{"id":105354,"date":"2025-02-23T14:39:41","date_gmt":"2025-02-23T14:39:41","guid":{"rendered":"https:\/\/peraltafinancing.com\/agriculture\/two-independent-sample-t-test\/"},"modified":"2025-02-23T14:39:41","modified_gmt":"2025-02-23T14:39:41","slug":"two-independent-sample-t-test","status":"publish","type":"post","link":"https:\/\/fivemor.com\/?p=105354","title":{"rendered":"Two independent sample T-test"},"content":{"rendered":"


\n<\/p>\n

\n

(Reading time 10 min) This blog is about two sample t test theory, solved example and steps to perform analysis online along with interpretation in Agri Analyze platform<\/i><\/p>\n

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

A
\ntwo-sample independent t-test is a statistical method used to determine if
\nthere is a significant difference between the means of two independent groups.
\nThis test is particularly useful in comparing the average performance, outcomes
\nor measurements of two distinct groups to understand if they significantly
\ndiffer from each other, beyond what might be expected by random chance.<\/span><\/p>\n

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

The
\ntwo-sample t-test, also known as the independent samples t-test, is used to
\ncompare the means of two independent groups to determine if there is a
\nstatistically significant difference between them.<\/span><\/p>\n

3.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/span><\/span><\/b>3. Assumption of two sample
\nindependent t-test<\/span><\/b><\/p>\n

For
\nthe two-sample independent t-test to be valid, certain assumptions must be met:<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span><\/span>Independence of
\nobservation:<\/span><\/b> The observations in each group must
\nbe independent of each other. This means that the measurement of one
\nparticipant should not influence or be related to the measurement of another
\nparticipant within the same group or across groups.<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span><\/span>Normality:<\/span><\/b>
\nThe data in each group should be approximately normally distributed. This
\nassumption is particularly important for small sample sizes (n <\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span><\/span>Homogeneity of variance:<\/span><\/b>
\nThe variances of the two groups should be equal. This assumption is known as
\nhomoscedasticity. If the variances are not equal, a modified version of the
\nt-test, known as Two sample independent t-test with unequal variance (Welch’s
\nt-test), should be used. The Levene’s test or F-test can be used to check for
\nequality of variances.<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span><\/span>Scale of measurement:<\/span><\/b>
\nThe variables should be continuous and have meaningful numerical values with
\nequal intervals between them.<\/span><\/p>\n

4.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/span><\/span><\/b>4. Step to check
\nassumptions:<\/span><\/b><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span><\/span>Normality:<\/span><\/b>
\nUse graphical methods such as histograms or Q-Q plots to visually inspect the
\ndistribution of the data.<\/span> <\/span>Conduct
\nnormality tests like the Shapiro-Wilk test or Kolmogorov-Smirnov test.<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span><\/span>Homogeneity of variance:<\/span><\/b>
\nPerform Levene’s test, the F-test and Bartlett\u2019s test to check if the variances
\nof the two groups are significantly different.<\/span><\/p>\n

1.<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>\u00a0\u00a0\u00a0
\n<\/span><\/span><\/span><\/b><\/span>Two sample independent
\nt-test with equal variance<\/span><\/span><\/b><\/p>\n

The two-sample t-test with equal
\nvariance assesses whether there is a significant difference between the means
\nof two independent groups. This statistical test assumes homogeneity of
\nvariances and normal distribution within each group, making it suitable for
\ncomparing the means of two normally distributed populations.<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span><\/span>Checking homogeneity of
\nvariance by Bartlett\u2019s test:<\/span><\/b><\/p>\n

Bartlett’s test evaluates the
\nhomogeneity of variances across multiple samples. By calculating a test
\nstatistic from the sample variances, it determines if there are significant
\ndifferences. A p-value below a chosen significance level (e.g<\/i>., 0.05)
\nindicates unequal variances, while a higher p-value suggests equal variances.<\/span><\/p>\n

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

Example of Bartlett\u2019s test:<\/span><\/b><\/p>\n

A study is
\nconducted to compare the effectiveness of two different teaching methods
\n(Method A and Method B) on student test scores. The experiment involves two
\ngroups of students, with 10 students in each group. The test scores of the
\nstudents are recorded after they have been taught using their respective
\nmethods.<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span>Method
\nA: 60, 65, 70, 75, 80, 85, 90, 95, 100, 105<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span>Method
\nB: 55, 60, 65, 70, 75, 80, 85, 90, 95, 100<\/span><\/p>\n

Solution:<\/span><\/b><\/p>\n

Hypothesis:<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span>Null
\nhypothesis (H0<\/sub>): The variances of the test scores for both methods
\nare equal.<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span>Alternative
\nHypothesis (H1<\/sub>): The variances of the test scores for both methods
\nare not equal.<\/span><\/p>\n

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

1.\u00a0\u00a0\u00a0\u00a0 <\/span><\/span><\/span>5. Determine
\nthe p-value:<\/span><\/p>\n

The
\ntest statistic T follows a chi-squared distribution with k \u2013 1 = 2 – 1 = 1 degree
\nof freedom. In this case, T = 0, corresponding to a very high p-value (1).
\nThus, we do not reject the null hypothesis of equal variances.<\/span><\/p>\n

2.\u00a0\u00a0\u00a0\u00a0 <\/span><\/span><\/span>6. Conclusion:
\nBased on Bartlett’s test, there is no significant evidence to suggest that the
\nvariances of test scores differ between Method A and Method B.<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span>To perform a two-sample
\nindependent t-test with equal variances based on the provided example, we’ll
\nuse the test to compare the means of the test scores for Method A and Method B.<\/span><\/b><\/p>\n

Hypothesis:<\/span><\/p>\n

\u2022\u00a0\u00a0\u00a0\u00a0 Null hypothesis (H0<\/sub>): The means
\nof the test scores for Method A and Method B are equal.<\/span><\/p>\n

\u2022\u00a0\u00a0\u00a0\u00a0 Alternative Hypothesis (H1<\/sub>): The
\nmeans of the test scores for Method A and Method B are not equal.<\/span><\/p>\n

1.\u00a0\u00a0\u00a0\u00a0 <\/span><\/span>Calculate
\nthe mean and variance for each group:<\/span><\/p>\n

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

5.\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span>Find the critical value:<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span>For a two tailed test with <\/span><\/span>= 0.05 and df = 18, the critical value is
\napproximately <\/span><\/span>2.101.<\/span><\/p>\n

6.\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span>Compare the t-statistic and critical value:<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span>Calculated t (0.7385) is less than critical value of t (2.101), so we
\nfail to reject null hypothesis.<\/span><\/p>\n

7.\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span>Conclusion: There is not enough evidence to reject the null hypothesis.
\nThis suggests that there is no significant difference in the mean test scores
\nbetween Method A and Method B.<\/span><\/p>\n

2.<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0
\n<\/span><\/span><\/span>2<\/b>. Two sample independent t-test with unequal variance:<\/b><\/span><\/span><\/p>\n

The two-sample t-test with unequal variances, also
\nknown as Welch’s t-test, compares the means of two independent groups when
\ntheir variances differ. It’s robust when the assumption of equal variances is
\nviolated. Welch’s t-test adjusts the degrees of freedom and provides a more
\nreliable comparison under heterogeneous variances.<\/span><\/p>\n

Example of Two sample independent
\nt-test with unequal variance:<\/span><\/b><\/p>\n

\u00a0\u00a0 \u00a0<\/span>\u00a0\u00a0 \u00a0<\/span>\u00a0\u00a0 \u00a0<\/span>A new variety of cotton was evolved
\nby a breeder. In order to compare its yielding ability with that of a ruling
\nvariety, an experiment was conducted in CRD. The kapas yield (kg\/plot) was
\nobserved. The summary of the results are given below. Test whether the new
\nvariety of cotton gives higher yield than the ruling variety.\u00a0<\/span><\/p>\n

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

<\/p>\n

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

<\/p>\n

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

<\/p>\n

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

<\/p>\n

\n

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

problem analysis in AgriAnalyze:<\/span><\/b><\/p>\n

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

Step1:<\/span><\/b> Open link <\/span>https:\/\/www.agrianalyze.com\/TwoSamplePairedTTest.aspx<\/span><\/a><\/span> (For first time users free registration is
\nmandatory)<\/span><\/p>\n

Step2:<\/span><\/b> Prepare data in csv file as shown below:<\/span><\/p>\n

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

Step3:<\/span><\/b> Upload data, select conditions for variance of samples, add level of
\nsignificance, add variable name and category type<\/span><\/p>\n

<\/div>\n

\n

Step4:<\/span><\/b> Click on the submit and pay nominal fee<\/span><\/p>\n

Step5:<\/b>\u00a0Download the report<\/span><\/p>\n

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

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

Reference:<\/b><\/span><\/p>\n

Agri Analyze website for analysis\u00a0<\/span><\/p>\n

Rangaswamy R. (1995). A text book of Agricultural Statistics. New Age International.\u00a0<\/span><\/p>\n

The post is written by: Darshan Kothiya<\/span><\/p>\n

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

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


<\/span><\/div>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"

(Reading time 10 min) This blog is about two sample t test theory, solved example and steps to perform analysis online along with interpretation in Agri Analyze platform 1.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a01.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Introduction A two-sample independent t-test is a statistical method used to determine if there is a significant difference between the […]<\/p>\n","protected":false},"author":1,"featured_media":105357,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12026],"tags":[15175,13861,48233],"dealstore":[],"offerexpiration":[],"class_list":["post-105354","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-agriculture","tag-independent","tag-sample","tag-ttest"],"yoast_head":"\nTwo independent sample T-test - 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=105354\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Two independent sample T-test - Som2ny Network\" \/>\n<meta property=\"og:description\" content=\"(Reading time 10 min) This blog is about two sample t test theory, solved example and steps to perform analysis online along with interpretation in Agri Analyze platform 1.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a01.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Introduction A two-sample independent t-test is a statistical method used to determine if there is a significant difference between the […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/fivemor.com\/?p=105354\" \/>\n<meta property=\"og:site_name\" content=\"Som2ny Network\" \/>\n<meta property=\"article:published_time\" content=\"2025-02-23T14:39:41+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/02\/bartletts20test.png\" \/>\n\t<meta property=\"og:image:width\" content=\"826\" \/>\n\t<meta property=\"og:image:height\" content=\"563\" \/>\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=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/fivemor.com\/?p=105354#article\",\"isPartOf\":{\"@id\":\"https:\/\/fivemor.com\/?p=105354\"},\"author\":{\"name\":\"admin\",\"@id\":\"https:\/\/fivemor.com\/#\/schema\/person\/b85e3c3dc0e1daea076524dc8810c371\"},\"headline\":\"Two independent sample T-test\",\"datePublished\":\"2025-02-23T14:39:41+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/fivemor.com\/?p=105354\"},\"wordCount\":986,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/fivemor.com\/#organization\"},\"image\":{\"@id\":\"https:\/\/fivemor.com\/?p=105354#primaryimage\"},\"thumbnailUrl\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/02\/bartletts20test.png\",\"keywords\":[\"Independent\",\"Sample\",\"Ttest\"],\"articleSection\":[\"Agriculture\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/fivemor.com\/?p=105354#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/fivemor.com\/?p=105354\",\"url\":\"https:\/\/fivemor.com\/?p=105354\",\"name\":\"Two independent sample T-test - Som2ny Network\",\"isPartOf\":{\"@id\":\"https:\/\/fivemor.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/fivemor.com\/?p=105354#primaryimage\"},\"image\":{\"@id\":\"https:\/\/fivemor.com\/?p=105354#primaryimage\"},\"thumbnailUrl\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/02\/bartletts20test.png\",\"datePublished\":\"2025-02-23T14:39:41+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/fivemor.com\/?p=105354#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/fivemor.com\/?p=105354\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/fivemor.com\/?p=105354#primaryimage\",\"url\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/02\/bartletts20test.png\",\"contentUrl\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/02\/bartletts20test.png\",\"width\":826,\"height\":563},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/fivemor.com\/?p=105354#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/fivemor.com\/?bp_activities=1\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Two independent sample T-test\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/fivemor.com\/#website\",\"url\":\"https:\/\/fivemor.com\/\",\"name\":\"Som2ny Network\",\"description\":\"Daily Deals\",\"publisher\":{\"@id\":\"https:\/\/fivemor.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/fivemor.com\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/fivemor.com\/#organization\",\"name\":\"Som2ny Network\",\"url\":\"https:\/\/fivemor.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/fivemor.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/07\/4a0953c4-logo-300x86-1.png\",\"contentUrl\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/07\/4a0953c4-logo-300x86-1.png\",\"width\":300,\"height\":86,\"caption\":\"Som2ny Network\"},\"image\":{\"@id\":\"https:\/\/fivemor.com\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/fivemor.com\/#\/schema\/person\/b85e3c3dc0e1daea076524dc8810c371\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/fivemor.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/729ae85bf62b9917e93538db2f2688ca?s=96&r=g&default=https%3A%2F%2Ffivemor.com%2Fwp-content%2Fplugins%2Fbuddypress-first-letter-avatar%2Fimages%2Fdefault%2F96%2Flatin_a.png\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/729ae85bf62b9917e93538db2f2688ca?s=96&r=g&default=https%3A%2F%2Ffivemor.com%2Fwp-content%2Fplugins%2Fbuddypress-first-letter-avatar%2Fimages%2Fdefault%2F96%2Flatin_a.png\",\"caption\":\"admin\"},\"sameAs\":[\"https:\/\/fivemor.com\"],\"url\":\"https:\/\/fivemor.com\/?author=1\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Two independent sample T-test - Som2ny Network","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/fivemor.com\/?p=105354","og_locale":"en_US","og_type":"article","og_title":"Two independent sample T-test - Som2ny Network","og_description":"(Reading time 10 min) This blog is about two sample t test theory, solved example and steps to perform analysis online along with interpretation in Agri Analyze platform 1.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a01.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Introduction A two-sample independent t-test is a statistical method used to determine if there is a significant difference between the […]","og_url":"https:\/\/fivemor.com\/?p=105354","og_site_name":"Som2ny Network","article_published_time":"2025-02-23T14:39:41+00:00","og_image":[{"width":826,"height":563,"url":"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/02\/bartletts20test.png","type":"image\/png"}],"author":"admin","twitter_card":"summary_large_image","twitter_misc":{"Written by":"admin","Est. reading time":"5 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/fivemor.com\/?p=105354#article","isPartOf":{"@id":"https:\/\/fivemor.com\/?p=105354"},"author":{"name":"admin","@id":"https:\/\/fivemor.com\/#\/schema\/person\/b85e3c3dc0e1daea076524dc8810c371"},"headline":"Two independent sample T-test","datePublished":"2025-02-23T14:39:41+00:00","mainEntityOfPage":{"@id":"https:\/\/fivemor.com\/?p=105354"},"wordCount":986,"commentCount":0,"publisher":{"@id":"https:\/\/fivemor.com\/#organization"},"image":{"@id":"https:\/\/fivemor.com\/?p=105354#primaryimage"},"thumbnailUrl":"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/02\/bartletts20test.png","keywords":["Independent","Sample","Ttest"],"articleSection":["Agriculture"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/fivemor.com\/?p=105354#respond"]}]},{"@type":"WebPage","@id":"https:\/\/fivemor.com\/?p=105354","url":"https:\/\/fivemor.com\/?p=105354","name":"Two independent sample T-test - Som2ny Network","isPartOf":{"@id":"https:\/\/fivemor.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/fivemor.com\/?p=105354#primaryimage"},"image":{"@id":"https:\/\/fivemor.com\/?p=105354#primaryimage"},"thumbnailUrl":"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/02\/bartletts20test.png","datePublished":"2025-02-23T14:39:41+00:00","breadcrumb":{"@id":"https:\/\/fivemor.com\/?p=105354#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/fivemor.com\/?p=105354"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/fivemor.com\/?p=105354#primaryimage","url":"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/02\/bartletts20test.png","contentUrl":"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/02\/bartletts20test.png","width":826,"height":563},{"@type":"BreadcrumbList","@id":"https:\/\/fivemor.com\/?p=105354#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/fivemor.com\/?bp_activities=1"},{"@type":"ListItem","position":2,"name":"Two independent sample T-test"}]},{"@type":"WebSite","@id":"https:\/\/fivemor.com\/#website","url":"https:\/\/fivemor.com\/","name":"Som2ny Network","description":"Daily Deals","publisher":{"@id":"https:\/\/fivemor.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/fivemor.com\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/fivemor.com\/#organization","name":"Som2ny Network","url":"https:\/\/fivemor.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/fivemor.com\/#\/schema\/logo\/image\/","url":"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/07\/4a0953c4-logo-300x86-1.png","contentUrl":"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/07\/4a0953c4-logo-300x86-1.png","width":300,"height":86,"caption":"Som2ny Network"},"image":{"@id":"https:\/\/fivemor.com\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/fivemor.com\/#\/schema\/person\/b85e3c3dc0e1daea076524dc8810c371","name":"admin","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/fivemor.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/729ae85bf62b9917e93538db2f2688ca?s=96&r=g&default=https%3A%2F%2Ffivemor.com%2Fwp-content%2Fplugins%2Fbuddypress-first-letter-avatar%2Fimages%2Fdefault%2F96%2Flatin_a.png","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/729ae85bf62b9917e93538db2f2688ca?s=96&r=g&default=https%3A%2F%2Ffivemor.com%2Fwp-content%2Fplugins%2Fbuddypress-first-letter-avatar%2Fimages%2Fdefault%2F96%2Flatin_a.png","caption":"admin"},"sameAs":["https:\/\/fivemor.com"],"url":"https:\/\/fivemor.com\/?author=1"}]}},"_links":{"self":[{"href":"https:\/\/fivemor.com\/index.php?rest_route=\/wp\/v2\/posts\/105354","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fivemor.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/fivemor.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=105354"}],"version-history":[{"count":0,"href":"https:\/\/fivemor.com\/index.php?rest_route=\/wp\/v2\/posts\/105354\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=\/wp\/v2\/media\/105357"}],"wp:attachment":[{"href":"https:\/\/fivemor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=105354"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=105354"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=105354"},{"taxonomy":"dealstore","embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fdealstore&post=105354"},{"taxonomy":"offerexpiration","embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fofferexpiration&post=105354"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}