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Repeated measures anova calculator


ANOVA is analysis of variance. There are many types of ANOVA test. This calculator is one way Repeated measures ANOVA calculator. It is also called a within subjects ANOVA calculator. Every step is provided as if it is solved by hand. You can learn how to calculate a Repeated measures ANOVA by submitting any sample values. F statistic and the p-value is calculated and shown in Table

INSTRUCTION: Use ',' or new line to separate between values

You can see a sample solution below. Enter your data to get the solution for your question

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$$ \displaylines{---} $$
$$ \displaylines{ \mathbf{\color{Green}{H_{0}:\;there\;is\;no\;difference\;in\;means}} \\ \\ \mathbf{\color{Green}{H_{a}:\;At\;least\;2\;means\;differ}} \\ \\ } $$
$$ $$
$$ Treatment\;1 $$
$$ Treatment\;2 $$
$$ Treatment\;3 $$
$$ Subject\;Total $$
$$ Subject\;1 $$
$$ 1 $$
$$ 1 $$
$$ 3 $$
$$ 5 $$
$$ Subject\;2 $$
$$ 2 $$
$$ 3 $$
$$ 6 $$
$$ 11 $$
$$ Subject\;3 $$
$$ 3 $$
$$ 4 $$
$$ 7 $$
$$ 14 $$
$$ Subject\;4 $$
$$ 4 $$
$$ 4 $$
$$ 1 $$
$$ 9 $$
$$ Subject\;5 $$
$$ 5 $$
$$ 3 $$
$$ 2 $$
$$ 10 $$
$$ Treatment\;Total $$
$$ 15 $$
$$ 15 $$
$$ 19 $$
$$ 49 $$
$$ \displaylines{} $$
$$ \displaylines{Total\;number\;of\;values\;=\;N\;= 15 \\ \\ \mathbf{\color{Green}{From\;the\;table\;we\;get\;Total\;(Bottom\;right)}} \\ \\ Total= 49 \\ \\ \mathbf{\color{Green}{First\;we\;have\;to\;find\;total\;mean}} \\ \\ \bar{x} = \frac{Total}{N} \\ \\ \Rightarrow \frac{49}{15} \\ \\ \Rightarrow 3.266667 \\ \\ \mathbf{\color{Green}{For\;finding\;SS_{subject}\;make\;below\;table.}} } $$
$$ \displaylines{\\ \\ } $$
$$ Subject\;Name $$
$$ Total $$
$$ Mean(\bar{x_{s}}) $$
$$ \bar{x} $$
$$ \bar{x_{s}} - \bar{x} $$
$$ (\bar{x_{s}} - \bar{x})^{2} $$
$$ Subject\;1 $$
$$ 5 $$
$$ 1.666667 $$
$$ 3.266667 $$
$$ -1.6 $$
$$ 2.56 $$
$$ Subject\;2 $$
$$ 11 $$
$$ 3.666667 $$
$$ 3.266667 $$
$$ 0.4 $$
$$ 0.16 $$
$$ Subject\;3 $$
$$ 14 $$
$$ 4.666667 $$
$$ 3.266667 $$
$$ 1.4 $$
$$ 1.96 $$
$$ Subject\;4 $$
$$ 9 $$
$$ 3.0 $$
$$ 3.266667 $$
$$ -0.266667 $$
$$ 0.071111 $$
$$ Subject\;5 $$
$$ 10 $$
$$ 3.333333 $$
$$ 3.266667 $$
$$ 0.066666 $$
$$ 0.004444 $$
$$ Total $$
$$ $$
$$ $$
$$ $$
$$ $$
$$ 4.755555 $$
$$ \displaylines{} $$
$$ \displaylines{ \mathbf{\color{Green}{From\;table\;}} \sum_{i=0}^{n}(\bar{x_{s}} - \bar{x}) = 4.755555 \\ \\ Total\;number\;of\;treatments\;=\;k\;=\; 3 \\ \\ SS_{Subject} = k* \sum_{i=0}^{n}(\bar{x_{s}} - \bar{x}) \\ \\ \Rightarrow 3*4.755555 \\ \\ \Rightarrow 14.266665 \\ \\ \mathbf{\color{Green}{For\;finding\;SS_{treatment}\;make\;below\;table.}} } $$
$$ \displaylines{} $$
$$ Treatment\;Name $$
$$ Total $$
$$ Mean(\bar{x_{t}}) $$
$$ \bar{x} $$
$$ \bar{x_{t}} - \bar{x} $$
$$ (\bar{x_{t}} - \bar{x})^{2} $$
$$ Treatment\;1 $$
$$ 15 $$
$$ 3.0 $$
$$ 3.266667 $$
$$ -0.266667 $$
$$ 0.071111 $$
$$ Treatment\;2 $$
$$ 15 $$
$$ 3.0 $$
$$ 3.266667 $$
$$ -0.266667 $$
$$ 0.071111 $$
$$ Treatment\;3 $$
$$ 19 $$
$$ 3.8 $$
$$ 3.266667 $$
$$ 0.533333 $$
$$ 0.284444 $$
$$ Total $$
$$ $$
$$ $$
$$ $$
$$ $$
$$ 0.426666 $$
$$ \displaylines{} $$
$$ \displaylines{ \mathbf{\color{Green}{From\;table\;}} \sum_{i=0}^{n}(\bar{x_{t}} - \bar{x}) = 0.426666 \\ \\ Total\;number\;of\;subjects\;=\;s\;= 5 \\ \\ SS_{Treatment} = s* \sum_{i=0}^{n}(\bar{x_{s}} - \bar{x}) \\ \\ \Rightarrow 5*0.426666 \\ \\ \Rightarrow 2.13333 \\ \\ } $$
$$ \displaylines{ \mathbf{\color{Green}{For\;finding\;SS_{total}\;make\;below\;table.}} } $$
$$ x $$
$$ \bar{x} $$
$$ x - \bar{x} $$
$$ (x - \bar{x})^{2} $$
$$ 1 $$
$$ 3.266667 $$
$$ -2.266667 $$
$$ 5.137779 $$
$$ 2 $$
$$ 3.266667 $$
$$ -1.266667 $$
$$ 1.604445 $$
$$ 3 $$
$$ 3.266667 $$
$$ -0.266667 $$
$$ 0.071111 $$
$$ 4 $$
$$ 3.266667 $$
$$ 0.733333 $$
$$ 0.537777 $$
$$ 5 $$
$$ 3.266667 $$
$$ 1.733333 $$
$$ 3.004443 $$
$$ 1 $$
$$ 3.266667 $$
$$ -2.266667 $$
$$ 5.137779 $$
$$ 3 $$
$$ 3.266667 $$
$$ -0.266667 $$
$$ 0.071111 $$
$$ 4 $$
$$ 3.266667 $$
$$ 0.733333 $$
$$ 0.537777 $$
$$ 4 $$
$$ 3.266667 $$
$$ 0.733333 $$
$$ 0.537777 $$
$$ 3 $$
$$ 3.266667 $$
$$ -0.266667 $$
$$ 0.071111 $$
$$ 3 $$
$$ 3.266667 $$
$$ -0.266667 $$
$$ 0.071111 $$
$$ 6 $$
$$ 3.266667 $$
$$ 2.733333 $$
$$ 7.471109 $$
$$ 7 $$
$$ 3.266667 $$
$$ 3.733333 $$
$$ 13.937775 $$
$$ 1 $$
$$ 3.266667 $$
$$ -2.266667 $$
$$ 5.137779 $$
$$ 2 $$
$$ 3.266667 $$
$$ -1.266667 $$
$$ 1.604445 $$
$$ Total $$
$$ $$
$$ $$
$$ 44.933329 $$
$$ \displaylines{} $$
$$ \displaylines{ \mathbf{\color{Green}{From\;table\;}} \sum_{i=0}^{n}(x - \bar{x}) = 44.933329 \\ \\ SS_{Total} = \sum_{i=0}^{n}(x - \bar{x}) \\ \\ \Rightarrow 44.933329 } $$
$$ \displaylines{ \mathbf{\color{Green}{SS_{within}\;=\;SS_{total}\;-\;SS_{treatment}\;-\;SS_{subject}}} \\ \\ \Rightarrow 44.933329-2.13333-14.266665 \\ \\ \Rightarrow SS_{within} = \mathbf{\color{Red}{28.533334}} \\ \\ \mathbf{\color{Green}{Now\;make\;ANOVA\;table\;like\;below}} } $$
$$ Source\;of\;Variation $$
$$ Sum\;of\;Squres $$
$$ df $$
$$ MS $$
$$ F $$
$$ Between\;Subjects $$
$$ SS_{subject} $$
$$ s-1 $$
$$ $$
$$ $$
$$ Between\;treatments $$
$$ SS_{treatment} $$
$$ k-1 $$
$$ MS_{treatment} $$
$$ F $$
$$ Within $$
$$ SS_{within} $$
$$ (s-1)(k-1) $$
$$ MS_{within} $$
$$ $$
$$ Total $$
$$ SS_{total} $$
$$ sk - 1 $$
$$ $$
$$ $$
$$ \displaylines{} $$
$$ \displaylines{ \mathbf{\color{Green}{Where,\;s\;=\;number\;of\;subjects}} = \mathbf{\color{Red}{5}} \\ \\ df\;is\;Degrees\;of\;Freedom \\ \\ MS\;=\;Mean\;of\;Squares \\ \\ \mathbf{\color{Green}{k\;=\;number\;of\;treatments}} = \mathbf{\color{Red}{3}} \\ \\ MS_{treatment} = \frac{SS_{treatment}}{k-1} = \frac{2.13333}{2} = \mathbf{\color{Red}{1.066665}} \\ \\ MS_{within} = \frac{SS_{within}}{(s-1)(k-1)} = \frac{28.533334}{8} = \mathbf{\color{Red}{3.566667}} \\ \\ F = \frac{MS_{treatment}}{MS_{within}} = \frac{1.066665}{3.566667} = \mathbf{\color{Red}{0.299065}} \\ \\ p\;value\;is\;\;\mathbf{\color{Red}{0.749452}} \\ \\ } $$
$$ Source\;of\;Variation $$
$$ Sum\;of\;Squres $$
$$ df $$
$$ MS $$
$$ F $$
$$ p\;value $$
$$ Between\;Subjects $$
$$ 14.266665 $$
$$ 4 $$
$$ $$
$$ $$
$$ $$
$$ Between\;treatments $$
$$ 2.13333 $$
$$ 2 $$
$$ 1.066665 $$
$$ 0.299065 $$
$$ 0.749452 $$
$$ Within $$
$$ 28.533334 $$
$$ 8 $$
$$ 3.566667 $$
$$ $$
$$ $$
$$ Total $$
$$ 44.933329 $$
$$ 14 $$
$$ $$
$$ $$
$$ $$
$$ \displaylines{} $$
$$ \displaylines{\alpha\;=\;0.05 \\ \\ p\;is\;more\;than\;\alpha\;.\; So,\;Failed\;to\;Reject\;H_{0} \\ \\ } $$