","slug":"paired-t-test-with-solved-example","status":"publish","type":"post","link":"https:\/\/fivemor.com\/?p=100294","title":{"rendered":"Paired T test with solved example"},"content":{"rendered":"


\n<\/p>\n

\n

1.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span><\/b>Introduction<\/span><\/b><\/p>\n

\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0<\/span><\/span>A paired t-test compares the means of two related
\ngroups to determine if there is a statistically significant difference between
\nthem. This test is used when the same subjects are measured twice, such as
\nbefore and after a treatment. By analyzing the differences between paired
\nobservations, the paired t-test accounts for variability within subjects,
\nmaking it a powerful tool for detecting changes or effects in experiments and
\nrepeated-measures studies.<\/span><\/p>\n

2.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/span><\/b>When to use paired t test<\/span><\/b><\/p>\n

A paired t-test is used to compare the means of
\ntwo related groups to determine if there is a statistically significant
\ndifference. This test is applicable when the same subjects are measured\u00a0<\/span>twice or when pairs of related subjects are
\nmatched. Use a paired t-test in the following scenarios:<\/span><\/p>\n

1.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span>The same subjects are
\nmeasured twice, such as before and after treatment.<\/span><\/p>\n

2.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span>Pairs of related subjects
\nare matched based on specific criteria.<\/span><\/p>\n

3.\u00a0 \u00a0 <\/span><\/span>The objective is to
\ndetect significant changes within subjects by analyzing differences between
\npaired observations.<\/span><\/p>\n

3.\u00a0\u00a0\u00a0\u00a0 <\/span><\/span><\/span><\/b>Assumptions
\nof paired t-test<\/span><\/b><\/p>\n

1.\u00a0 \u00a0<\/span><\/span><\/span>Paired Observations<\/span><\/b>:
\nThe data consists of pairs of related observations (e.g<\/i>., measurements
\nbefore and after treatment on the same subjects).<\/span><\/p>\n

2.\u00a0\u00a0<\/span><\/span><\/span>Continuous Data<\/span><\/b>:
\nThe differences between paired observations are continuous and measured on an
\ninterval or ratio scale.<\/span><\/p>\n

3.\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/span><\/span>Normality<\/span><\/b>:
\nThe differences between the paired observations are approximately normally
\ndistributed.<\/span><\/p>\n

4.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span><\/span>Independence<\/span><\/b>:
\nThe pairs are independent of each other.<\/span><\/p>\n

5.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/span><\/span>Scale of Measurement<\/span><\/b>:
\nThe data should be measured at least at the interval level, allowing for the
\ncalculation of meaningful differences.<\/span><\/p>\n

4.\u00a0\u00a0\u00a0\u00a0 <\/span><\/span><\/span><\/b>How
\nis paired t-test is different from two sample independent t-test<\/span><\/b><\/p>\n

The
\npaired t-test compares the means of two related groups, focusing on differences
\nwithin the same subjects, assuming paired observations. In contrast, the
\ntwo-sample independent t-test compares the means of two independent groups,
\nassuming observations are independent and unrelated. The paired t-test controls
\nfor within-subject variability, while the independent t-test assesses
\ndifferences between separate groups, each with its own distinct subjects.<\/span><\/p>\n

\u00a0<\/p>\n

<\/a><\/div>\n

<\/p>\n

<\/a><\/div>\n

6.\u00a0\u00a0\u00a0\u00a0 <\/span><\/span><\/span>Solved
\nexample<\/span><\/h3>\n

The data of the
\nfollowing table indicates the milk production of 12 cows for evening and
\nmorning milking. Test that the milk production of both the time is same.<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n
\n

Milk yield in
\n liter<\/span><\/p>\n<\/td>\n<\/tr>\n

\n

Cows<\/span><\/b><\/p>\n<\/td>\n

\n

Morning
\n (Xi<\/sub>)<\/span><\/b><\/p>\n<\/td>\n

\n

Evening
\n (Yi<\/sub>)<\/span><\/b><\/p>\n<\/td>\n

\n

Cows<\/span><\/b><\/p>\n<\/td>\n

\n

Morning
\n (Xi<\/sub>)<\/span><\/b><\/p>\n<\/td>\n

\n

Evening
\n (Yi<\/sub>)<\/span><\/b><\/p>\n<\/td>\n<\/tr>\n

\n

1<\/span><\/b><\/p>\n<\/td>\n

\n

4.5<\/span><\/p>\n<\/td>\n

\n

4.0<\/span><\/p>\n<\/td>\n

\n

7<\/span><\/b><\/p>\n<\/td>\n

\n

5.0<\/span><\/p>\n<\/td>\n

\n

4.5<\/span><\/p>\n<\/td>\n<\/tr>\n

\n

2<\/span><\/b><\/p>\n<\/td>\n

\n

5.6<\/span><\/p>\n<\/td>\n

\n

4.5<\/span><\/p>\n<\/td>\n

\n

8<\/span><\/b><\/p>\n<\/td>\n

\n

7.5<\/span><\/p>\n<\/td>\n

\n

7.5<\/span><\/p>\n<\/td>\n<\/tr>\n

\n

3<\/span><\/b><\/p>\n<\/td>\n

\n

7.5<\/span><\/p>\n<\/td>\n

\n

7.5<\/span><\/p>\n<\/td>\n

\n

9<\/span><\/b><\/p>\n<\/td>\n

\n

10.5<\/span><\/p>\n<\/td>\n

\n

10.0<\/span><\/p>\n<\/td>\n<\/tr>\n

\n

4<\/span><\/b><\/p>\n<\/td>\n

\n

8.0<\/span><\/p>\n<\/td>\n

\n

7.6<\/span><\/p>\n<\/td>\n

\n

10<\/span><\/b><\/p>\n<\/td>\n

\n

7.0<\/span><\/p>\n<\/td>\n

\n

7.0<\/span><\/p>\n<\/td>\n<\/tr>\n

\n

5<\/span><\/b><\/p>\n<\/td>\n

\n

8.0<\/span><\/p>\n<\/td>\n

\n

5.5<\/span><\/p>\n<\/td>\n

\n

11<\/span><\/b><\/p>\n<\/td>\n

\n

10.0<\/span><\/p>\n<\/td>\n

\n

9.5<\/span><\/p>\n<\/td>\n<\/tr>\n

\n

6<\/span><\/b><\/p>\n<\/td>\n

\n

8.5<\/span><\/p>\n<\/td>\n

\n

8.5<\/span><\/p>\n<\/td>\n

\n

12<\/span><\/b><\/p>\n<\/td>\n

\n

8.5<\/span><\/p>\n<\/td>\n

\n

8.5<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

<\/p>\n

<\/a><\/div>\n

<\/p>\n

<\/a><\/div>\n

<\/a><\/p>\n

\n

Same problem analysis in Agri Analyze:<\/span><\/b><\/h3>\n

The best part of performing analysis
\nwith Agri Analyze is that auto interpretation along with assumption testing.<\/span><\/p>\n

Step 1:<\/b> Open link <\/span>https:\/\/agrianalyze.com\/OneSampleTTest.aspx<\/span><\/a><\/span>
\n(For first time users free registration is mandatory)<\/span><\/p>\n

Step 2:<\/b> Prepare data in csv file as shown below:<\/span><\/p>\n

<\/a><\/div>\n

Link of the dataset<\/a><\/span><\/b><\/p>\n

Step3:<\/span><\/b> Upload data, add level of significance and average difference, add
\nvariable name and category type<\/span><\/p>\n

<\/a><\/div>\n

Add level of Significance: we have kept 0.05 i.e. 5%;\u00a0<\/span><\/p>\n

Add variable name : Milk production in Liter<\/span><\/p>\n

Category Type: As we are comparing milk production in Morning and Evening we have wrote “Time of Milking”<\/p><\/div>\n

\n

Step4:<\/span><\/b> Click on the submit and pay nominal fee and get the output along with interpretation in report.<\/span><\/p>\n

Output:<\/span><\/h2>\n<\/div>\n
\n
<\/a><\/div>\n


<\/span><\/b><\/div>\n

<\/a><\/div>\n

Link of the output report<\/a>
<\/span><\/b><\/span><\/p>\n

Reference:<\/span><\/b>
<\/span><\/p>\n
Gupta, S. C., & Kapoor, V. K. (2020).
\nFundamentals of mathematical statistics. Sultan Chand & Sons.<\/span><\/p>\n

The blog is written by:<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"

1.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Introduction \u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0A paired t-test compares the means of two related groups to determine if there is a statistically significant difference between them. This test is used when the same subjects are measured twice, such as before and after a treatment. By analyzing the differences between paired observations, the paired t-test accounts for […]<\/p>\n","protected":false},"author":1,"featured_media":100295,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12026],"tags":[46713,25332,13597],"dealstore":[],"offerexpiration":[],"class_list":["post-100294","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-agriculture","tag-paired","tag-solved","tag-test"],"yoast_head":"\nPaired T test with solved example - Som2ny Network<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/fivemor.com\/?p=100294\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Paired T test with solved example - Som2ny Network\" \/>\n<meta property=\"og:description\" content=\"1.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Introduction \u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0A paired t-test compares the means of two related groups to determine if there is a statistically significant difference between them. This test is used when the same subjects are measured twice, such as before and after a treatment. By analyzing the differences between paired observations, the paired t-test accounts for […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/fivemor.com\/?p=100294\" \/>\n<meta property=\"og:site_name\" content=\"Som2ny Network\" \/>\n<meta property=\"article:published_time\" content=\"2025-02-20T22:42:55+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/02\/paired20t20test201.png\" \/>\n\t<meta property=\"og:image:width\" content=\"822\" \/>\n\t<meta property=\"og:image:height\" content=\"598\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/fivemor.com\/?p=100294#article\",\"isPartOf\":{\"@id\":\"https:\/\/fivemor.com\/?p=100294\"},\"author\":{\"name\":\"admin\",\"@id\":\"https:\/\/fivemor.com\/#\/schema\/person\/b85e3c3dc0e1daea076524dc8810c371\"},\"headline\":\"Paired T test with solved example\",\"datePublished\":\"2025-02-20T22:42:55+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/fivemor.com\/?p=100294\"},\"wordCount\":515,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/fivemor.com\/#organization\"},\"image\":{\"@id\":\"https:\/\/fivemor.com\/?p=100294#primaryimage\"},\"thumbnailUrl\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/02\/paired20t20test201.png\",\"keywords\":[\"Paired\",\"Solved\",\"Test\"],\"articleSection\":[\"Agriculture\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/fivemor.com\/?p=100294#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/fivemor.com\/?p=100294\",\"url\":\"https:\/\/fivemor.com\/?p=100294\",\"name\":\"Paired T test with solved example - 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This test is used when the same subjects are measured twice, such as before and after a treatment. 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